## Meghan Sullivan
## Chong Xing
## 2017-06-01

## SEM Examples for Using Likert Items from hbsc Data
## Section-1: One-Factor Categorical CFA (with Likert Items)
## Section-2: Three-Factor Categorical CFA (Likert)
## Section-3: Two-Factor Categorical Structural Model (Likert)
## Section-4: Indirect-Effect (Mediation) Structural Model (Likert)
## Section-5: One-Factor Two-Group Measurement Invariance Testing (Likert)

wdir <- "workingdata"
ddir <- "../../data"
odir <- "output"

library(kutils)
library(foreign)
library(lavaan)
## This is lavaan 0.5-22
## lavaan is BETA software! Please report any bugs.
pdf.options(onefile=FALSE, family="Times", paper="special", height=4,
            width=6, pointsize=10)

## Read in Data
hbsc <- readRDS(file = file.path(ddir, "hbsc-subset.rds"))
summary(hbsc)
##    StudentID       SchoolID        Gender          Age       
##  Min.   :   1   Min.   :  1.0   Male  :4456   Min.   :11.00  
##  1st Qu.:2308   1st Qu.: 59.0   Female:4742   1st Qu.:12.00  
##  Median :4614   Median :113.0   NA's  :  29   Median :13.00  
##  Mean   :4614   Mean   :114.7                 Mean   :13.42  
##  3rd Qu.:6920   3rd Qu.:171.0                 3rd Qu.:15.00  
##  Max.   :9227   Max.   :227.0                 Max.   :17.00  
##                                               NA's   :126    
##       Grade                             Race         BodyFeelings1_f
##  Grade_6 :2404   White                    :4030   s agree    :2498  
##  Grade_7 :1880   Other                    :1960   agree      :1849  
##  Grade_8 :1830   Black or African American:1692   undecided  :1495  
##  Grade_9 :1486   Two or more races        : 893   not agree  :1239  
##  Grade_10:1627   Asian                    : 261   s not agree: 761  
##                  (Other)                  : 240   NA's       :1385  
##                  NA's                     : 151                     
##  BodyFeelings1_i    BodyFeelings2_f BodyFeelings2_i    BodyFeelings3_f
##  Min.   :0.000   s not agree: 662   Min.   :0.000   s agree    :4399  
##  1st Qu.:0.000   not agree  :1133   1st Qu.:2.000   agree      :1562  
##  Median :1.000   undecided  :1520   Median :3.000   undecided  : 824  
##  Mean   :1.479   agree      :2733   Mean   :2.488   not agree  : 546  
##  3rd Qu.:3.000   s agree    :1771   3rd Qu.:3.000   s not agree: 487  
##  Max.   :4.000   NA's       :1408   Max.   :4.000   NA's       :1409  
##  NA's   :1385                       NA's   :1408                      
##  BodyFeelings3_i     BodyFeelings4_f BodyFeelings4_i    BodyFeelings5_f
##  Min.   :0.0000   s not agree: 766   Min.   :0.000   s agree    :4799  
##  1st Qu.:0.0000   not agree  : 901   1st Qu.:2.000   agree      :1325  
##  Median :0.0000   undecided  :1272   Median :3.000   undecided  : 860  
##  Mean   :0.8693   agree      :2535   Mean   :2.614   not agree  : 427  
##  3rd Qu.:1.0000   s agree    :2349   3rd Qu.:4.000   s not agree: 411  
##  Max.   :4.0000   NA's       :1404   Max.   :4.000   NA's       :1405  
##  NA's   :1409                        NA's   :1404                      
##  BodyFeelings5_i                PhysHealth1_f  PhysHealth1_i  
##  Min.   :0.0000   everyday             : 706   Min.   :0.000  
##  1st Qu.:0.0000   every week           :1177   1st Qu.:2.000  
##  Median :0.0000   More than once a week: 908   Median :3.000  
##  Mean   :0.7632   every month          :2474   Mean   :2.828  
##  3rd Qu.:1.0000   never                :3817   3rd Qu.:4.000  
##  Max.   :4.0000   NA's                 : 145   Max.   :4.000  
##  NA's   :1405                                  NA's   :145    
##                PhysHealth2_f  PhysHealth2_i                 PhysHealth3_f 
##  everyday             : 421   Min.   :0.000   everyday             : 762  
##  every week           : 895   1st Qu.:3.000   every week           : 859  
##  More than once a week: 884   Median :3.000   More than once a week: 847  
##  every month          :2887   Mean   :3.004   every month          :1695  
##  never                :3976   3rd Qu.:4.000   never                :4878  
##  NA's                 : 164   Max.   :4.000   NA's                 : 186  
##                               NA's   :164                                 
##  PhysHealth3_i                 PhysHealth4_f  PhysHealth4_i  
##  Min.   :0.000   everyday             : 754   Min.   :0.000  
##  1st Qu.:2.000   every week           : 796   1st Qu.:2.000  
##  Median :4.000   More than once a week: 827   Median :4.000  
##  Mean   :3.003   every month          :1779   Mean   :3.018  
##  3rd Qu.:4.000   never                :4840   3rd Qu.:4.000  
##  Max.   :4.000   NA's                 : 231   Max.   :4.000  
##  NA's   :186                                  NA's   :231    
##                PhysHealth5_f  PhysHealth5_i                 PhysHealth6_f 
##  everyday             :1186   Min.   :0.000   everyday             : 932  
##  every week           :1351   1st Qu.:1.000   every week           :1235  
##  More than once a week:1208   Median :3.000   More than once a week:1365  
##  every month          :2224   Mean   :2.512   every month          :2190  
##  never                :3062   3rd Qu.:4.000   never                :3294  
##  NA's                 : 196   Max.   :4.000   NA's                 : 211  
##                               NA's   :196                                 
##  PhysHealth6_i                PhysHealth7_f  PhysHealth7_i  
##  Min.   :0.00   everyday             :1477   Min.   :0.000  
##  1st Qu.:2.00   every week           :1036   1st Qu.:1.000  
##  Median :3.00   More than once a week: 912   Median :3.000  
##  Mean   :2.63   every month          :1394   Mean   :2.648  
##  3rd Qu.:4.00   never                :4228   3rd Qu.:4.000  
##  Max.   :4.00   NA's                 : 180   Max.   :4.000  
##  NA's   :211                                 NA's   :180    
##                PhysHealth8_f  PhysHealth8_i       Depress1_f  
##  everyday             : 533   Min.   :0.000   Never    :2343  
##  every week           : 640   1st Qu.:3.000   Seldom   :2519  
##  More than once a week: 594   Median :4.000   Sometimes:2792  
##  every month          :1349   Mean   :3.271   Often    :1030  
##  never                :5924   3rd Qu.:4.000   Always   : 386  
##  NA's                 : 187   Max.   :4.000   NA's     : 157  
##                               NA's   :187                     
##    Depress1_i        Depress2_f     Depress2_i        Depress3_f  
##  Min.   :0.000   Never    :1420   Min.   :0.000   Never    :5077  
##  1st Qu.:2.000   Seldom   :2083   1st Qu.:2.000   Seldom   :1482  
##  Median :3.000   Sometimes:3321   Median :2.000   Sometimes:1331  
##  Mean   :2.596   Often    :1640   Mean   :2.232   Often    : 659  
##  3rd Qu.:4.000   Always   : 592   3rd Qu.:3.000   Always   : 494  
##  Max.   :4.000   NA's     : 171   Max.   :4.000   NA's     : 184  
##  NA's   :157                      NA's   :171                     
##    Depress3_i        Depress4_f     Depress4_i        Depress5_f  
##  Min.   :0.000   Never    :3948   Min.   :0.000   Never    :2974  
##  1st Qu.:2.000   Seldom   :1375   1st Qu.:2.000   Seldom   :1667  
##  Median :4.000   Sometimes:1904   Median :3.000   Sometimes:2086  
##  Mean   :3.105   Often    :1091   Mean   :2.751   Often    :1315  
##  3rd Qu.:4.000   Always   : 702   3rd Qu.:4.000   Always   : 969  
##  Max.   :4.000   NA's     : 207   Max.   :4.000   NA's     : 216  
##  NA's   :184                      NA's   :207                     
##    Depress5_i        Depress6_f     Depress6_i               GotBully1_f  
##  Min.   :0.000   Never    :2524   Min.   :0.000   havn't been      :5116  
##  1st Qu.:1.000   Seldom   :1828   1st Qu.:1.000   1 or 2           :1442  
##  Median :3.000   Sometimes:2301   Median :2.000   2 or 3 a month   : 350  
##  Mean   :2.484   Often    :1316   Mean   :2.376   1 a week         : 320  
##  3rd Qu.:4.000   Always   :1079   3rd Qu.:4.000   Several in a week: 507  
##  Max.   :4.000   NA's     : 179   Max.   :4.000   NA's             :1492  
##  NA's   :216                      NA's   :179                             
##   GotBully1_i                GotBully2_f    GotBully2_i    
##  Min.   :0.0000   havn't been      :5616   Min.   :0.0000  
##  1st Qu.:0.0000   1 or 2           :1189   1st Qu.:0.0000  
##  Median :0.0000   2 or 3 a month   : 311   Median :0.0000  
##  Mean   :0.6632   1 a week         : 283   Mean   :0.5118  
##  3rd Qu.:1.0000   Several in a week: 323   3rd Qu.:1.0000  
##  Max.   :4.0000   NA's             :1505   Max.   :4.0000  
##  NA's   :1492                              NA's   :1505    
##             GotBully3_f    GotBully3_i                GotBully4_f  
##  havn't been      :6591   Min.   :0.0000   havn't been      :5089  
##  1 or 2           : 585   1st Qu.:0.0000   1 or 2           :1570  
##  2 or 3 a month   : 186   Median :0.0000   2 or 3 a month   : 409  
##  1 a week         : 145   Mean   :0.2815   1 a week         : 268  
##  Several in a week: 194   3rd Qu.:0.0000   Several in a week: 382  
##  NA's             :1526   Max.   :4.0000   NA's             :1509  
##                           NA's   :1526                             
##   GotBully4_i                GotBully5_f    GotBully5_i    
##  Min.   :0.0000   havn't been      :6624   Min.   :0.0000  
##  1st Qu.:0.0000   1 or 2           : 537   1st Qu.:0.0000  
##  Median :0.0000   2 or 3 a month   : 171   Median :0.0000  
##  Mean   :0.6116   1 a week         : 151   Mean   :0.2785  
##  3rd Qu.:1.0000   Several in a week: 202   3rd Qu.:0.0000  
##  Max.   :4.0000   NA's             :1542   Max.   :4.0000  
##  NA's   :1509                              NA's   :1542    
##             GotBully6_f    GotBully6_i                GotBully7_f  
##  havn't been      :6944   Min.   :0.0000   havn't been      :5728  
##  1 or 2           : 365   1st Qu.:0.0000   1 or 2           : 979  
##  2 or 3 a month   : 129   Median :0.0000   2 or 3 a month   : 345  
##  1 a week         : 105   Mean   :0.1895   1 a week         : 281  
##  Several in a week: 129   3rd Qu.:0.0000   Several in a week: 358  
##  NA's             :1555   Max.   :4.0000   NA's             :1536  
##                           NA's   :1555                             
##   GotBully7_i                GotBully8_f    GotBully8_i    
##  Min.   :0.0000   havn't been      :7036   Min.   :0.0000  
##  1st Qu.:0.0000   1 or 2           : 348   1st Qu.:0.0000  
##  Median :0.0000   2 or 3 a month   : 112   Median :0.0000  
##  Mean   :0.5128   1 a week         :  74   Mean   :0.1592  
##  3rd Qu.:1.0000   Several in a week: 107   3rd Qu.:0.0000  
##  Max.   :4.0000   NA's             :1550   Max.   :4.0000  
##  NA's   :1536                              NA's   :1550    
##             GotBully9_f    GotBully9_i                BullyOth1_f  
##  havn't been      :7194   Min.   :0.0000   havn't           :4994  
##  1 or 2           : 245   1st Qu.:0.0000   1 or 2           :1806  
##  2 or 3 a month   :  82   Median :0.0000   2 or 3 a month   : 331  
##  1 a week         :  60   Mean   :0.1303   1 a week         : 255  
##  Several in a week: 103   3rd Qu.:0.0000   Several in a week: 305  
##  NA's             :1543   Max.   :4.0000   NA's             :1536  
##                           NA's   :1543                             
##   BullyOth1_i               BullyOth2_f    BullyOth2_i    
##  Min.   :0.000   havn't           :5810   Min.   :0.0000  
##  1st Qu.:0.000   1 or 2           :1222   1st Qu.:0.0000  
##  Median :0.000   2 or 3 a month   : 260   Median :0.0000  
##  Mean   :0.579   1 a week         : 185   Mean   :0.3997  
##  3rd Qu.:1.000   Several in a week: 192   3rd Qu.:0.0000  
##  Max.   :4.000   NA's             :1558   Max.   :4.0000  
##  NA's   :1536                             NA's   :1558    
##             BullyOth3_f    BullyOth3_i                BullyOth4_f  
##  havn't           :6529   Min.   :0.0000   havn't           :6719  
##  1 or 2           : 633   1st Qu.:0.0000   1 or 2           : 558  
##  2 or 3 a month   : 195   Median :0.0000   2 or 3 a month   : 133  
##  1 a week         : 142   Mean   :0.2664   1 a week         : 124  
##  Several in a week: 147   3rd Qu.:0.0000   Several in a week: 114  
##  NA's             :1581   Max.   :4.0000   NA's             :1579  
##                           NA's   :1581                             
##   BullyOth4_i               BullyOth5_f    BullyOth5_i    
##  Min.   :0.000   havn't           :6946   Min.   :0.0000  
##  1st Qu.:0.000   1 or 2           : 370   1st Qu.:0.0000  
##  Median :0.000   2 or 3 a month   : 116   Median :0.0000  
##  Mean   :0.216   1 a week         : 102   Mean   :0.1853  
##  3rd Qu.:0.000   Several in a week: 128   3rd Qu.:0.0000  
##  Max.   :4.000   NA's             :1565   Max.   :4.0000  
##  NA's   :1579                             NA's   :1565    
##             BullyOth6_f    BullyOth6_i                BullyOth7_f  
##  havn't           :7153   Min.   :0.0000   havn't           :6611  
##  1 or 2           : 211   1st Qu.:0.0000   1 or 2           : 568  
##  2 or 3 a month   : 121   Median :0.0000   2 or 3 a month   : 189  
##  1 a week         :  84   Mean   :0.1375   1 a week         : 114  
##  Several in a week:  87   3rd Qu.:0.0000   Several in a week: 165  
##  NA's             :1571   Max.   :4.0000   NA's             :1580  
##                           NA's   :1571                             
##   BullyOth7_i                BullyOth8_f    BullyOth8_i    
##  Min.   :0.0000   havn't           :7120   Min.   :0.0000  
##  1st Qu.:0.0000   1 or 2           : 256   1st Qu.:0.0000  
##  Median :0.0000   2 or 3 a month   : 109   Median :0.0000  
##  Mean   :0.2547   1 a week         :  76   Mean   :0.1332  
##  3rd Qu.:0.0000   Several in a week:  79   3rd Qu.:0.0000  
##  Max.   :4.0000   NA's             :1587   Max.   :4.0000  
##  NA's   :1580                              NA's   :1587    
##             BullyOth9_f    BullyOth9_i             Alc1_f    
##  havn't           :7160   Min.   :0.0000   Never      :6853  
##  1 or 2           : 231   1st Qu.:0.0000   Rarely     :1322  
##  2 or 3 a month   :  89   Median :0.0000   Every month: 350  
##  1 a week         :  70   Mean   :0.1317   Every week : 252  
##  Several in a week:  97   3rd Qu.:0.0000   Everyday   :  90  
##  NA's             :1580   Max.   :4.0000   NA's       : 360  
##                           NA's   :1580                       
##      Alc1_i              Alc2_f         Alc2_i              Alc3_f    
##  Min.   :2.000   Never      :6731   Min.   :2.000   Never      :6899  
##  1st Qu.:2.000   Rarely     :1643   1st Qu.:2.000   Rarely     :1041  
##  Median :2.000   Every month: 237   Median :2.000   Every month: 426  
##  Mean   :2.354   Every week : 162   Mean   :2.325   Every week : 280  
##  3rd Qu.:2.000   Everyday   :  68   3rd Qu.:2.000   Everyday   :  89  
##  Max.   :6.000   NA's       : 386   Max.   :6.000   NA's       : 492  
##  NA's   :360                        NA's   :386                       
##      Alc3_i              Alc4_f         Alc4_i              Alc5_f    
##  Min.   :2.000   Never      :6238   Min.   :2.000   Never      :6530  
##  1st Qu.:2.000   Rarely     :1495   1st Qu.:2.000   Rarely     :1411  
##  Median :2.000   Every month: 589   Median :2.000   Every month: 486  
##  Mean   :2.354   Every week : 305   Mean   :2.463   Every week : 307  
##  3rd Qu.:2.000   Everyday   : 115   3rd Qu.:3.000   Everyday   : 107  
##  Max.   :6.000   NA's       : 485   Max.   :6.000   NA's       : 386  
##  NA's   :492                        NA's   :485                       
##      Alc5_i     
##  Min.   :2.000  
##  1st Qu.:2.000  
##  Median :2.000  
##  Mean   :2.422  
##  3rd Qu.:3.000  
##  Max.   :6.000  
##  NA's   :386
####---------------------------------------------####
#### Section-1: One-Factor CFA with Likert Items ####
####---------------------------------------------####

#### Three Versions of One-Factor CFA for Depression Items
#### A Six-Item Five-Point Likert Scale
#### ("Depress1_f" Coded as Factor Variable)
#### ("Deqpress1_i" Coded as Integer Varable)
#### peek() function in kutils package gives
#### a quick inspection of the variables  

class(hbsc$Depress1_f)
## [1] "factor"
class(hbsc$Depress1_i)
## [1] "integer"
if(interactive()) peek(hbsc[ , c("Depress1_f", "Depress1_i", "Depress2_f", "Depress2_i",
               "Depress3_f", "Depress3_i", "Depress4_f", "Depress4_i",
               "Depress5_f", "Depress5_i", "Depress6_f", "Depress6_i")])

## Version 1 - ML Estimation with Factor Variables
## lavaan Gives an Error Message about Unordered Factor(s)
## lavaan will still Provide Parameter Estimates
## But NAs will be Assigned to Loglikelihood, AIC, and BIC

model.depress.factor <- '
depress =~ NA*Depress1_f + Depress2_f + Depress3_f + Depress4_f
           + Depress5_f + Depress6_f
depress ~~ 1*depress
'

fit.depress.ML.factor <- cfa(model = model.depress.factor, data = hbsc,
                             mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label =
## group.label, : lavaan WARNING: unordered factor(s) with more than 2 levels
## detected in data: Depress1_f Depress2_f Depress3_f Depress4_f Depress5_f
## Depress6_f
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   73 90 184 215 252 382 400 417 466 477 628 660 679 771 934 988 1015 1055 1073 1117 1132 1179 1360 1404 1447 1501 1571 1670 1709 1717 1739 1789 1790 1882 1922 1966 1998 2035 2137 2168 2375 2397 2505 2555 2563 2606 2623 2627 2636 2665 2715 2995 3032 3098 3213 3261 3271 3333 3410 3423 3457 3526 3550 3567 3568 3600 3782 3807 3950 3985 4092 4122 4141 4148 4209 4268 4320 4388 4415 4480 4693 4720 4804 4833 4850 4865 4884 4925 4973 5093 5101 5110 5276 5289 5303 5577 5753 5872 5942 5994 6053 6055 6089 6105 6181 6473 6501 6564 6599 7032 7114 7239 7344 7357 7531 7667 7823 7935 8034 8117 8133 8233 8356 8432 8443 8491 8493 8598 8607 8664 8763 8789 8816 8952 9041 9049 9132 9135 9159 9165
summary(fit.depress.ML.factor, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  23 iterations
## 
##                                                   Used       Total
##   Number of observations                          9087        9227
## 
##   Number of missing patterns                        31
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              580.043
##   Degrees of freedom                                 9
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            13929.900
##   Degrees of freedom                                15
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.959
##   Tucker-Lewis Index (TLI)                       0.932
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)                     NA
##   Loglikelihood unrestricted model (H1)             NA
## 
##   Number of free parameters                         18
##   Akaike (AIC)                                      NA
##   Bayesian (BIC)                                    NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.084
##   90 Percent Confidence Interval          0.078  0.089
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.029
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Depress1_f        0.776    0.011   67.706    0.000    0.776    0.697
##     Depress2_f        0.703    0.012   59.854    0.000    0.703    0.630
##     Depress3_f        0.809    0.013   63.982    0.000    0.809    0.664
##     Depress4_f        0.879    0.014   63.232    0.000    0.879    0.661
##     Depress5_f        0.779    0.015   53.051    0.000    0.779    0.573
##     Depress6_f        0.761    0.014   52.768    0.000    0.761    0.567
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        2.405    0.012  205.715    0.000    2.405    2.159
##    .Depress2_f        2.769    0.012  236.125    0.000    2.769    2.480
##    .Depress3_f        1.895    0.013  148.219    0.000    1.895    1.558
##    .Depress4_f        2.249    0.014  160.731    0.000    2.249    1.691
##    .Depress5_f        2.516    0.014  175.938    0.000    2.516    1.852
##    .Depress6_f        2.624    0.014  186.221    0.000    2.624    1.957
##     depress           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           1.000                               1.000    1.000
##    .Depress1_f        0.637    0.013   50.870    0.000    0.637    0.514
##    .Depress2_f        0.752    0.013   56.089    0.000    0.752    0.603
##    .Depress3_f        0.827    0.015   53.895    0.000    0.827    0.559
##    .Depress4_f        0.997    0.019   53.696    0.000    0.997    0.563
##    .Depress5_f        1.240    0.021   58.480    0.000    1.240    0.672
##    .Depress6_f        1.220    0.021   59.224    0.000    1.220    0.678
## Version 2 - ML Estimation with Integer Variables
## The Error Message about Unordered Factor Is Gone
## Estimates on Loglikelihood, AIC, and BIC Are Provided
## All the Parameter Estimates Are Identical to the Version 1

model.depress.integer <- '
depress =~ NA*Depress1_i + Depress2_i + Depress3_i + Depress4_i
           + Depress5_i + Depress6_i
depress ~~ 1*depress
'

fit.depress.ML.integer <- cfa(model = model.depress.integer, data = hbsc,
                              mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   63 69 93 96 179 187 276 412 439 465 564 621 630 735 737 785 796 872 995 1095 1111 1194 1293 1405 1561 1697 1871 1884 1989 2114 2196 2629 2664 2727 2755 3047 3123 3139 3173 3175 3234 3286 3356 3475 3651 3925 3939 3952 4118 4127 4135 4255 4303 4344 4363 4378 4395 4424 4508 4535 4748 4813 4840 4908 4960 5019 5080 5087 5106 5136 5243 5278 5421 5446 5628 5660 5661 5678 5702 5771 5805 5818 5895 5957 5967 6015 6130 6196 6233 6513 6563 6592 6601 6605 6622 6665 6673 6723 6831 6853 7060 7091 7193 7230 7262 7306 7346 7438 7439 7489 7511 7519 7558 7657 7727 7781 7824 7868 8049 8096 8111 8155 8173 8213 8240 8294 8457 8549 8568 8600 8751 8762 8811 8828 8846 8976 9013 9044 9138 9155
summary(fit.depress.ML.integer, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  25 iterations
## 
##                                                   Used       Total
##   Number of observations                          9087        9227
## 
##   Number of missing patterns                        31
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              580.043
##   Degrees of freedom                                 9
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            13929.900
##   Degrees of freedom                                15
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.959
##   Tucker-Lewis Index (TLI)                       0.932
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -82045.027
##   Loglikelihood unrestricted model (H1)     -81755.006
## 
##   Number of free parameters                         18
##   Akaike (AIC)                              164126.054
##   Bayesian (BIC)                            164254.117
##   Sample-size adjusted Bayesian (BIC)       164196.916
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.084
##   90 Percent Confidence Interval          0.078  0.089
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.029
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Depress1_i        0.776    0.011   67.706    0.000    0.776    0.697
##     Depress2_i        0.703    0.012   59.854    0.000    0.703    0.630
##     Depress3_i        0.809    0.013   63.982    0.000    0.809    0.664
##     Depress4_i        0.879    0.014   63.232    0.000    0.879    0.661
##     Depress5_i        0.779    0.015   53.051    0.000    0.779    0.573
##     Depress6_i        0.761    0.014   52.768    0.000    0.761    0.567
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        2.595    0.012  221.976    0.000    2.595    2.330
##    .Depress2_i        2.231    0.012  190.300    0.000    2.231    1.999
##    .Depress3_i        3.105    0.013  242.795    0.000    3.105    2.551
##    .Depress4_i        2.751    0.014  196.564    0.000    2.751    2.067
##    .Depress5_i        2.484    0.014  173.721    0.000    2.484    1.828
##    .Depress6_i        2.376    0.014  168.570    0.000    2.376    1.771
##     depress           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           1.000                               1.000    1.000
##    .Depress1_i        0.637    0.013   50.870    0.000    0.637    0.514
##    .Depress2_i        0.752    0.013   56.089    0.000    0.752    0.603
##    .Depress3_i        0.827    0.015   53.895    0.000    0.827    0.559
##    .Depress4_i        0.997    0.019   53.696    0.000    0.997    0.563
##    .Depress5_i        1.240    0.021   58.480    0.000    1.240    0.672
##    .Depress6_i        1.220    0.021   59.224    0.000    1.220    0.678
## Categorical Treatment of the Items (WLSMV)
## peek() Function Showed Items 1, 3, 4, 5, 6
## Were Not Normally Distributed (They Are Declared as "ordered") 

fit.depress.WLSMV.factor <-
    cfa(model = model.depress.factor, data = hbsc,
        mimic = "Mplus", estimator = "WLSMV",
        ordered = c("Depress1_f", "Depress2_f", "Depress3_f",
                    "Depress4_f", "Depress5_f", "Depress6_f"))

summary(fit.depress.WLSMV.factor, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  12 iterations
## 
##                                                   Used       Total
##   Number of observations                          8923        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              380.150     738.573
##   Degrees of freedom                                 9           9
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.515
##   Shift parameter                                            0.231
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            42237.702   28021.369
##   Degrees of freedom                                15          15
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.991       0.974
##   Tucker-Lewis Index (TLI)                       0.985       0.957
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.068       0.095
##   90 Percent Confidence Interval          0.062  0.074       0.090  0.101
##   P-value RMSEA <= 0.05                          0.000       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.033       0.033
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           3.122       3.122
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Depress1_f        0.741    0.006  116.476    0.000    0.741    0.741
##     Depress2_f        0.670    0.007   93.754    0.000    0.670    0.670
##     Depress3_f        0.745    0.007  105.409    0.000    0.745    0.745
##     Depress4_f        0.722    0.007  103.166    0.000    0.722    0.722
##     Depress5_f        0.630    0.008   79.802    0.000    0.630    0.630
##     Depress6_f        0.611    0.008   74.485    0.000    0.611    0.611
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##     depress           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f|t1    -0.653    0.014  -45.508    0.000   -0.653   -0.653
##     Depress1_f|t2     0.090    0.013    6.785    0.000    0.090    0.090
##     Depress1_f|t3     1.010    0.016   62.927    0.000    1.010    1.010
##     Depress1_f|t4     1.719    0.024   73.030    0.000    1.719    1.719
##     Depress2_f|t1    -1.006    0.016  -62.802    0.000   -1.006   -1.006
##     Depress2_f|t2    -0.288    0.013  -21.407    0.000   -0.288   -0.288
##     Depress2_f|t3     0.685    0.014   47.379    0.000    0.685    0.685
##     Depress2_f|t4     1.512    0.021   73.550    0.000    1.512    1.512
##     Depress3_f|t1     0.156    0.013   11.735    0.000    0.156    0.156
##     Depress3_f|t2     0.600    0.014   42.334    0.000    0.600    0.600
##     Depress3_f|t3     1.140    0.017   67.324    0.000    1.140    1.140
##     Depress3_f|t4     1.602    0.022   73.654    0.000    1.602    1.602
##     Depress4_f|t1    -0.155    0.013  -11.608    0.000   -0.155   -0.155
##     Depress4_f|t2     0.230    0.013   17.145    0.000    0.230    0.230
##     Depress4_f|t3     0.847    0.015   55.884    0.000    0.847    0.847
##     Depress4_f|t4     1.420    0.019   72.891    0.000    1.420    1.420
##     Depress5_f|t1    -0.438    0.014  -31.869    0.000   -0.438   -0.438
##     Depress5_f|t2     0.039    0.013    2.975    0.003    0.039    0.039
##     Depress5_f|t3     0.666    0.014   46.282    0.000    0.666    0.666
##     Depress5_f|t4     1.242    0.018   69.977    0.000    1.242    1.242
##     Depress6_f|t1    -0.585    0.014  -41.428    0.000   -0.585   -0.585
##     Depress6_f|t2    -0.045    0.013   -3.398    0.001   -0.045   -0.045
##     Depress6_f|t3     0.630    0.014   44.119    0.000    0.630    0.630
##     Depress6_f|t4     1.180    0.017   68.468    0.000    1.180    1.180
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           1.000                               1.000    1.000
##    .Depress1_f        0.451                               0.451    0.451
##    .Depress2_f        0.552                               0.552    0.552
##    .Depress3_f        0.445                               0.445    0.445
##    .Depress4_f        0.479                               0.479    0.479
##    .Depress5_f        0.603                               0.603    0.603
##    .Depress6_f        0.626                               0.626    0.626
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
#### One-Factor CFA for Bullying Others Items (e.g., "BullyOth1")
#### A Nine-Item Five-Point Likert Scale
#### ("BullyOther1_f" Coded as Factor Variable)
#### ("BullyOther1_i" Coded as Integer Varable)

if(interactive()) peek(hbsc[ , c("BullyOth1_f", "BullyOth1_i", "BullyOth2_f", "BullyOth2_i",
               "BullyOth3_f", "BullyOth3_i", "BullyOth4_f", "BullyOth4_i",
               "BullyOth5_f", "BullyOth5_i", "BullyOth6_f", "BullyOth6_i",
               "BullyOth7_f", "BullyOth7_i", "BullyOth8_f", "BullyOth8_i",
               "BullyOth9_f", "BullyOth9_i")])

## Continuous Treatment of the Items (ML)
model.bullyOther.integer <- '
bullyOther =~ NA*BullyOth1_i + BullyOth2_i + BullyOth3_i
              + BullyOth4_i  + BullyOth5_i + BullyOth6_i
              + BullyOth7_i + BullyOth8_i  + BullyOth9_i
bullyOther ~~ 1*bullyOther
'

fit.bullyOther.ML.integer <-
    cfa(model = model.bullyOther.integer, data = hbsc,
        mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   10 15 28 34 43 47 48 71 72 73 80 81 84 89 90 93 103 131 137 142 148 150 151 163 168 169 177 178 184 190 195 226 232 235 242 247 251 252 253 256 259 260 272 280 287 292 297 323 328 333 356 360 366 373 375 376 381 382 385 396 398 400 402 403 410 412 417 418 420 426 431 434 439 447 449 450 452 461 466 474 477 486 489 490 507 508 526 530 541 542 548 550 553 554 557 561 563 578 579 582 591 593 594 595 603 608 613 616 622 628 636 639 649 652 654 655 660 664 666 670 674 679 684 686 688 690 695 706 726 727 728 729 730 732 746 751 753 760 766 771 781 785 799 813 821 831 836 853 868 872 883 891 892 896 897 901 904 911 912 919 920 934 942 946 952 953 969 971 972 977 1000 1013 1015 1017 1023 1025 1043 1045 1048 1049 1052 1055 1056 1062 1063 1068 1072 1073 1076 1091 1092 1098 1101 1109 1110 1111 1120 1123 1125 1132 1144 1150 1156 1158 1160 1166 1171 1173 1179 1188 1190 1193 1196 1203 1204 1206 1213 1214 1216 1235 1247 1262 1272 1273 1285 1286 1287 1288 1302 1306 1314 1320 1330 1332 1348 1350 1352 1353 1354 1360 1363 1369 1377 1382 1385 1387 1390 1391 1396 1398 1404 1413 1419 1438 1441 1442 1447 1450 1454 1477 1479 1484 1487 1498 1508 1509 1512 1515 1516 1519 1521 1526 1527 1530 1534 1536 1537 1538 1539 1542 1553 1555 1558 1559 1560 1568 1569 1573 1577 1588 1594 1598 1601 1618 1623 1625 1628 1648 1656 1666 1670 1672 1681 1683 1688 1691 1693 1694 1695 1700 1708 1710 1712 1715 1717 1718 1730 1735 1739 1740 1741 1742 1747 1751 1752 1761 1772 1774 1787 1789 1790 1794 1798 1799 1805 1809 1813 1820 1832 1838 1843 1857 1864 1875 1879 1882 1897 1902 1903 1914 1921 1922 1927 1929 1945 1951 1953 1962 1963 1966 1967 1969 1971 1984 1988 1990 1997 1998 2003 2007 2009 2012 2014 2034 2040 2048 2059 2092 2108 2117 2125 2129 2137 2154 2156 2159 2167 2175 2176 2178 2186 2194 2202 2203 2217 2221 2223 2234 2242 2249 2264 2268 2282 2308 2309 2315 2319 2325 2338 2357 2360 2363 2364 2374 2380 2386 2387 2391 2397 2422 2436 2440 2444 2445 2447 2450 2454 2473 2478 2491 2496 2497 2505 2518 2521 2523 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3705 3708 3711 3719 3720 3725 3731 3736 3745 3747 3748 3757 3758 3764 3765 3775 3776 3781 3782 3787 3793 3795 3796 3797 3800 3802 3809 3817 3818 3831 3836 3839 3860 3864 3870 3886 3889 3897 3902 3906 3908 3909 3914 3923 3949 3952 3958 3961 3968 3974 3975 3978 3979 3987 3991 3995 3999 4001 4012 4017 4033 4038 4043 4061 4065 4070 4080 4087 4092 4093 4098 4101 4104 4115 4122 4125 4127 4133 4137 4141 4148 4152 4155 4157 4161 4163 4164 4167 4179 4183 4201 4205 4209 4231 4238 4244 4248 4257 4262 4268 4282 4286 4288 4291 4292 4294 4303 4307 4319 4339 4343 4355 4356 4357 4361 4363 4378 4388 4393 4408 4412 4413 4415 4420 4421 4457 4458 4463 4469 4470 4471 4472 4477 4478 4480 4489 4491 4492 4494 4496 4501 4506 4516 4526 4535 4536 4538 4541 4542 4551 4552 4565 4566 4574 4576 4580 4586 4593 4610 4614 4624 4630 4638 4644 4648 4654 4655 4657 4658 4661 4667 4670 4671 4687 4692 4695 4699 4719 4720 4723 4732 4736 4741 4751 4759 4762 4770 4783 4788 4789 4791 4793 4794 4804 4807 4810 4818 4820 4826 4828 4833 4838 4865 4868 4884 4888 4901 4917 4920 4939 4943 4950 4956 4965 4966 4973 4977 4998 5016 5019 5028 5033 5034 5062 5068 5075 5080 5092 5093 5110 5111 5117 5122 5132 5136 5140 5144 5146 5153 5166 5169 5170 5176 5178 5181 5185 5187 5190 5199 5204 5212 5217 5232 5240 5241 5249 5259 5267 5274 5275 5276 5279 5291 5293 5303 5305 5327 5336 5367 5368 5378 5384 5385 5386 5392 5397 5423 5440 5445 5459 5463 5470 5474 5486 5496 5508 5511 5513 5518 5527 5529 5537 5538 5543 5550 5552 5553 5555 5556 5570 5575 5576 5577 5593 5599 5600 5601 5603 5615 5620 5632 5639 5641 5651 5658 5679 5682 5699 5709 5728 5733 5737 5753 5766 5772 5781 5785 5791 5801 5813 5816 5817 5825 5827 5837 5846 5847 5856 5861 5872 5874 5875 5909 5918 5924 5928 5938 5941 5942 5956 5959 5969 5982 5983 5986 5994 6003 6005 6022 6024 6031 6033 6037 6038 6039 6047 6053 6061 6068 6087 6088 6089 6102 6105 6117 6123 6133 6141 6170 6183 6184 6186 6205 6206 6210 6215 6216 6217 6220 6239 6249 6263 6275 6280 6282 6286 6291 6293 6294 6307 6310 6313 6316 6319 6328 6329 6337 6345 6348 6356 6361 6366 6372 6375 6376 6412 6421 6426 6434 6439 6441 6442 6445 6446 6452 6454 6457 6460 6465 6466 6467 6471 6473 6477 6488 6492 6499 6501 6515 6521 6524 6526 6545 6550 6551 6556 6559 6564 6595 6597 6599 6619 6624 6631 6633 6640 6643 6644 6646 6666 6673 6676 6679 6681 6686 6688 6689 6693 6695 6707 6708 6719 6726 6727 6739 6746 6749 6753 6782 6785 6788 6795 6796 6800 6801 6804 6816 6817 6827 6833 6834 6835 6852 6859 6869 6884 6885 6891 6896 6903 6909 6911 6917 6924 6933 6941 6942 6943 6950 6968 6971 6972 6976 6979 6987 6991 6996 6999 7002 7023 7027 7032 7036 7049 7064 7074 7081 7085 7088 7092 7099 7101 7112 7114 7122 7136 7142 7143 7148 7159 7162 7165 7173 7185 7186 7188 7220 7228 7234 7239 7254 7255 7259 7262 7265 7266 7271 7280 7288 7294 7298 7301 7311 7312 7332 7344 7347 7348 7351 7352 7353 7355 7358 7361 7367 7381 7386 7398 7406 7418 7420 7422 7438 7459 7461 7470 7471 7472 7479 7482 7484 7488 7489 7505 7514 7517 7518 7520 7525 7527 7530 7535 7536 7542 7547 7553 7559 7567 7571 7576 7577 7582 7607 7610 7612 7633 7641 7644 7648 7655 7662 7663 7667 7670 7687 7688 7691 7692 7708 7709 7717 7720 7721 7724 7731 7738 7742 7751 7761 7767 7776 7780 7787 7788 7792 7794 7798 7825 7840 7841 7858 7860 7862 7867 7879 7884 7904 7910 7921 7926 7931 7932 7943 7952 7959 7962 7969 7992 7996 7999 8003 8007 8012 8015 8019 8024 8031 8032 8034 8035 8041 8042 8043 8052 8064 8074 8078 8080 8089 8098 8108 8113 8115 8117 8119 8125 8127 8138 8143 8150 8153 8155 8159 8161 8169 8171 8175 8181 8184 8185 8190 8195 8198 8203 8209 8211 8222 8227 8231 8235 8238 8241 8242 8250 8269 8273 8275 8276 8281 8283 8291 8292 8296 8299 8300 8301 8304 8305 8307 8310 8316 8317 8319 8323 8336 8340 8341 8348 8358 8364 8388 8389 8396 8414 8416 8421 8438 8443 8457 8458 8466 8472 8485 8491 8493 8497 8506 8507 8518 8520 8526 8533 8534 8538 8541 8545 8553 8561 8570 8578 8584 8586 8595 8598 8603 8607 8618 8622 8626 8640 8641 8643 8646 8647 8648 8652 8664 8669 8670 8672 8676 8679 8684 8685 8686 8689 8698 8699 8703 8716 8724 8734 8740 8747 8764 8772 8789 8793 8799 8808 8811 8816 8823 8827 8833 8837 8850 8852 8864 8876 8887 8915 8919 8930 8933 8935 8937 8941 8944 8952 8953 8981 8982 8990 8996 9000 9018 9023 9026 9028 9033 9039 9040 9041 9049 9059 9061 9072 9078 9082 9090 9101 9114 9124 9132 9135 9141 9144 9149 9155 9156 9157 9159 9165 9166 9169 9170 9171 9173 9174 9177 9180 9189 9192 9201 9203 9208 9209 9211 9218 9220
summary(fit.bullyOther.ML.integer, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  36 iterations
## 
##                                                   Used       Total
##   Number of observations                          7700        9227
## 
##   Number of missing patterns                        35
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             3185.539
##   Degrees of freedom                                27
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            37420.866
##   Degrees of freedom                                36
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.916
##   Tucker-Lewis Index (TLI)                       0.887
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -57435.643
##   Loglikelihood unrestricted model (H1)     -55842.873
## 
##   Number of free parameters                         27
##   Akaike (AIC)                              114925.285
##   Bayesian (BIC)                            115112.907
##   Sample-size adjusted Bayesian (BIC)       115027.107
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.123
##   90 Percent Confidence Interval          0.120  0.127
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.049
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   bullyOther =~                                                         
##     BullyOth1_i       0.571    0.011   52.183    0.000    0.571    0.570
##     BullyOth2_i       0.539    0.009   58.156    0.000    0.539    0.621
##     BullyOth3_i       0.553    0.008   69.987    0.000    0.553    0.719
##     BullyOth4_i       0.524    0.007   75.612    0.000    0.524    0.755
##     BullyOth5_i       0.531    0.007   79.125    0.000    0.531    0.780
##     BullyOth6_i       0.483    0.006   84.013    0.000    0.483    0.813
##     BullyOth7_i       0.539    0.008   68.106    0.000    0.539    0.702
##     BullyOth8_i       0.443    0.006   76.924    0.000    0.443    0.770
##     BullyOth9_i       0.463    0.006   79.385    0.000    0.463    0.785
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .BullyOth1_i       0.580    0.011   50.710    0.000    0.580    0.578
##    .BullyOth2_i       0.401    0.010   40.441    0.000    0.401    0.462
##    .BullyOth3_i       0.270    0.009   30.669    0.000    0.270    0.350
##    .BullyOth4_i       0.217    0.008   27.413    0.000    0.217    0.313
##    .BullyOth5_i       0.187    0.008   24.036    0.000    0.187    0.274
##    .BullyOth6_i       0.139    0.007   20.522    0.000    0.139    0.234
##    .BullyOth7_i       0.256    0.009   29.254    0.000    0.256    0.334
##    .BullyOth8_i       0.136    0.007   20.747    0.000    0.136    0.237
##    .BullyOth9_i       0.134    0.007   19.920    0.000    0.134    0.227
##     bullyOther        0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     bullyOther        1.000                               1.000    1.000
##    .BullyOth1_i       0.679    0.012   58.838    0.000    0.679    0.675
##    .BullyOth2_i       0.463    0.008   58.056    0.000    0.463    0.614
##    .BullyOth3_i       0.287    0.005   55.382    0.000    0.287    0.484
##    .BullyOth4_i       0.206    0.004   54.169    0.000    0.206    0.429
##    .BullyOth5_i       0.181    0.003   52.770    0.000    0.181    0.391
##    .BullyOth6_i       0.120    0.002   50.437    0.000    0.120    0.340
##    .BullyOth7_i       0.299    0.005   56.156    0.000    0.299    0.507
##    .BullyOth8_i       0.135    0.003   52.922    0.000    0.135    0.407
##    .BullyOth9_i       0.133    0.003   51.999    0.000    0.133    0.383
## Categorical Treatment of the Items (WLSMV)
model.bullyOther.factor <- '
bullyOther =~ NA*BullyOth1_f + BullyOth2_f + BullyOth3_f
              + BullyOth4_f + BullyOth5_f + BullyOth6_f
              + BullyOth7_f + BullyOth8_f + BullyOth9_f
bullyOther ~~ 1*bullyOther
'

fit.bullyOther.WLSMV.factor <-
    cfa(model = model.bullyOther.factor, data = hbsc,
        mimic = "Mplus", estimator = "WLSMV",
        ordered = c("BullyOth1_f", "BullyOth2_f",
                    "BullyOth3_f", "BullyOth4_f",
                    "BullyOth5_f", "BullyOth6_f",
                    "BullyOth7_f", "BullyOth8_f",
                    "BullyOth9_f"))

summary(fit.bullyOther.WLSMV.factor, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  14 iterations
## 
##                                                   Used       Total
##   Number of observations                          7522        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              371.833     760.315
##   Degrees of freedom                                27          27
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.492
##   Shift parameter                                            4.128
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic           131752.160   51683.289
##   Degrees of freedom                                36          36
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.997       0.986
##   Tucker-Lewis Index (TLI)                       0.997       0.981
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.041       0.060
##   90 Percent Confidence Interval          0.038  0.045       0.056  0.064
##   P-value RMSEA <= 0.05                          1.000       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.034       0.034
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           2.273       2.273
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   bullyOther =~                                                         
##     BullyOth1_f       0.743    0.009   80.842    0.000    0.743    0.743
##     BullyOth2_f       0.778    0.009   86.542    0.000    0.778    0.778
##     BullyOth3_f       0.842    0.008  108.802    0.000    0.842    0.842
##     BullyOth4_f       0.857    0.007  115.833    0.000    0.857    0.857
##     BullyOth5_f       0.894    0.007  132.362    0.000    0.894    0.894
##     BullyOth6_f       0.938    0.006  157.584    0.000    0.938    0.938
##     BullyOth7_f       0.835    0.008  100.650    0.000    0.835    0.835
##     BullyOth8_f       0.914    0.007  137.786    0.000    0.914    0.914
##     BullyOth9_f       0.928    0.006  148.946    0.000    0.928    0.928
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .BullyOth1_f       0.000                               0.000    0.000
##    .BullyOth2_f       0.000                               0.000    0.000
##    .BullyOth3_f       0.000                               0.000    0.000
##    .BullyOth4_f       0.000                               0.000    0.000
##    .BullyOth5_f       0.000                               0.000    0.000
##    .BullyOth6_f       0.000                               0.000    0.000
##    .BullyOth7_f       0.000                               0.000    0.000
##    .BullyOth8_f       0.000                               0.000    0.000
##    .BullyOth9_f       0.000                               0.000    0.000
##     bullyOther        0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     BullyOth1_f|t1    0.393    0.015   26.446    0.000    0.393    0.393
##     BullyOth1_f|t2    1.209    0.019   63.543    0.000    1.209    1.209
##     BullyOth1_f|t3    1.468    0.022   67.306    0.000    1.468    1.468
##     BullyOth1_f|t4    1.768    0.027   66.591    0.000    1.768    1.768
##     BullyOth2_f|t1    0.711    0.016   44.812    0.000    0.711    0.711
##     BullyOth2_f|t2    1.403    0.021   66.754    0.000    1.403    1.403
##     BullyOth2_f|t3    1.670    0.025   67.384    0.000    1.670    1.670
##     BullyOth2_f|t4    1.969    0.031   63.444    0.000    1.969    1.969
##     BullyOth3_f|t1    1.069    0.018   59.749    0.000    1.069    1.069
##     BullyOth3_f|t2    1.547    0.023   67.623    0.000    1.547    1.547
##     BullyOth3_f|t3    1.792    0.027   66.315    0.000    1.792    1.792
##     BullyOth3_f|t4    2.075    0.034   61.100    0.000    2.075    2.075
##     BullyOth4_f|t1    1.183    0.019   62.935    0.000    1.183    1.183
##     BullyOth4_f|t2    1.681    0.025   67.322    0.000    1.681    1.681
##     BullyOth4_f|t3    1.888    0.029   64.941    0.000    1.888    1.888
##     BullyOth4_f|t4    2.177    0.037   58.457    0.000    2.177    2.177
##     BullyOth5_f|t1    1.346    0.020   66.061    0.000    1.346    1.346
##     BullyOth5_f|t2    1.725    0.026   67.002    0.000    1.725    1.725
##     BullyOth5_f|t3    1.910    0.030   64.560    0.000    1.910    1.910
##     BullyOth5_f|t4    2.142    0.036   59.383    0.000    2.142    2.142
##     BullyOth6_f|t1    1.538    0.023   67.604    0.000    1.538    1.538
##     BullyOth6_f|t2    1.802    0.027   66.192    0.000    1.802    1.802
##     BullyOth6_f|t3    2.028    0.033   62.186    0.000    2.028    2.028
##     BullyOth6_f|t4    2.289    0.041   55.187    0.000    2.289    2.289
##     BullyOth7_f|t1    1.120    0.018   61.269    0.000    1.120    1.120
##     BullyOth7_f|t2    1.563    0.023   67.641    0.000    1.563    1.563
##     BullyOth7_f|t3    1.811    0.027   66.084    0.000    1.811    1.811
##     BullyOth7_f|t4    2.041    0.033   61.885    0.000    2.041    2.041
##     BullyOth8_f|t1    1.505    0.022   67.498    0.000    1.505    1.505
##     BullyOth8_f|t2    1.832    0.028   65.802    0.000    1.832    1.832
##     BullyOth8_f|t3    2.058    0.033   61.504    0.000    2.058    2.058
##     BullyOth8_f|t4    2.313    0.042   54.465    0.000    2.313    2.313
##     BullyOth9_f|t1    1.542    0.023   67.613    0.000    1.542    1.542
##     BullyOth9_f|t2    1.859    0.028   65.402    0.000    1.859    1.859
##     BullyOth9_f|t3    2.039    0.033   61.946    0.000    2.039    2.039
##     BullyOth9_f|t4    2.254    0.040   56.243    0.000    2.254    2.254
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     bullyOther        1.000                               1.000    1.000
##    .BullyOth1_f       0.448                               0.448    0.448
##    .BullyOth2_f       0.395                               0.395    0.395
##    .BullyOth3_f       0.291                               0.291    0.291
##    .BullyOth4_f       0.265                               0.265    0.265
##    .BullyOth5_f       0.200                               0.200    0.200
##    .BullyOth6_f       0.120                               0.120    0.120
##    .BullyOth7_f       0.302                               0.302    0.302
##    .BullyOth8_f       0.165                               0.165    0.165
##    .BullyOth9_f       0.140                               0.140    0.140
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     BullyOth1_f       1.000                               1.000    1.000
##     BullyOth2_f       1.000                               1.000    1.000
##     BullyOth3_f       1.000                               1.000    1.000
##     BullyOth4_f       1.000                               1.000    1.000
##     BullyOth5_f       1.000                               1.000    1.000
##     BullyOth6_f       1.000                               1.000    1.000
##     BullyOth7_f       1.000                               1.000    1.000
##     BullyOth8_f       1.000                               1.000    1.000
##     BullyOth9_f       1.000                               1.000    1.000
#### One-Factor CFA for Got Bullied Items
#### A Nine-Item Five-Point Likert Scale
#### ("GotBully1_f" Coded as Factor Variable)
#### ("GotBully1_i" Coded as Integer Varable)

if(interactive()) peek(hbsc[ , c("GotBully1_f", "GotBully1_i", "GotBully2_f", "GotBully2_i",
               "GotBully3_f", "GotBully3_i", "GotBully4_f", "GotBully4_i",
               "GotBully5_f", "GotBully5_i", "GotBully6_f", "GotBully6_i",
               "GotBully7_f", "GotBully7_i", "GotBully8_f", "GotBully8_i",
               "GotBully9_f", "GotBully9_i")])

## Continuous Treatment of the Items (ML)
model.gotBully.integer <- '
gotBully =~ NA*GotBully1_i + GotBully2_i + GotBully3_i
            + GotBully4_i  + GotBully5_i + GotBully6_i 
            + GotBully7_i + GotBully8_i + GotBully9_i
gotBully ~~ 1*gotBully
'

fit.gotBully.ML.integer <- cfa(model = model.gotBully.integer, data = hbsc,
                               mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   10 15 28 34 43 47 48 71 72 73 80 81 84 89 90 93 103 131 137 142 148 150 151 163 168 169 177 178 184 190 195 226 232 235 242 247 251 252 253 256 259 260 272 280 287 292 297 323 328 333 356 360 366 373 375 376 381 382 385 396 398 400 402 403 410 412 417 418 420 426 434 439 447 449 450 452 461 466 474 477 486 489 490 507 508 526 530 541 542 548 550 553 554 557 563 578 579 582 591 593 594 595 603 608 613 616 622 628 636 639 649 652 654 655 660 664 666 670 674 679 684 686 688 690 695 726 727 728 729 730 732 746 751 753 760 766 771 781 785 799 813 821 831 836 853 868 872 883 891 892 896 897 901 904 911 912 919 920 934 942 946 952 953 969 971 972 977 1000 1013 1015 1017 1023 1025 1043 1045 1048 1049 1052 1055 1056 1062 1063 1068 1072 1073 1076 1091 1092 1101 1109 1111 1120 1123 1125 1132 1140 1144 1150 1156 1158 1160 1166 1171 1173 1179 1188 1190 1193 1196 1203 1204 1206 1213 1214 1216 1235 1247 1262 1272 1273 1285 1288 1302 1306 1314 1320 1330 1332 1350 1352 1353 1354 1360 1363 1369 1377 1382 1385 1387 1390 1391 1396 1398 1404 1419 1438 1441 1442 1447 1450 1454 1479 1484 1487 1498 1508 1509 1512 1515 1516 1519 1521 1526 1527 1530 1534 1536 1537 1538 1539 1542 1553 1555 1558 1559 1560 1568 1569 1573 1577 1588 1594 1601 1618 1623 1625 1628 1648 1656 1666 1670 1672 1681 1683 1688 1691 1693 1694 1695 1700 1708 1710 1712 1715 1717 1718 1730 1735 1739 1740 1741 1742 1747 1751 1752 1761 1772 1774 1787 1789 1790 1794 1798 1799 1805 1809 1813 1820 1832 1838 1843 1857 1864 1875 1879 1882 1890 1897 1902 1903 1914 1920 1921 1922 1927 1929 1945 1951 1953 1962 1963 1966 1967 1969 1971 1984 1988 1990 1997 1998 2003 2007 2009 2012 2014 2034 2040 2048 2059 2108 2117 2125 2129 2137 2154 2156 2159 2167 2175 2176 2178 2186 2194 2202 2203 2217 2221 2223 2234 2242 2249 2264 2268 2282 2308 2309 2319 2325 2338 2357 2360 2363 2364 2374 2380 2386 2387 2391 2397 2422 2436 2440 2444 2445 2447 2450 2454 2473 2478 2491 2496 2505 2518 2521 2523 2524 2529 2544 2553 2556 2557 2563 2571 2587 2591 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6466 6467 6471 6473 6477 6488 6492 6499 6501 6515 6521 6524 6526 6545 6550 6551 6556 6559 6564 6595 6599 6619 6624 6631 6633 6640 6643 6644 6646 6666 6673 6676 6679 6681 6686 6688 6689 6693 6695 6707 6719 6726 6739 6746 6749 6753 6782 6785 6788 6795 6796 6800 6801 6804 6816 6817 6827 6834 6835 6852 6859 6869 6884 6885 6889 6891 6896 6903 6909 6911 6917 6924 6933 6941 6942 6943 6950 6968 6971 6972 6976 6979 6987 6991 6996 6999 7002 7023 7027 7032 7036 7049 7064 7074 7081 7085 7088 7092 7099 7101 7112 7114 7122 7136 7142 7143 7148 7159 7162 7165 7173 7185 7186 7188 7220 7228 7234 7239 7254 7255 7259 7262 7265 7266 7271 7280 7288 7294 7298 7301 7311 7312 7332 7344 7347 7348 7351 7352 7353 7355 7358 7361 7381 7386 7398 7406 7418 7420 7422 7438 7459 7461 7470 7471 7472 7479 7482 7484 7488 7489 7505 7514 7517 7518 7520 7525 7527 7530 7535 7542 7547 7553 7559 7567 7571 7576 7577 7582 7607 7610 7612 7633 7641 7644 7648 7655 7662 7663 7667 7687 7688 7691 7692 7708 7709 7717 7720 7721 7724 7731 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summary(fit.gotBully.ML.integer, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  29 iterations
## 
##                                                   Used       Total
##   Number of observations                          7747        9227
## 
##   Number of missing patterns                        43
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             4264.678
##   Degrees of freedom                                27
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            27845.225
##   Degrees of freedom                                36
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.848
##   Tucker-Lewis Index (TLI)                       0.797
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -75132.615
##   Loglikelihood unrestricted model (H1)     -73000.276
## 
##   Number of free parameters                         27
##   Akaike (AIC)                              150319.231
##   Bayesian (BIC)                            150507.018
##   Sample-size adjusted Bayesian (BIC)       150421.217
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.142
##   90 Percent Confidence Interval          0.139  0.146
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.064
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_i       0.741    0.013   58.391    0.000    0.741    0.638
##     GotBully2_i       0.654    0.011   58.345    0.000    0.654    0.637
##     GotBully3_i       0.566    0.009   65.525    0.000    0.566    0.692
##     GotBully4_i       0.712    0.012   61.765    0.000    0.712    0.665
##     GotBully5_i       0.568    0.009   64.812    0.000    0.568    0.689
##     GotBully6_i       0.478    0.007   65.043    0.000    0.478    0.695
##     GotBully7_i       0.658    0.012   56.773    0.000    0.658    0.622
##     GotBully8_i       0.414    0.007   60.495    0.000    0.414    0.662
##     GotBully9_i       0.379    0.006   58.455    0.000    0.379    0.645
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_i       0.664    0.013   50.264    0.000    0.664    0.571
##    .GotBully2_i       0.514    0.012   43.964    0.000    0.514    0.500
##    .GotBully3_i       0.284    0.009   30.479    0.000    0.284    0.347
##    .GotBully4_i       0.613    0.012   50.314    0.000    0.613    0.572
##    .GotBully5_i       0.281    0.009   29.876    0.000    0.281    0.340
##    .GotBully6_i       0.192    0.008   24.503    0.000    0.192    0.279
##    .GotBully7_i       0.516    0.012   42.769    0.000    0.516    0.487
##    .GotBully8_i       0.162    0.007   22.784    0.000    0.162    0.260
##    .GotBully9_i       0.133    0.007   19.857    0.000    0.133    0.226
##     gotBully          0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##    .GotBully1_i       0.800    0.015   54.658    0.000    0.800    0.593
##    .GotBully2_i       0.626    0.011   55.048    0.000    0.626    0.594
##    .GotBully3_i       0.348    0.006   53.680    0.000    0.348    0.521
##    .GotBully4_i       0.640    0.012   53.999    0.000    0.640    0.558
##    .GotBully5_i       0.358    0.007   53.441    0.000    0.358    0.526
##    .GotBully6_i       0.245    0.005   52.418    0.000    0.245    0.517
##    .GotBully7_i       0.688    0.012   56.074    0.000    0.688    0.614
##    .GotBully8_i       0.220    0.004   53.579    0.000    0.220    0.562
##    .GotBully9_i       0.201    0.004   54.156    0.000    0.201    0.584
## Categorical Treatment of the Items (WLSMV)
model.gotBully.factor <- '
gotBully =~ NA*GotBully1_f + GotBully2_f + GotBully3_f
            + GotBully4_f  + GotBully5_f + GotBully6_f 
            + GotBully7_f + GotBully8_f  + GotBully9_f
gotBully ~~ 1*gotBully
'

fit.gotBully.WLSMV.factor <-
    cfa(model = model.gotBully.factor, data = hbsc,
        mimic = "Mplus", estimator = "WLSMV",
        ordered = c("GotBully1_f", "GotBully2_f",
                    "GotBully3_f", "GotBully4_f",
                    "GotBully5_f", "GotBully6_f",
                    "GotBully7_f", "GotBully8_f",
                    "GotBully9_f"))

summary(fit.gotBully.WLSMV.factor, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  14 iterations
## 
##                                                   Used       Total
##   Number of observations                          7526        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              728.460    1214.776
##   Degrees of freedom                                27          27
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.601
##   Shift parameter                                            3.567
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            79174.972   38684.865
##   Degrees of freedom                                36          36
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.991       0.969
##   Tucker-Lewis Index (TLI)                       0.988       0.959
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.059       0.076
##   90 Percent Confidence Interval          0.055  0.062       0.073  0.080
##   P-value RMSEA <= 0.05                          0.000       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.054       0.054
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           3.181       3.181
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_f       0.777    0.008   93.907    0.000    0.777    0.777
##     GotBully2_f       0.771    0.008   91.170    0.000    0.771    0.771
##     GotBully3_f       0.803    0.009   89.447    0.000    0.803    0.803
##     GotBully4_f       0.782    0.008  101.800    0.000    0.782    0.782
##     GotBully5_f       0.815    0.009   94.006    0.000    0.815    0.815
##     GotBully6_f       0.846    0.009   91.692    0.000    0.846    0.846
##     GotBully7_f       0.747    0.009   81.022    0.000    0.747    0.747
##     GotBully8_f       0.861    0.009  100.022    0.000    0.861    0.861
##     GotBully9_f       0.889    0.009   94.807    0.000    0.889    0.889
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_f       0.000                               0.000    0.000
##    .GotBully2_f       0.000                               0.000    0.000
##    .GotBully3_f       0.000                               0.000    0.000
##    .GotBully4_f       0.000                               0.000    0.000
##    .GotBully5_f       0.000                               0.000    0.000
##    .GotBully6_f       0.000                               0.000    0.000
##    .GotBully7_f       0.000                               0.000    0.000
##    .GotBully8_f       0.000                               0.000    0.000
##    .GotBully9_f       0.000                               0.000    0.000
##     gotBully          0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f|t1    0.431    0.015   28.857    0.000    0.431    0.431
##     GotBully1_f|t2    1.043    0.018   58.914    0.000    1.043    1.043
##     GotBully1_f|t3    1.254    0.019   64.520    0.000    1.254    1.254
##     GotBully1_f|t4    1.520    0.022   67.572    0.000    1.520    1.520
##     GotBully2_f|t1    0.618    0.015   39.860    0.000    0.618    0.618
##     GotBully2_f|t2    1.193    0.019   63.170    0.000    1.193    1.193
##     GotBully2_f|t3    1.421    0.021   66.944    0.000    1.421    1.421
##     GotBully2_f|t4    1.733    0.026   66.954    0.000    1.733    1.733
##     GotBully3_f|t1    1.082    0.018   60.180    0.000    1.082    1.082
##     GotBully3_f|t2    1.512    0.022   67.546    0.000    1.512    1.512
##     GotBully3_f|t3    1.727    0.026   67.005    0.000    1.727    1.727
##     GotBully3_f|t4    1.976    0.031   63.314    0.000    1.976    1.976
##     GotBully4_f|t1    0.424    0.015   28.379    0.000    0.424    0.424
##     GotBully4_f|t2    1.103    0.018   60.796    0.000    1.103    1.103
##     GotBully4_f|t3    1.385    0.021   66.570    0.000    1.385    1.385
##     GotBully4_f|t4    1.654    0.025   67.481    0.000    1.654    1.654
##     GotBully5_f|t1    1.108    0.018   60.939    0.000    1.108    1.108
##     GotBully5_f|t2    1.510    0.022   67.538    0.000    1.510    1.510
##     GotBully5_f|t3    1.709    0.025   67.147    0.000    1.709    1.709
##     GotBully5_f|t4    1.965    0.031   63.549    0.000    1.965    1.965
##     GotBully6_f|t1    1.339    0.020   65.965    0.000    1.339    1.339
##     GotBully6_f|t2    1.691    0.025   67.277    0.000    1.691    1.691
##     GotBully6_f|t3    1.894    0.029   64.854    0.000    1.894    1.894
##     GotBully6_f|t4    2.136    0.036   59.567    0.000    2.136    2.136
##     GotBully7_f|t1    0.671    0.016   42.729    0.000    0.671    0.671
##     GotBully7_f|t2    1.148    0.019   62.058    0.000    1.148    1.148
##     GotBully7_f|t3    1.395    0.021   66.689    0.000    1.395    1.395
##     GotBully7_f|t4    1.685    0.025   67.313    0.000    1.685    1.685
##     GotBully8_f|t1    1.398    0.021   66.718    0.000    1.398    1.398
##     GotBully8_f|t2    1.787    0.027   66.388    0.000    1.787    1.787
##     GotBully8_f|t3    2.003    0.032   62.757    0.000    2.003    2.003
##     GotBully8_f|t4    2.218    0.039   57.316    0.000    2.218    2.218
##     GotBully9_f|t1    1.535    0.023   67.615    0.000    1.535    1.535
##     GotBully9_f|t2    1.871    0.029   65.239    0.000    1.871    1.871
##     GotBully9_f|t3    2.044    0.033   61.835    0.000    2.044    2.044
##     GotBully9_f|t4    2.230    0.039   56.974    0.000    2.230    2.230
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##    .GotBully1_f       0.397                               0.397    0.397
##    .GotBully2_f       0.406                               0.406    0.406
##    .GotBully3_f       0.356                               0.356    0.356
##    .GotBully4_f       0.388                               0.388    0.388
##    .GotBully5_f       0.335                               0.335    0.335
##    .GotBully6_f       0.284                               0.284    0.284
##    .GotBully7_f       0.442                               0.442    0.442
##    .GotBully8_f       0.258                               0.258    0.258
##    .GotBully9_f       0.210                               0.210    0.210
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f       1.000                               1.000    1.000
##     GotBully2_f       1.000                               1.000    1.000
##     GotBully3_f       1.000                               1.000    1.000
##     GotBully4_f       1.000                               1.000    1.000
##     GotBully5_f       1.000                               1.000    1.000
##     GotBully6_f       1.000                               1.000    1.000
##     GotBully7_f       1.000                               1.000    1.000
##     GotBully8_f       1.000                               1.000    1.000
##     GotBully9_f       1.000                               1.000    1.000
#### One-Factor CFA for Body Feelings items
#### A Five-Item Five-Point Likert Scale
#### ("BodyFeelings1_f" Coded as Factor Variable)
#### ("BodyFeelings1_i" Coded as Integer Varable)

if(interactive()) peek(hbsc[ , c("BodyFeelings1_f", "BodyFeelings1_i",
               "BodyFeelings2_f", "BodyFeelings2_i",
               "BodyFeelings3_f", "BodyFeelings3_i",
               "BodyFeelings4_f", "BodyFeelings4_i",
               "BodyFeelings5_f", "BodyFeelings5_i")])

model.bodyFeelings.integer <- '
bodyFeelings =~ NA*BodyFeelings1_i + BodyFeelings2_i
                + BodyFeelings3_i + BodyFeelings4_i
                + BodyFeelings5_i
bodyFeelings ~~ 1*bodyFeelings'

## Continuous Treatment of the Items (ML)
fit.bodyFeelings.ML.integer <-
    cfa(model = model.bodyFeelings.integer, data = hbsc,
        mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   4 5 17 20 21 22 29 30 54 61 67 70 71 73 78 90 102 115 117 123 124 125 131 147 156 161 175 183 184 186 192 209 217 225 227 231 240 241 249 263 272 281 285 301 306 313 320 327 342 344 358 364 369 372 377 382 387 401 406 411 416 424 431 432 435 441 445 448 466 468 473 477 481 492 510 536 540 551 560 566 569 589 599 605 614 626 627 628 631 632 645 647 651 658 659 662 673 679 683 694 716 725 744 752 754 758 761 771 780 782 784 794 802 805 809 830 839 841 846 853 884 886 887 891 892 911 914 918 930 934 962 968 970 976 979 987 989 990 992 993 1007 1020 1036 1039 1060 1073 1090 1096 1097 1117 1126 1128 1132 1140 1142 1147 1151 1159 1169 1174 1177 1179 1191 1200 1225 1228 1230 1232 1233 1239 1241 1243 1249 1266 1268 1269 1281 1289 1293 1320 1321 1333 1335 1360 1367 1372 1379 1386 1401 1404 1405 1417 1422 1425 1440 1445 1468 1481 1484 1492 1501 1516 1555 1569 1571 1581 1586 1595 1622 1634 1636 1639 1649 1654 1659 1670 1687 1690 1699 1705 1709 1717 1723 1724 1726 1730 1735 1736 1738 1739 1744 1745 1753 1754 1765 1768 1785 1789 1790 1791 1810 1819 1829 1833 1836 1837 1839 1845 1848 1853 1854 1863 1866 1882 1888 1890 1900 1901 1910 1913 1916 1917 1922 1923 1933 1959 1961 1965 1966 1972 1974 1980 1981 1982 1985 1987 1991 1998 2000 2017 2019 2028 2053 2054 2060 2063 2070 2077 2079 2089 2091 2097 2101 2107 2110 2116 2119 2123 2126 2128 2137 2141 2145 2147 2163 2166 2168 2182 2184 2189 2204 2214 2219 2224 2237 2239 2243 2245 2254 2274 2276 2278 2300 2314 2318 2324 2332 2338 2347 2353 2361 2375 2377 2378 2382 2384 2388 2390 2396 2397 2399 2403 2404 2407 2410 2411 2417 2418 2423 2429 2448 2457 2460 2471 2477 2483 2487 2497 2503 2504 2509 2516 2532 2537 2554 2555 2560 2563 2568 2574 2575 2585 2586 2590 2593 2598 2606 2607 2612 2617 2623 2627 2632 2636 2640 2653 2654 2658 2665 2689 2690 2693 2705 2717 2720 2728 2731 2734 2741 2743 2745 2746 2747 2756 2759 2765 2768 2769 2783 2789 2808 2822 2823 2824 2825 2828 2835 2837 2842 2849 2853 2855 2856 2860 2864 2865 2883 2887 2891 2892 2893 2895 2903 2904 2907 2917 2933 2935 2937 2956 2971 2980 2986 2991 2995 3001 3018 3022 3024 3025 3029 3032 3052 3064 3066 3084 3087 3088 3093 3098 3122 3135 3137 3148 3161 3164 3175 3177 3191 3194 3199 3200 3212 3213 3217 3219 3221 3222 3236 3244 3247 3261 3271 3274 3280 3290 3298 3311 3312 3314 3328 3333 3338 3341 3344 3365 3367 3368 3377 3385 3386 3390 3406 3410 3416 3423 3430 3440 3450 3457 3465 3477 3489 3501 3510 3515 3516 3521 3523 3527 3537 3545 3550 3556 3560 3563 3567 3569 3575 3577 3583 3585 3599 3606 3613 3624 3629 3631 3640 3650 3655 3692 3694 3703 3710 3716 3717 3718 3721 3749 3772 3782 3784 3789 3794 3799 3807 3814 3823 3827 3840 3845 3846 3848 3856 3857 3869 3873 3884 3887 3891 3895 3903 3915 3923 3925 3928 3934 3941 3950 3953 3957 3962 3976 3986 3993 4021 4023 4027 4046 4056 4057 4058 4059 4061 4069 4089 4092 4100 4112 4118 4122 4123 4141 4146 4148 4149 4154 4182 4187 4195 4202 4203 4209 4215 4221 4229 4233 4235 4250 4252 4253 4258 4268 4272 4281 4290 4295 4305 4309 4316 4320 4328 4335 4355 4360 4364 4377 4378 4380 4388 4397 4406 4415 4429 4430 4433 4436 4456 4459 4466 4475 4480 4486 4512 4523 4531 4550 4558 4564 4566 4584 4589 4601 4605 4616 4623 4626 4631 4653 4666 4670 4674 4690 4700 4708 4728 4742 4795 4815 4817 4832 4833 4852 4857 4863 4865 4866 4869 4871 4873 4879 4880 4884 4890 4895 4903 4905 4907 4908 4911 4914 4916 4925 4932 4933 4934 4941 4945 4949 4950 4965 4969 4972 4973 4974 4977 4993 4997 5000 5008 5010 5011 5012 5013 5014 5015 5020 5027 5051 5060 5071 5073 5077 5083 5085 5091 5093 5098 5101 5104 5106 5108 5114 5118 5146 5150 5154 5155 5156 5163 5167 5175 5178 5187 5205 5215 5219 5240 5241 5254 5258 5260 5266 5270 5276 5277 5285 5290 5297 5303 5304 5311 5317 5321 5323 5325 5330 5338 5341 5347 5353 5357 5379 5383 5388 5396 5402 5415 5421 5424 5427 5434 5435 5439 5446 5449 5450 5451 5466 5477 5484 5485 5493 5507 5508 5528 5533 5545 5551 5564 5567 5571 5573 5593 5594 5614 5618 5625 5638 5644 5657 5672 5673 5688 5700 5704 5708 5722 5725 5739 5748 5753 5754 5757 5768 5779 5786 5792 5794 5808 5814 5829 5830 5834 5844 5855 5860 5862 5871 5881 5884 5887 5888 5890 5893 5897 5902 5916 5918 5922 5929 5930 5941 5949 5953 5958 5963 5966 5970 5977 5979 5986 5999 6000 6002 6004 6028 6041 6043 6053 6055 6058 6064 6070 6071 6074 6077 6089 6093 6095 6103 6107 6112 6113 6122 6126 6127 6140 6145 6148 6153 6173 6181 6190 6201 6202 6207 6223 6228 6231 6241 6251 6256 6261 6270 6282 6285 6295 6305 6318 6323 6333 6346 6352 6359 6360 6364 6374 6396 6398 6422 6437 6456 6459 6462 6465 6473 6489 6492 6494 6501 6509 6517 6522 6546 6548 6552 6555 6560 6564 6565 6573 6585 6587 6599 6607 6612 6616 6617 6621 6628 6652 6653 6655 6663 6667 6692 6694 6696 6702 6706 6708 6717 6723 6743 6747 6749 6758 6764 6768 6775 6790 6793 6796 6803 6823 6826 6838 6841 6845 6860 6862 6872 6877 6879 6881 6886 6893 6900 6902 6905 6914 6931 6934 6964 6977 6986 6989 7009 7013 7017 7018 7020 7029 7032 7038 7045 7060 7068 7081 7082 7083 7084 7096 7097 7102 7107 7113 7114 7115 7125 7130 7134 7147 7162 7172 7177 7191 7200 7201 7204 7205 7208 7219 7223 7227 7231 7238 7240 7252 7256 7273 7276 7281 7293 7317 7327 7328 7335 7344 7346 7357 7374 7378 7384 7388 7390 7405 7411 7413 7416 7418 7423 7428 7431 7439 7442 7452 7453 7459 7460 7463 7469 7473 7490 7493 7500 7501 7504 7537 7540 7543 7561 7570 7585 7589 7590 7595 7599 7600 7606 7613 7631 7634 7639 7652 7667 7671 7673 7685 7704 7710 7712 7715 7717 7729 7732 7736 7739 7743 7748 7753 7754 7755 7769 7771 7779 7783 7795 7806 7821 7824 7829 7830 7831 7838 7848 7854 7882 7888 7889 7890 7891 7893 7903 7911 7919 7923 7928 7935 7939 7955 7956 7960 7973 7980 7984 7987 7991 7995 8005 8006 8011 8018 8021 8022 8026 8051 8053 8070 8076 8085 8096 8098 8109 8114 8117 8122 8129 8130 8132 8142 8145 8165 8178 8182 8183 8188 8191 8211 8212 8213 8216 8217 8221 8247 8256 8258 8285 8297 8314 8321 8327 8329 8343 8344 8345 8356 8357 8360 8378 8380 8394 8396 8417 8420 8427 8432 8435 8436 8441 8448 8449 8454 8468 8481 8496 8497 8502 8504 8508 8524 8527 8540 8542 8547 8555 8559 8566 8580 8581 8586 8587 8598 8607 8612 8617 8623 8637 8645 8650 8657 8664 8666 8700 8703 8704 8705 8716 8717 8718 8727 8733 8735 8736 8744 8746 8755 8757 8758 8759 8761 8767 8776 8777 8778 8779 8781 8784 8786 8789 8791 8797 8814 8816 8817 8831 8835 8857 8858 8862 8885 8889 8900 8907 8908 8910 8912 8920 8923 8929 8932 8943 8946 8947 8957 8959 8962 8972 8974 8977 8983 9004 9006 9009 9010 9012 9026 9029 9034 9036 9037 9041 9043 9049 9056 9059 9070 9076 9081 9083 9086 9088 9089 9096 9103 9121 9126 9127 9131 9132 9135 9159 9168 9189 9190 9193 9195 9197 9209 9214 9221
summary(fit.bodyFeelings.ML.integer, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  23 iterations
## 
##                                                   Used       Total
##   Number of observations                          7874        9227
## 
##   Number of missing patterns                        23
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             1513.390
##   Degrees of freedom                                 5
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            18808.555
##   Degrees of freedom                                10
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.920
##   Tucker-Lewis Index (TLI)                       0.840
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -55457.378
##   Loglikelihood unrestricted model (H1)     -54700.683
## 
##   Number of free parameters                         15
##   Akaike (AIC)                              110944.755
##   Bayesian (BIC)                            111049.325
##   Sample-size adjusted Bayesian (BIC)       111001.658
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.196
##   90 Percent Confidence Interval          0.188  0.204
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.044
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   bodyFeelings =~                                                       
##     BodyFeelings1_    1.013    0.014   74.387    0.000    1.013    0.758
##     BodyFeelings2_   -0.897    0.013  -69.646    0.000   -0.897   -0.732
##     BodyFeelings3_    0.993    0.012   81.238    0.000    0.993    0.814
##     BodyFeelings4_   -0.942    0.013  -70.514    0.000   -0.942   -0.732
##     BodyFeelings5_    0.866    0.012   71.391    0.000    0.866    0.743
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .BodyFeelings1_    1.479    0.015   98.125    0.000    1.479    1.107
##    .BodyFeelings2_    2.486    0.014  179.675    0.000    2.486    2.029
##    .BodyFeelings3_    0.870    0.014   63.137    0.000    0.870    0.713
##    .BodyFeelings4_    2.612    0.015  179.719    0.000    2.612    2.029
##    .BodyFeelings5_    0.764    0.013   58.035    0.000    0.764    0.655
##     bodyFeelings      0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     bodyFeelings      1.000                               1.000    1.000
##    .BodyFeelings1_    0.759    0.016   48.758    0.000    0.759    0.425
##    .BodyFeelings2_    0.697    0.014   48.598    0.000    0.697    0.464
##    .BodyFeelings3_    0.503    0.012   40.668    0.000    0.503    0.338
##    .BodyFeelings4_    0.769    0.015   50.248    0.000    0.769    0.464
##    .BodyFeelings5_    0.609    0.013   48.272    0.000    0.609    0.448
## Categorical Treatment of the Items (WLSMV)
model.bodyFeelings.factor <- '
bodyFeelings =~ NA*BodyFeelings1_f + BodyFeelings2_f
                + BodyFeelings3_f + BodyFeelings4_f
                + BodyFeelings5_f
bodyFeelings ~~ 1*bodyFeelings
'

fit.bodyFeelings.WLSMV.factor <-
    cfa(model = model.bodyFeelings.factor, data = hbsc,
        mimic = "Mplus", estimator = "WLSMV",
        ordered = c("BodyFeelings1_f", "BodyFeelings2_f",
                    "BodyFeelings3_f", "BodyFeelings4_f",
                    "BodyFeelings5_f"))

summary(fit.bodyFeelings.WLSMV.factor, fit.measures = TRUE,
        standardized = TRUE)
## lavaan (0.5-22) converged normally after  18 iterations
## 
##                                                   Used       Total
##   Number of observations                          7723        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              731.399    1663.755
##   Degrees of freedom                                 5           5
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.440
##   Shift parameter                                            0.678
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic           110919.008   62733.876
##   Degrees of freedom                                10          10
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.993       0.974
##   Tucker-Lewis Index (TLI)                       0.987       0.947
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.137       0.207
##   90 Percent Confidence Interval          0.129  0.146       0.199  0.216
##   P-value RMSEA <= 0.05                          0.000       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.042       0.042
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           4.938       4.938
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   bodyFeelings =~                                                       
##     BodyFeelngs1_f    0.809    0.005  176.752    0.000    0.809    0.809
##     BodyFeelngs2_f   -0.816    0.005 -178.624    0.000   -0.816   -0.816
##     BodyFeelngs3_f    0.888    0.004  230.053    0.000    0.888    0.888
##     BodyFeelngs4_f   -0.800    0.005 -164.600    0.000   -0.800   -0.800
##     BodyFeelngs5_f    0.839    0.005  166.781    0.000    0.839    0.839
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .BodyFeelngs1_f    0.000                               0.000    0.000
##    .BodyFeelngs2_f    0.000                               0.000    0.000
##    .BodyFeelngs3_f    0.000                               0.000    0.000
##    .BodyFeelngs4_f    0.000                               0.000    0.000
##    .BodyFeelngs5_f    0.000                               0.000    0.000
##     bodyFeelings      0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     BdyFlngs1_f|t1   -0.471    0.015  -31.740    0.000   -0.471   -0.471
##     BdyFlngs1_f|t2    0.137    0.014    9.589    0.000    0.137    0.137
##     BdyFlngs1_f|t3    0.664    0.015   42.924    0.000    0.664    0.664
##     BdyFlngs1_f|t4    1.302    0.020   66.241    0.000    1.302    1.302
##     BdyFlngs2_f|t1   -1.375    0.020  -67.318    0.000   -1.375   -1.375
##     BdyFlngs2_f|t2   -0.740    0.016  -46.896    0.000   -0.740   -0.740
##     BdyFlngs2_f|t3   -0.190    0.014  -13.248    0.000   -0.190   -0.190
##     BdyFlngs2_f|t4    0.749    0.016   47.369    0.000    0.749    0.749
##     BdyFlngs3_f|t1    0.162    0.014   11.294    0.000    0.162    0.162
##     BdyFlngs3_f|t2    0.722    0.016   46.012    0.000    0.722    0.722
##     BdyFlngs3_f|t3    1.124    0.018   62.193    0.000    1.124    1.124
##     BdyFlngs3_f|t4    1.541    0.022   68.509    0.000    1.541    1.541
##     BdyFlngs4_f|t1   -1.296    0.020  -66.137    0.000   -1.296   -1.296
##     BdyFlngs4_f|t2   -0.799    0.016  -49.800    0.000   -0.799   -0.799
##     BdyFlngs4_f|t3   -0.317    0.015  -21.844    0.000   -0.317   -0.317
##     BdyFlngs4_f|t4    0.525    0.015   35.006    0.000    0.525    0.525
##     BdyFlngs5_f|t1    0.291    0.014   20.078    0.000    0.291    0.291
##     BdyFlngs5_f|t2    0.784    0.016   49.079    0.000    0.784    0.784
##     BdyFlngs5_f|t3    1.246    0.019   65.181    0.000    1.246    1.246
##     BdyFlngs5_f|t4    1.628    0.024   68.461    0.000    1.628    1.628
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     bodyFeelings      1.000                               1.000    1.000
##    .BodyFeelngs1_f    0.345                               0.345    0.345
##    .BodyFeelngs2_f    0.334                               0.334    0.334
##    .BodyFeelngs3_f    0.212                               0.212    0.212
##    .BodyFeelngs4_f    0.360                               0.360    0.360
##    .BodyFeelngs5_f    0.297                               0.297    0.297
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     BodyFeelngs1_f    1.000                               1.000    1.000
##     BodyFeelngs2_f    1.000                               1.000    1.000
##     BodyFeelngs3_f    1.000                               1.000    1.000
##     BodyFeelngs4_f    1.000                               1.000    1.000
##     BodyFeelngs5_f    1.000                               1.000    1.000
#### One-Factor CFA for Physical Health Items
#### An Eight-Item Five-Point Likert Scale
#### ("PhysHealth1_f" Coded as Factor Variable)
#### ("PhysHealth1_i" Coded as Integer Varable)

if(interactive()) peek(hbsc[ , c("PhysHealth1_f", "PhysHealth1_i", "PhysHealth2_f", "PhysHealth2_i",
               "PhysHealth3_f", "PhysHealth3_i", "PhysHealth4_f", "PhysHealth4_i",
               "PhysHealth5_f", "PhysHealth5_i", "PhysHealth6_f", "PhysHealth6_i",
               "PhysHealth7_f", "PhysHealth7_i", "PhysHealth8_f", "PhysHealth8_i")])

## Continuous Treatment of the Items (ML)
model.physHealth.integer <- '
physHealth =~ NA*PhysHealth1_i + PhysHealth2_i
               + PhysHealth3_i + PhysHealth4_i
               + PhysHealth5_i + PhysHealth6_i
               + PhysHealth7_i + PhysHealth8_i
physHealth ~~ 1*physHealth'

fit.physHealth.ML.integer <-
    cfa(model = model.physHealth.integer, data = hbsc,
        mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   73 90 184 247 382 466 477 628 660 679 771 892 934 988 1015 1055 1073 1117 1179 1360 1404 1447 1501 1571 1670 1709 1717 1735 1739 1763 1789 1790 1882 1922 1966 1998 2137 2168 2375 2397 2555 2563 2606 2623 2627 2636 2665 2983 2995 3032 3098 3213 3261 3271 3333 3410 3423 3457 3550 3567 3568 3646 3782 3870 4092 4122 4141 4148 4268 4320 4388 4415 4480 4833 4865 4925 4933 4973 4977 5093 5101 5276 5303 5753 5941 6053 6055 6089 6181 6473 6501 6564 6599 6708 6796 7032 7114 7332 7344 7357 7386 7531 7667 7935 8034 8117 8233 8386 8432 8443 8491 8598 8607 8664 8789 8816 8850 9041 9049 9132 9135 9159 9165 9182
summary(fit.physHealth.ML.integer, fit.measures = TRUE,
        standardized = TRUE)
## lavaan (0.5-22) converged normally after  30 iterations
## 
##                                                   Used       Total
##   Number of observations                          9103        9227
## 
##   Number of missing patterns                        60
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              601.015
##   Degrees of freedom                                20
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            16363.895
##   Degrees of freedom                                28
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.964
##   Tucker-Lewis Index (TLI)                       0.950
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -115169.781
##   Loglikelihood unrestricted model (H1)     -114869.273
## 
##   Number of free parameters                         24
##   Akaike (AIC)                              230387.561
##   Bayesian (BIC)                            230558.354
##   Sample-size adjusted Bayesian (BIC)       230482.086
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.056
##   90 Percent Confidence Interval          0.053  0.060
##   P-value RMSEA <= 0.05                          0.003
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.026
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   physHealth =~                                                         
##     PhysHealth1_i     0.781    0.014   56.361    0.000    0.781    0.597
##     PhysHealth2_i     0.709    0.012   57.953    0.000    0.709    0.611
##     PhysHealth3_i     0.688    0.014   47.516    0.000    0.688    0.517
##     PhysHealth4_i     0.871    0.014   63.816    0.000    0.871    0.661
##     PhysHealth5_i     0.808    0.015   53.115    0.000    0.808    0.569
##     PhysHealth6_i     0.738    0.015   50.161    0.000    0.738    0.542
##     PhysHealth7_i     0.877    0.016   53.243    0.000    0.877    0.570
##     PhysHealth8_i     0.755    0.013   59.702    0.000    0.755    0.625
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .PhysHealth1_i     2.827    0.014  206.103    0.000    2.827    2.162
##    .PhysHealth2_i     3.003    0.012  246.309    0.000    3.003    2.586
##    .PhysHealth3_i     3.001    0.014  214.424    0.000    3.001    2.254
##    .PhysHealth4_i     3.017    0.014  217.537    0.000    3.017    2.289
##    .PhysHealth5_i     2.510    0.015  168.100    0.000    2.510    1.767
##    .PhysHealth6_i     2.629    0.014  183.283    0.000    2.629    1.928
##    .PhysHealth7_i     2.646    0.016  163.482    0.000    2.646    1.718
##    .PhysHealth8_i     3.271    0.013  257.525    0.000    3.271    2.706
##     physHealth        0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     physHealth        1.000                               1.000    1.000
##    .PhysHealth1_i     1.099    0.019   58.201    0.000    1.099    0.643
##    .PhysHealth2_i     0.846    0.015   57.579    0.000    0.846    0.627
##    .PhysHealth3_i     1.300    0.021   61.433    0.000    1.300    0.733
##    .PhysHealth4_i     0.978    0.018   54.510    0.000    0.978    0.563
##    .PhysHealth5_i     1.364    0.023   59.432    0.000    1.364    0.676
##    .PhysHealth6_i     1.313    0.022   60.461    0.000    1.313    0.707
##    .PhysHealth7_i     1.603    0.027   59.503    0.000    1.603    0.676
##    .PhysHealth8_i     0.890    0.016   56.946    0.000    0.890    0.609
## Categorical Treatment of the Items (WLSMV)
model.physHealth.factor <- '
physHealth =~ NA*PhysHealth1_f + PhysHealth2_f
              + PhysHealth3_f + PhysHealth4_f
              + PhysHealth5_f + PhysHealth6_f
              + PhysHealth7_f + PhysHealth8_f
physHealth ~~ 1*physHealth'

fit.physHealth.WLSMV.factor <-
    cfa(model = model.physHealth.factor, data = hbsc, mimic = "Mplus",
        estimator = "WLSMV",
        ordered = c("PhysHealth1_f", "PhysHealth2_f",
                    "PhysHealth3_f", "PhysHealth4_f",
                    "PhysHealth5_f", "PhysHealth6_f",
                    "PhysHealth7_f", "PhysHealth8_f"))

summary(fit.physHealth.WLSMV.factor, fit.measures = TRUE,
        standardized = TRUE)
## lavaan (0.5-22) converged normally after  11 iterations
## 
##                                                   Used       Total
##   Number of observations                          8790        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              395.362     698.672
##   Degrees of freedom                                20          20
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.566
##   Shift parameter                                            0.434
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            44677.484   27959.802
##   Degrees of freedom                                28          28
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.992       0.976
##   Tucker-Lewis Index (TLI)                       0.988       0.966
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.046       0.062
##   90 Percent Confidence Interval          0.042  0.050       0.058  0.066
##   P-value RMSEA <= 0.05                          0.939       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.030       0.030
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           2.567       2.567
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   physHealth =~                                                         
##     PhysHealth1_f     0.654    0.008   79.794    0.000    0.654    0.654
##     PhysHealth2_f     0.662    0.008   82.597    0.000    0.662    0.662
##     PhysHealth3_f     0.573    0.010   59.324    0.000    0.573    0.573
##     PhysHealth4_f     0.731    0.008   95.587    0.000    0.731    0.731
##     PhysHealth5_f     0.621    0.008   74.073    0.000    0.621    0.621
##     PhysHealth6_f     0.589    0.009   67.774    0.000    0.589    0.589
##     PhysHealth7_f     0.634    0.009   73.761    0.000    0.634    0.634
##     PhysHealth8_f     0.718    0.008   85.271    0.000    0.718    0.718
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .PhysHealth1_f     0.000                               0.000    0.000
##    .PhysHealth2_f     0.000                               0.000    0.000
##    .PhysHealth3_f     0.000                               0.000    0.000
##    .PhysHealth4_f     0.000                               0.000    0.000
##    .PhysHealth5_f     0.000                               0.000    0.000
##    .PhysHealth6_f     0.000                               0.000    0.000
##    .PhysHealth7_f     0.000                               0.000    0.000
##    .PhysHealth8_f     0.000                               0.000    0.000
##     physHealth        0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     PhysHlth1_f|t1   -1.423    0.020  -72.374    0.000   -1.423   -1.423
##     PhysHlth1_f|t2   -0.813    0.015  -53.808    0.000   -0.813   -0.813
##     PhysHlth1_f|t3   -0.506    0.014  -36.087    0.000   -0.506   -0.506
##     PhysHlth1_f|t4    0.198    0.013   14.731    0.000    0.198    0.198
##     PhysHlth2_f|t1   -1.681    0.023  -72.777    0.000   -1.681   -1.681
##     PhysHlth2_f|t2   -1.061    0.016  -64.309    0.000   -1.061   -1.061
##     PhysHlth2_f|t3   -0.701    0.015  -47.885    0.000   -0.701   -0.701
##     PhysHlth2_f|t4    0.151    0.013   11.216    0.000    0.151    0.151
##     PhysHlth3_f|t1   -1.378    0.019  -71.859    0.000   -1.378   -1.378
##     PhysHlth3_f|t2   -0.920    0.016  -58.805    0.000   -0.920   -0.920
##     PhysHlth3_f|t3   -0.605    0.014  -42.318    0.000   -0.605   -0.605
##     PhysHlth3_f|t4   -0.103    0.013   -7.721    0.000   -0.103   -0.103
##     PhysHlth4_f|t1   -1.385    0.019  -71.944    0.000   -1.385   -1.385
##     PhysHlth4_f|t2   -0.953    0.016  -60.193    0.000   -0.953   -0.953
##     PhysHlth4_f|t3   -0.641    0.014  -44.465    0.000   -0.641   -0.641
##     PhysHlth4_f|t4   -0.103    0.013   -7.721    0.000   -0.103   -0.103
##     PhysHlth5_f|t1   -1.125    0.017  -66.371    0.000   -1.125   -1.125
##     PhysHlth5_f|t2   -0.584    0.014  -41.011    0.000   -0.584   -0.584
##     PhysHlth5_f|t3   -0.219    0.013  -16.263    0.000   -0.219   -0.219
##     PhysHlth5_f|t4    0.410    0.014   29.775    0.000    0.410    0.410
##     PhysHlth6_f|t1   -1.267    0.018  -69.987    0.000   -1.267   -1.267
##     PhysHlth6_f|t2   -0.707    0.015  -48.210    0.000   -0.707   -0.707
##     PhysHlth6_f|t3   -0.279    0.014  -20.580    0.000   -0.279   -0.279
##     PhysHlth6_f|t4    0.340    0.014   24.887    0.000    0.340    0.340
##     PhysHlth7_f|t1   -0.980    0.016  -61.300    0.000   -0.980   -0.980
##     PhysHlth7_f|t2   -0.591    0.014  -41.489    0.000   -0.591   -0.591
##     PhysHlth7_f|t3   -0.314    0.014  -23.085    0.000   -0.314   -0.314
##     PhysHlth7_f|t4    0.078    0.013    5.801    0.000    0.078    0.078
##     PhysHlth8_f|t1   -1.568    0.021  -73.124    0.000   -1.568   -1.568
##     PhysHlth8_f|t2   -1.127    0.017  -66.436    0.000   -1.127   -1.127
##     PhysHlth8_f|t3   -0.860    0.015  -56.081    0.000   -0.860   -0.860
##     PhysHlth8_f|t4   -0.403    0.014  -29.247    0.000   -0.403   -0.403
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     physHealth        1.000                               1.000    1.000
##    .PhysHealth1_f     0.573                               0.573    0.573
##    .PhysHealth2_f     0.562                               0.562    0.562
##    .PhysHealth3_f     0.672                               0.672    0.672
##    .PhysHealth4_f     0.466                               0.466    0.466
##    .PhysHealth5_f     0.615                               0.615    0.615
##    .PhysHealth6_f     0.653                               0.653    0.653
##    .PhysHealth7_f     0.598                               0.598    0.598
##    .PhysHealth8_f     0.485                               0.485    0.485
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     PhysHealth1_f     1.000                               1.000    1.000
##     PhysHealth2_f     1.000                               1.000    1.000
##     PhysHealth3_f     1.000                               1.000    1.000
##     PhysHealth4_f     1.000                               1.000    1.000
##     PhysHealth5_f     1.000                               1.000    1.000
##     PhysHealth6_f     1.000                               1.000    1.000
##     PhysHealth7_f     1.000                               1.000    1.000
##     PhysHealth8_f     1.000                               1.000    1.000
#### One-Factor CFA for Alcohol-Use Items
#### A Five-Item Five-Point Likert Scale
#### ("Alc1_f" Coded as Factor Variable)
#### ("Alc1_i" Coded as Integer Varable)

if(interactive()) peek(hbsc[ , c("Alc1_f", "Alc1_i", "Alc2_f", "Alc2_i",
               "Alc3_f", "Alc3_i", "Alc4_f", "Alc4_i",
               "Alc5_f", "Alc5_i")])

## Continuous Treatment of the Items (ML)
model.alcohol.integer <- '
alcohol =~ NA*Alc1_i + Alc2_i + Alc3_i + Alc4_i + Alc5_i
alcohol ~~ 1*alcohol
'

fit.alcohol.ML.integer <-
    cfa(model = model.alcohol.integer, data = hbsc,
        mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   34 47 48 71 73 75 80 84 90 103 131 184 235 242 247 259 382 396 400 417 431 466 477 489 530 557 628 679 727 771 853 891 892 896 911 934 969 988 1015 1052 1055 1056 1062 1063 1073 1110 1132 1179 1190 1286 1287 1320 1330 1354 1360 1385 1431 1450 1477 1555 1560 1670 1672 1717 1718 1730 1735 1739 1789 1790 1805 1832 1847 1878 1882 1914 1922 1963 1966 1998 2048 2092 2137 2156 2176 2186 2220 2234 2315 2338 2341 2374 2386 2397 2491 2497 2505 2544 2556 2563 2571 2587 2603 2627 2636 2665 2708 2716 2739 2744 2808 2856 2887 2992 2995 3032 3041 3098 3198 3209 3245 3256 3276 3317 3318 3333 3342 3345 3363 3398 3399 3410 3416 3423 3439 3457 3485 3542 3550 3551 3553 3567 3568 3580 3597 3634 3638 3646 3700 3720 3736 3765 3775 3782 3796 3797 3800 3817 3831 3857 3870 3886 3923 3961 3978 3991 4061 4080 4092 4093 4122 4141 4148 4152 4161 4167 4183 4185 4209 4268 4355 4361 4388 4415 4469 4470 4471 4478 4480 4551 4552 4566 4576 4614 4655 4670 4699 4720 4833 4865 4868 4918 4939 4950 4973 4977 5019 5075 5093 5110 5153 5163 5173 5178 5187 5188 5190 5199 5241 5258 5276 5303 5378 5392 5486 5513 5570 5577 5593 5611 5615 5699 5753 5781 5783 5785 5813 5846 5918 5942 5959 5970 5994 6043 6053 6124 6150 6170 6282 6337 6426 6452 6471 6473 6492 6501 6515 6521 6541 6545 6564 6597 6599 6688 6689 6693 6708 6749 6833 6859 6879 6933 6999 7032 7049 7064 7088 7092 7107 7114 7142 7159 7234 7239 7311 7332 7344 7370 7380 7386 7418 7459 7489 7536 7577 7667 7670 7720 7742 7761 7780 7860 7931 8034 8098 8117 8153 8169 8300 8341 8344 8394 8396 8416 8421 8441 8443 8491 8493 8533 8580 8584 8595 8598 8607 8622 8641 8716 8775 8789 8792 8944 8992 9000 9005 9026 9039 9049 9061 9124 9132 9135 9159 9165 9170 9189 9209
summary(fit.alcohol.ML.integer, fit.measures = TRUE,
        standardized = TRUE)
## lavaan (0.5-22) converged normally after  35 iterations
## 
##                                                   Used       Total
##   Number of observations                          8880        9227
## 
##   Number of missing patterns                        18
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              276.556
##   Degrees of freedom                                 5
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            27680.725
##   Degrees of freedom                                10
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.990
##   Tucker-Lewis Index (TLI)                       0.980
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -38486.475
##   Loglikelihood unrestricted model (H1)     -38348.197
## 
##   Number of free parameters                         15
##   Akaike (AIC)                               77002.950
##   Bayesian (BIC)                             77109.324
##   Sample-size adjusted Bayesian (BIC)        77061.656
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.078
##   90 Percent Confidence Interval          0.071  0.086
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.016
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   alcohol =~                                                            
##     Alc1_i            0.593    0.007   82.963    0.000    0.593    0.765
##     Alc2_i            0.411    0.007   59.312    0.000    0.411    0.595
##     Alc3_i            0.715    0.007  103.931    0.000    0.715    0.890
##     Alc4_i            0.736    0.008   96.044    0.000    0.736    0.846
##     Alc5_i            0.754    0.007  104.738    0.000    0.754    0.892
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Alc1_i            2.355    0.008  286.201    0.000    2.355    3.038
##    .Alc2_i            2.327    0.007  317.074    0.000    2.327    3.370
##    .Alc3_i            2.359    0.009  275.861    0.000    2.359    2.935
##    .Alc4_i            2.469    0.009  266.744    0.000    2.469    2.839
##    .Alc5_i            2.425    0.009  270.231    0.000    2.425    2.870
##     alcohol           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     alcohol           1.000                               1.000    1.000
##    .Alc1_i            0.249    0.004   58.160    0.000    0.249    0.415
##    .Alc2_i            0.308    0.005   63.366    0.000    0.308    0.646
##    .Alc3_i            0.134    0.003   43.382    0.000    0.134    0.208
##    .Alc4_i            0.215    0.004   51.601    0.000    0.215    0.284
##    .Alc5_i            0.145    0.003   43.125    0.000    0.145    0.204
## Categorical Treatment of the Items (WLSMV)
model.alcohol.factor <- '
alcohol =~ NA*Alc1_f + Alc2_f + Alc3_f + Alc4_f + Alc5_f
alcohol ~~ 1*alcohol
'

fit.alcohol.WLSMV.factor <-
    cfa(model = model.alcohol.factor, data = hbsc, mimic = "Mplus",
        estimator = "WLSMV",
        ordered = c("Alc1_f", "Alc2_f", "Alc3_f", "Alc4_f", "Alc5_f"))

summary(fit.alcohol.WLSMV.factor, fit.measures = TRUE,
        standardized = TRUE)
## lavaan (0.5-22) converged normally after  17 iterations
## 
##                                                   Used       Total
##   Number of observations                          8574        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic               42.176     150.905
##   Degrees of freedom                                 5           5
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.280
##   Shift parameter                                            0.221
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic           181107.193   95425.390
##   Degrees of freedom                                10          10
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    1.000       0.998
##   Tucker-Lewis Index (TLI)                       1.000       0.997
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.029       0.058
##   90 Percent Confidence Interval          0.022  0.038       0.051  0.067
##   P-value RMSEA <= 0.05                          1.000       0.040
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.013       0.013
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           1.186       1.186
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   alcohol =~                                                            
##     Alc1_f            0.859    0.005  166.799    0.000    0.859    0.859
##     Alc2_f            0.719    0.009   81.678    0.000    0.719    0.719
##     Alc3_f            0.948    0.003  362.913    0.000    0.948    0.948
##     Alc4_f            0.914    0.003  269.148    0.000    0.914    0.914
##     Alc5_f            0.943    0.003  375.926    0.000    0.943    0.943
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Alc1_f            0.000                               0.000    0.000
##    .Alc2_f            0.000                               0.000    0.000
##    .Alc3_f            0.000                               0.000    0.000
##    .Alc4_f            0.000                               0.000    0.000
##    .Alc5_f            0.000                               0.000    0.000
##     alcohol           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Alc1_f|t1         0.764    0.015   50.665    0.000    0.764    0.764
##     Alc1_f|t2         1.433    0.020   71.574    0.000    1.433    1.433
##     Alc1_f|t3         1.778    0.025   70.971    0.000    1.778    1.778
##     Alc1_f|t4         2.330    0.040   57.589    0.000    2.330    2.330
##     Alc2_f|t1         0.725    0.015   48.624    0.000    0.725    0.725
##     Alc2_f|t2         1.631    0.023   72.124    0.000    1.631    1.631
##     Alc2_f|t3         1.955    0.029   68.045    0.000    1.955    1.955
##     Alc2_f|t4         2.423    0.045   54.390    0.000    2.423    2.423
##     Alc3_f|t1         0.825    0.015   53.723    0.000    0.825    0.825
##     Alc3_f|t2         1.354    0.019   70.634    0.000    1.354    1.354
##     Alc3_f|t3         1.739    0.024   71.406    0.000    1.739    1.739
##     Alc3_f|t4         2.330    0.040   57.589    0.000    2.330    2.330
##     Alc4_f|t1         0.581    0.014   40.327    0.000    0.581    0.581
##     Alc4_f|t2         1.212    0.018   67.918    0.000    1.212    1.212
##     Alc4_f|t3         1.678    0.023   71.893    0.000    1.678    1.678
##     Alc4_f|t4         2.228    0.037   60.866    0.000    2.228    2.228
##     Alc5_f|t1         0.663    0.015   45.157    0.000    0.663    0.663
##     Alc5_f|t2         1.285    0.018   69.484    0.000    1.285    1.285
##     Alc5_f|t3         1.685    0.023   71.846    0.000    1.685    1.685
##     Alc5_f|t4         2.260    0.038   59.843    0.000    2.260    2.260
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     alcohol           1.000                               1.000    1.000
##    .Alc1_f            0.261                               0.261    0.261
##    .Alc2_f            0.483                               0.483    0.483
##    .Alc3_f            0.100                               0.100    0.100
##    .Alc4_f            0.164                               0.164    0.164
##    .Alc5_f            0.110                               0.110    0.110
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Alc1_f            1.000                               1.000    1.000
##     Alc2_f            1.000                               1.000    1.000
##     Alc3_f            1.000                               1.000    1.000
##     Alc4_f            1.000                               1.000    1.000
##     Alc5_f            1.000                               1.000    1.000
####-------------------------------------------------####
#### Section-2: A Three-Factor CFA with Likert Items ####
#### Factors: Got Bullied, Depression, Alchol Use    ####
####-------------------------------------------------####

## The Continous Treatment (ML) of the Items Coded as Interger Variables
model.CFA.integer <- '
gotBully =~ NA*GotBully1_i + GotBully2_i + GotBully3_i
            + GotBully4_i + GotBully5_i + GotBully6_i
            + GotBully7_i + GotBully8_i + GotBully9_i
gotBully ~~ 1*gotBully

depress =~ NA*Depress1_i + Depress2_i + Depress3_i
           + Depress4_i + Depress5_i + Depress6_i
depress ~~ 1*depress
alcohol =~ NA*Alc1_i + Alc2_i + Alc3_i + Alc4_i + Alc5_i
alcohol ~~ 1*alcohol
'

fit.CFA.ML.integer <- cfa(model = model.CFA.integer, data = hbsc,
                          mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   7489
summary(fit.CFA.ML.integer, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  51 iterations
## 
##                                                   Used       Total
##   Number of observations                          9226        9227
## 
##   Number of missing patterns                       144
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             5605.569
##   Degrees of freedom                               167
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            70049.784
##   Degrees of freedom                               190
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.922
##   Tucker-Lewis Index (TLI)                       0.911
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -195609.297
##   Loglikelihood unrestricted model (H1)     -192806.513
## 
##   Number of free parameters                         63
##   Akaike (AIC)                              391344.594
##   Bayesian (BIC)                            391793.770
##   Sample-size adjusted Bayesian (BIC)       391593.566
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.059
##   90 Percent Confidence Interval          0.058  0.061
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.039
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_i       0.738    0.013   58.099    0.000    0.738    0.636
##     GotBully2_i       0.652    0.011   58.097    0.000    0.652    0.635
##     GotBully3_i       0.565    0.009   65.443    0.000    0.565    0.691
##     GotBully4_i       0.711    0.012   61.733    0.000    0.711    0.664
##     GotBully5_i       0.568    0.009   64.877    0.000    0.568    0.689
##     GotBully6_i       0.478    0.007   65.195    0.000    0.478    0.695
##     GotBully7_i       0.659    0.012   56.885    0.000    0.659    0.622
##     GotBully8_i       0.415    0.007   60.721    0.000    0.415    0.664
##     GotBully9_i       0.380    0.006   58.715    0.000    0.380    0.647
##   depress =~                                                            
##     Depress1_i        0.776    0.011   67.712    0.000    0.776    0.697
##     Depress2_i        0.703    0.012   59.863    0.000    0.703    0.630
##     Depress3_i        0.808    0.013   63.979    0.000    0.808    0.664
##     Depress4_i        0.879    0.014   63.234    0.000    0.879    0.661
##     Depress5_i        0.779    0.015   53.048    0.000    0.779    0.573
##     Depress6_i        0.761    0.014   52.764    0.000    0.761    0.567
##   alcohol =~                                                            
##     Alc1_i            0.593    0.007   82.992    0.000    0.593    0.765
##     Alc2_i            0.411    0.007   59.398    0.000    0.411    0.596
##     Alc3_i            0.715    0.007  103.913    0.000    0.715    0.890
##     Alc4_i            0.736    0.008   96.041    0.000    0.736    0.846
##     Alc5_i            0.754    0.007  104.710    0.000    0.754    0.892
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully ~~                                                           
##     depress          -0.032    0.014   -2.364    0.018   -0.032   -0.032
##     alcohol           0.126    0.012   10.303    0.000    0.126    0.126
##   depress ~~                                                            
##     alcohol           0.002    0.012    0.163    0.871    0.002    0.002
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_i       0.660    0.013   49.959    0.000    0.660    0.568
##    .GotBully2_i       0.510    0.012   43.659    0.000    0.510    0.497
##    .GotBully3_i       0.280    0.009   30.146    0.000    0.280    0.343
##    .GotBully4_i       0.609    0.012   49.995    0.000    0.609    0.569
##    .GotBully5_i       0.278    0.009   29.543    0.000    0.278    0.337
##    .GotBully6_i       0.189    0.008   24.168    0.000    0.189    0.275
##    .GotBully7_i       0.512    0.012   42.471    0.000    0.512    0.484
##    .GotBully8_i       0.160    0.007   22.467    0.000    0.160    0.256
##    .GotBully9_i       0.131    0.007   19.546    0.000    0.131    0.223
##    .Depress1_i        2.595    0.012  221.977    0.000    2.595    2.330
##    .Depress2_i        2.231    0.012  190.300    0.000    2.231    1.999
##    .Depress3_i        3.105    0.013  242.795    0.000    3.105    2.551
##    .Depress4_i        2.751    0.014  196.566    0.000    2.751    2.067
##    .Depress5_i        2.484    0.014  173.721    0.000    2.484    1.828
##    .Depress6_i        2.376    0.014  168.570    0.000    2.376    1.771
##    .Alc1_i            2.355    0.008  286.206    0.000    2.355    3.038
##    .Alc2_i            2.327    0.007  317.071    0.000    2.327    3.370
##    .Alc3_i            2.359    0.009  275.861    0.000    2.359    2.935
##    .Alc4_i            2.469    0.009  266.751    0.000    2.469    2.839
##    .Alc5_i            2.426    0.009  270.218    0.000    2.426    2.870
##     gotBully          0.000                               0.000    0.000
##     depress           0.000                               0.000    0.000
##     alcohol           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##     depress           1.000                               1.000    1.000
##     alcohol           1.000                               1.000    1.000
##    .GotBully1_i       0.804    0.015   54.753    0.000    0.804    0.596
##    .GotBully2_i       0.629    0.011   55.132    0.000    0.629    0.597
##    .GotBully3_i       0.348    0.006   53.731    0.000    0.348    0.522
##    .GotBully4_i       0.640    0.012   54.024    0.000    0.640    0.559
##    .GotBully5_i       0.358    0.007   53.460    0.000    0.358    0.526
##    .GotBully6_i       0.244    0.005   52.424    0.000    0.244    0.516
##    .GotBully7_i       0.687    0.012   56.048    0.000    0.687    0.613
##    .GotBully8_i       0.219    0.004   53.523    0.000    0.219    0.560
##    .GotBully9_i       0.200    0.004   54.087    0.000    0.200    0.581
##    .Depress1_i        0.637    0.013   50.870    0.000    0.637    0.514
##    .Depress2_i        0.752    0.013   56.087    0.000    0.752    0.603
##    .Depress3_i        0.827    0.015   53.900    0.000    0.827    0.559
##    .Depress4_i        0.997    0.019   53.698    0.000    0.997    0.563
##    .Depress5_i        1.240    0.021   58.484    0.000    1.240    0.672
##    .Depress6_i        1.220    0.021   59.227    0.000    1.220    0.678
##    .Alc1_i            0.249    0.004   58.160    0.000    0.249    0.414
##    .Alc2_i            0.308    0.005   63.351    0.000    0.308    0.645
##    .Alc3_i            0.135    0.003   43.452    0.000    0.135    0.208
##    .Alc4_i            0.215    0.004   51.619    0.000    0.215    0.284
##    .Alc5_i            0.146    0.003   43.197    0.000    0.146    0.204
## The Categorical Treatment (WLSMV) of the Items Coded as Factor Variables
model.CFA.factor <- '
gotBully =~ NA*GotBully1_f + GotBully2_f + GotBully3_f
            + GotBully4_f + GotBully5_f + GotBully6_f
            + GotBully7_f + GotBully8_f + GotBully9_f
gotBully ~~ 1*gotBully

depress =~ NA*Depress1_f + Depress2_f + Depress3_f
           + Depress4_f + Depress5_f + Depress6_f
depress ~~ 1*depress

alcohol =~ NA*Alc1_f + Alc2_f + Alc3_f + Alc4_f + Alc5_f
alcohol ~~ 1*alcohol
'

fit.CFA.WLSMV.factor <-
    cfa(model = model.CFA.factor, data = hbsc, mimic = "Mplus",
        estimator = "WLSMV",
        ordered = c("GotBully1_f", "GotBully2_f","GotBully3_f",
                    "GotBully4_f", "GotBully5_f", "GotBully6_f",
                    "GotBully7_f", "GotBully8_f", "GotBully9_f",
                    "Depress1_f", "Depress2_f", "Depress3_f",
                    "Depress4_f", "Depress5_f", "Depress6_f",
                    "Alc1_f", "Alc2_f", "Alc3_f", "Alc4_f", "Alc5_f"))
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc1_f
## x GotBully5_f
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc2_f
## x GotBully6_f
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc3_f
## x Alc1_f
summary(fit.CFA.WLSMV.factor, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  23 iterations
## 
##                                                   Used       Total
##   Number of observations                          7118        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic             2633.734    2956.403
##   Degrees of freedom                               167         167
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.908
##   Shift parameter                                           54.705
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic           281854.962  116758.089
##   Degrees of freedom                               190         190
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.991       0.976
##   Tucker-Lewis Index (TLI)                       0.990       0.973
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.046       0.048
##   90 Percent Confidence Interval          0.044  0.047       0.047  0.050
##   P-value RMSEA <= 0.05                          1.000       0.952
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.056       0.056
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           3.123       3.123
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_f       0.770    0.009   88.670    0.000    0.770    0.770
##     GotBully2_f       0.768    0.009   86.818    0.000    0.768    0.768
##     GotBully3_f       0.788    0.010   82.757    0.000    0.788    0.788
##     GotBully4_f       0.798    0.008  100.315    0.000    0.798    0.798
##     GotBully5_f       0.811    0.009   89.131    0.000    0.811    0.811
##     GotBully6_f       0.833    0.010   85.049    0.000    0.833    0.833
##     GotBully7_f       0.770    0.009   83.040    0.000    0.770    0.770
##     GotBully8_f       0.858    0.009   93.706    0.000    0.858    0.858
##     GotBully9_f       0.883    0.010   87.972    0.000    0.883    0.883
##   depress =~                                                            
##     Depress1_f        0.735    0.008   97.433    0.000    0.735    0.735
##     Depress2_f        0.659    0.009   77.531    0.000    0.659    0.659
##     Depress3_f        0.756    0.008   90.034    0.000    0.756    0.756
##     Depress4_f        0.721    0.008   85.753    0.000    0.721    0.721
##     Depress5_f        0.634    0.009   67.906    0.000    0.634    0.634
##     Depress6_f        0.633    0.010   65.896    0.000    0.633    0.633
##   alcohol =~                                                            
##     Alc1_f            0.847    0.006  145.236    0.000    0.847    0.847
##     Alc2_f            0.701    0.010   70.730    0.000    0.701    0.701
##     Alc3_f            0.946    0.003  330.362    0.000    0.946    0.946
##     Alc4_f            0.916    0.004  256.281    0.000    0.916    0.916
##     Alc5_f            0.943    0.003  338.644    0.000    0.943    0.943
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully ~~                                                           
##     depress           0.394    0.015   26.613    0.000    0.394    0.394
##     alcohol           0.133    0.018    7.545    0.000    0.133    0.133
##   depress ~~                                                            
##     alcohol           0.308    0.015   20.479    0.000    0.308    0.308
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_f       0.000                               0.000    0.000
##    .GotBully2_f       0.000                               0.000    0.000
##    .GotBully3_f       0.000                               0.000    0.000
##    .GotBully4_f       0.000                               0.000    0.000
##    .GotBully5_f       0.000                               0.000    0.000
##    .GotBully6_f       0.000                               0.000    0.000
##    .GotBully7_f       0.000                               0.000    0.000
##    .GotBully8_f       0.000                               0.000    0.000
##    .GotBully9_f       0.000                               0.000    0.000
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##    .Alc1_f            0.000                               0.000    0.000
##    .Alc2_f            0.000                               0.000    0.000
##    .Alc3_f            0.000                               0.000    0.000
##    .Alc4_f            0.000                               0.000    0.000
##    .Alc5_f            0.000                               0.000    0.000
##     gotBully          0.000                               0.000    0.000
##     depress           0.000                               0.000    0.000
##     alcohol           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f|t1    0.435    0.015   28.301    0.000    0.435    0.435
##     GotBully1_f|t2    1.046    0.018   57.399    0.000    1.046    1.046
##     GotBully1_f|t3    1.262    0.020   62.898    0.000    1.262    1.262
##     GotBully1_f|t4    1.528    0.023   65.741    0.000    1.528    1.528
##     GotBully2_f|t1    0.618    0.016   38.776    0.000    0.618    0.618
##     GotBully2_f|t2    1.198    0.019   61.556    0.000    1.198    1.198
##     GotBully2_f|t3    1.422    0.022   65.116    0.000    1.422    1.422
##     GotBully2_f|t4    1.736    0.027   65.085    0.000    1.736    1.736
##     GotBully3_f|t1    1.088    0.019   58.696    0.000    1.088    1.088
##     GotBully3_f|t2    1.518    0.023   65.710    0.000    1.518    1.518
##     GotBully3_f|t3    1.734    0.027   65.099    0.000    1.734    1.734
##     GotBully3_f|t4    1.987    0.032   61.363    0.000    1.987    1.987
##     GotBully4_f|t1    0.425    0.015   27.691    0.000    0.425    0.425
##     GotBully4_f|t2    1.111    0.019   59.362    0.000    1.111    1.111
##     GotBully4_f|t3    1.399    0.022   64.893    0.000    1.399    1.399
##     GotBully4_f|t4    1.664    0.025   65.580    0.000    1.664    1.664
##     GotBully5_f|t1    1.119    0.019   59.563    0.000    1.119    1.119
##     GotBully5_f|t2    1.520    0.023   65.717    0.000    1.520    1.520
##     GotBully5_f|t3    1.711    0.026   65.288    0.000    1.711    1.711
##     GotBully5_f|t4    1.965    0.032   61.806    0.000    1.965    1.965
##     GotBully6_f|t1    1.340    0.021   64.166    0.000    1.340    1.340
##     GotBully6_f|t2    1.696    0.026   65.394    0.000    1.696    1.696
##     GotBully6_f|t3    1.890    0.030   63.136    0.000    1.890    1.890
##     GotBully6_f|t4    2.134    0.037   57.988    0.000    2.134    2.134
##     GotBully7_f|t1    0.677    0.016   41.906    0.000    0.677    0.677
##     GotBully7_f|t2    1.155    0.019   60.524    0.000    1.155    1.155
##     GotBully7_f|t3    1.405    0.022   64.960    0.000    1.405    1.405
##     GotBully7_f|t4    1.696    0.026   65.394    0.000    1.696    1.696
##     GotBully8_f|t1    1.404    0.022   64.941    0.000    1.404    1.404
##     GotBully8_f|t2    1.800    0.028   64.421    0.000    1.800    1.800
##     GotBully8_f|t3    2.027    0.033   60.528    0.000    2.027    2.027
##     GotBully8_f|t4    2.237    0.041   55.198    0.000    2.237    2.237
##     GotBully9_f|t1    1.544    0.023   65.776    0.000    1.544    1.544
##     GotBully9_f|t2    1.878    0.030   63.335    0.000    1.878    1.878
##     GotBully9_f|t3    2.058    0.034   59.830    0.000    2.058    2.058
##     GotBully9_f|t4    2.241    0.041   55.075    0.000    2.241    2.241
##     Depress1_f|t1    -0.666    0.016  -41.337    0.000   -0.666   -0.666
##     Depress1_f|t2     0.095    0.015    6.399    0.000    0.095    0.095
##     Depress1_f|t3     1.004    0.018   55.999    0.000    1.004    1.004
##     Depress1_f|t4     1.723    0.026   65.192    0.000    1.723    1.723
##     Depress2_f|t1    -1.046    0.018  -57.399    0.000   -1.046   -1.046
##     Depress2_f|t2    -0.295    0.015  -19.552    0.000   -0.295   -0.295
##     Depress2_f|t3     0.688    0.016   42.429    0.000    0.688    0.688
##     Depress2_f|t4     1.532    0.023   65.749    0.000    1.532    1.532
##     Depress3_f|t1     0.142    0.015    9.550    0.000    0.142    0.142
##     Depress3_f|t2     0.607    0.016   38.178    0.000    0.607    0.607
##     Depress3_f|t3     1.137    0.019   60.066    0.000    1.137    1.137
##     Depress3_f|t4     1.612    0.025   65.766    0.000    1.612    1.612
##     Depress4_f|t1    -0.174    0.015  -11.633    0.000   -0.174   -0.174
##     Depress4_f|t2     0.228    0.015   15.205    0.000    0.228    0.228
##     Depress4_f|t3     0.841    0.017   49.664    0.000    0.841    0.841
##     Depress4_f|t4     1.433    0.022   65.218    0.000    1.433    1.433
##     Depress5_f|t1    -0.456    0.015  -29.541    0.000   -0.456   -0.456
##     Depress5_f|t2     0.033    0.015    2.252    0.024    0.033    0.033
##     Depress5_f|t3     0.665    0.016   41.292    0.000    0.665    0.665
##     Depress5_f|t4     1.248    0.020   62.615    0.000    1.248    1.248
##     Depress6_f|t1    -0.618    0.016  -38.799    0.000   -0.618   -0.618
##     Depress6_f|t2    -0.055    0.015   -3.721    0.000   -0.055   -0.055
##     Depress6_f|t3     0.618    0.016   38.799    0.000    0.618    0.618
##     Depress6_f|t4     1.179    0.019   61.124    0.000    1.179    1.179
##     Alc1_f|t1         0.699    0.016   42.995    0.000    0.699    0.699
##     Alc1_f|t2         1.384    0.021   64.731    0.000    1.384    1.384
##     Alc1_f|t3         1.745    0.027   64.998    0.000    1.745    1.745
##     Alc1_f|t4         2.396    0.048   50.414    0.000    2.396    2.396
##     Alc2_f|t1         0.668    0.016   41.406    0.000    0.668    0.668
##     Alc2_f|t2         1.601    0.024   65.784    0.000    1.601    1.601
##     Alc2_f|t3         1.955    0.032   61.991    0.000    1.955    1.955
##     Alc2_f|t4         2.478    0.052   47.774    0.000    2.478    2.478
##     Alc3_f|t1         0.746    0.016   45.313    0.000    0.746    0.746
##     Alc3_f|t2         1.297    0.020   63.507    0.000    1.297    1.297
##     Alc3_f|t3         1.696    0.026   65.394    0.000    1.696    1.696
##     Alc3_f|t4         2.384    0.047   50.799    0.000    2.384    2.384
##     Alc4_f|t1         0.507    0.016   32.552    0.000    0.507    0.507
##     Alc4_f|t2         1.159    0.019   60.628    0.000    1.159    1.159
##     Alc4_f|t3         1.653    0.025   65.632    0.000    1.653    1.653
##     Alc4_f|t4         2.292    0.043   53.606    0.000    2.292    2.292
##     Alc5_f|t1         0.585    0.016   37.003    0.000    0.585    0.585
##     Alc5_f|t2         1.225    0.020   62.152    0.000    1.225    1.225
##     Alc5_f|t3         1.645    0.025   65.666    0.000    1.645    1.645
##     Alc5_f|t4         2.282    0.042   53.891    0.000    2.282    2.282
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##     depress           1.000                               1.000    1.000
##     alcohol           1.000                               1.000    1.000
##    .GotBully1_f       0.407                               0.407    0.407
##    .GotBully2_f       0.411                               0.411    0.411
##    .GotBully3_f       0.380                               0.380    0.380
##    .GotBully4_f       0.363                               0.363    0.363
##    .GotBully5_f       0.342                               0.342    0.342
##    .GotBully6_f       0.306                               0.306    0.306
##    .GotBully7_f       0.406                               0.406    0.406
##    .GotBully8_f       0.264                               0.264    0.264
##    .GotBully9_f       0.221                               0.221    0.221
##    .Depress1_f        0.460                               0.460    0.460
##    .Depress2_f        0.565                               0.565    0.565
##    .Depress3_f        0.428                               0.428    0.428
##    .Depress4_f        0.480                               0.480    0.480
##    .Depress5_f        0.598                               0.598    0.598
##    .Depress6_f        0.599                               0.599    0.599
##    .Alc1_f            0.282                               0.282    0.282
##    .Alc2_f            0.509                               0.509    0.509
##    .Alc3_f            0.106                               0.106    0.106
##    .Alc4_f            0.161                               0.161    0.161
##    .Alc5_f            0.110                               0.110    0.110
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f       1.000                               1.000    1.000
##     GotBully2_f       1.000                               1.000    1.000
##     GotBully3_f       1.000                               1.000    1.000
##     GotBully4_f       1.000                               1.000    1.000
##     GotBully5_f       1.000                               1.000    1.000
##     GotBully6_f       1.000                               1.000    1.000
##     GotBully7_f       1.000                               1.000    1.000
##     GotBully8_f       1.000                               1.000    1.000
##     GotBully9_f       1.000                               1.000    1.000
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
##     Alc1_f            1.000                               1.000    1.000
##     Alc2_f            1.000                               1.000    1.000
##     Alc3_f            1.000                               1.000    1.000
##     Alc4_f            1.000                               1.000    1.000
##     Alc5_f            1.000                               1.000    1.000
####------------------------------------------------------------####
#### Section-3: A Two-Factor Structural Model with Likert Items ####
#### Got Bullied Predicts Alcohol Use                           ####
####------------------------------------------------------------####

## The Continuous Treatment (ML) of the Structural Model
## The Variables for this Model Are Coded as Integers

model.struc.ML <- '
## the measurement model
gotBully =~ NA*GotBully1_i + GotBully2_i + GotBully3_i
            + GotBully4_i + GotBully5_i + GotBully6_i
            + GotBully7_i + GotBully8_i + GotBully9_i
gotBully ~~ 1*gotBully

alcohol =~ NA*Alc1_i + Alc2_i + Alc3_i + Alc4_i + Alc5_i
alcohol ~~ 1*alcohol

# regress 
alcohol ~ gotBully
'

fit.struc.ML <- sem(model = model.struc.ML, data = hbsc,
                    mimic = "Mplus", estimator = "ML")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   34 47 48 71 73 80 84 90 103 131 184 235 242 247 259 382 396 400 417 466 477 489 530 557 628 679 727 771 853 891 892 896 911 934 969 1015 1052 1055 1056 1062 1063 1073 1132 1179 1190 1320 1330 1354 1360 1385 1450 1555 1560 1670 1672 1717 1718 1730 1735 1739 1789 1790 1805 1832 1882 1914 1922 1963 1966 1998 2048 2137 2156 2176 2186 2234 2338 2374 2386 2397 2491 2505 2544 2556 2563 2571 2587 2603 2627 2636 2665 2708 2716 2739 2744 2808 2887 2992 2995 3032 3041 3098 3198 3209 3245 3256 3276 3317 3333 3342 3345 3363 3398 3399 3410 3423 3439 3457 3485 3542 3550 3551 3567 3568 3580 3597 3638 3700 3720 3736 3765 3775 3782 3796 3797 3800 3817 3831 3870 3886 3923 3961 3991 4061 4080 4092 4093 4122 4141 4148 4152 4161 4167 4183 4209 4268 4355 4361 4388 4415 4469 4470 4471 4478 4480 4552 4566 4576 4614 4670 4699 4720 4833 4865 4868 4939 4973 4977 5075 5093 5110 5153 5178 5187 5190 5199 5241 5276 5303 5378 5392 5513 5570 5577 5593 5615 5699 5753 5781 5785 5813 5846 5918 5942 5959 5994 6053 6170 6282 6337 6426 6452 6471 6473 6492 6501 6515 6521 6545 6564 6599 6688 6689 6693 6749 6859 6933 6999 7032 7049 7064 7088 7092 7114 7142 7159 7234 7239 7311 7332 7344 7386 7418 7459 7489 7577 7667 7720 7742 7761 7780 7931 8034 8098 8117 8153 8300 8341 8396 8416 8421 8443 8493 8584 8598 8607 8622 8641 8716 8789 8944 9000 9026 9039 9049 9061 9124 9132 9135 9159 9165 9209
summary(fit.struc.ML, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  47 iterations
## 
##                                                   Used       Total
##   Number of observations                          8945        9227
## 
##   Number of missing patterns                        85
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             4942.497
##   Degrees of freedom                                76
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            56031.094
##   Degrees of freedom                                91
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.913
##   Tucker-Lewis Index (TLI)                       0.896
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -113567.150
##   Loglikelihood unrestricted model (H1)     -111095.902
## 
##   Number of free parameters                         43
##   Akaike (AIC)                              227220.300
##   Bayesian (BIC)                            227525.551
##   Sample-size adjusted Bayesian (BIC)       227388.904
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.085
##   90 Percent Confidence Interval          0.083  0.087
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.052
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_i       0.738    0.013   58.090    0.000    0.738    0.636
##     GotBully2_i       0.652    0.011   58.094    0.000    0.652    0.635
##     GotBully3_i       0.565    0.009   65.444    0.000    0.565    0.691
##     GotBully4_i       0.711    0.012   61.729    0.000    0.711    0.664
##     GotBully5_i       0.568    0.009   64.873    0.000    0.568    0.689
##     GotBully6_i       0.478    0.007   65.200    0.000    0.478    0.695
##     GotBully7_i       0.659    0.012   56.883    0.000    0.659    0.622
##     GotBully8_i       0.415    0.007   60.728    0.000    0.415    0.664
##     GotBully9_i       0.380    0.006   58.713    0.000    0.380    0.647
##   alcohol =~                                                            
##     Alc1_i            0.588    0.007   82.822    0.000    0.593    0.765
##     Alc2_i            0.408    0.007   59.371    0.000    0.411    0.596
##     Alc3_i            0.709    0.007  103.518    0.000    0.715    0.890
##     Alc4_i            0.730    0.008   95.739    0.000    0.736    0.846
##     Alc5_i            0.748    0.007  104.304    0.000    0.754    0.892
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   alcohol ~                                                             
##     gotBully          0.128    0.013   10.143    0.000    0.127    0.127
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_i       0.659    0.013   49.950    0.000    0.659    0.568
##    .GotBully2_i       0.510    0.012   43.650    0.000    0.510    0.497
##    .GotBully3_i       0.280    0.009   30.137    0.000    0.280    0.343
##    .GotBully4_i       0.609    0.012   49.985    0.000    0.609    0.569
##    .GotBully5_i       0.277    0.009   29.534    0.000    0.277    0.336
##    .GotBully6_i       0.189    0.008   24.158    0.000    0.189    0.275
##    .GotBully7_i       0.512    0.012   42.462    0.000    0.512    0.484
##    .GotBully8_i       0.160    0.007   22.458    0.000    0.160    0.256
##    .GotBully9_i       0.131    0.007   19.538    0.000    0.131    0.223
##    .Alc1_i            2.355    0.008  286.206    0.000    2.355    3.038
##    .Alc2_i            2.327    0.007  317.072    0.000    2.327    3.370
##    .Alc3_i            2.359    0.009  275.862    0.000    2.359    2.935
##    .Alc4_i            2.469    0.009  266.752    0.000    2.469    2.839
##    .Alc5_i            2.426    0.009  270.218    0.000    2.426    2.870
##     gotBully          0.000                               0.000    0.000
##    .alcohol           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##    .alcohol           1.000                               0.984    0.984
##    .GotBully1_i       0.804    0.015   54.753    0.000    0.804    0.596
##    .GotBully2_i       0.629    0.011   55.131    0.000    0.629    0.597
##    .GotBully3_i       0.348    0.006   53.729    0.000    0.348    0.522
##    .GotBully4_i       0.640    0.012   54.024    0.000    0.640    0.559
##    .GotBully5_i       0.358    0.007   53.460    0.000    0.358    0.526
##    .GotBully6_i       0.244    0.005   52.421    0.000    0.244    0.516
##    .GotBully7_i       0.687    0.012   56.047    0.000    0.687    0.613
##    .GotBully8_i       0.219    0.004   53.519    0.000    0.219    0.559
##    .GotBully9_i       0.200    0.004   54.086    0.000    0.200    0.581
##    .Alc1_i            0.249    0.004   58.160    0.000    0.249    0.414
##    .Alc2_i            0.308    0.005   63.351    0.000    0.308    0.645
##    .Alc3_i            0.135    0.003   43.451    0.000    0.135    0.208
##    .Alc4_i            0.215    0.004   51.620    0.000    0.215    0.284
##    .Alc5_i            0.146    0.003   43.200    0.000    0.146    0.204
## The Categorical Treatment (WLSMV) of the Structural Model
## The Variables for this Model Are Coded as Factors

model.struc.WLSMV <- '
## the measurement model
gotBully =~ NA*GotBully1_f + GotBully2_f + GotBully3_f + GotBully4_f
            + GotBully5_f + GotBully6_f  + GotBully7_f + GotBully8_f
            + GotBully9_f
gotBully ~~ 1*gotBully

alcohol =~ NA*Alc1_f + Alc2_f + Alc3_f + Alc4_f + Alc5_f
alcohol ~~ 1*alcohol

## the structural model
alcohol ~ gotBully
'

fit.struc.WLSMV <-
    sem(model = model.struc.WLSMV, data = hbsc, mimic = "Mplus",
        estimator = "WLSMV", ordered = c("GotBully1_f", "GotBully2_f",
                                         "GotBully3_f", "GotBully4_f",
                                         "GotBully5_f", "GotBully6_f",
                                         "GotBully7_f", "GotBully8_f",
                                         "GotBully9_f",
                                         "Alc1_f", "Alc2_f", "Alc3_f",
                                         "Alc4_f", "Alc5_f"))
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc1_f
## x GotBully5_f
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc2_f
## x GotBully6_f
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc3_f
## x Alc1_f
summary(fit.struc.WLSMV, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  24 iterations
## 
##                                                   Used       Total
##   Number of observations                          7232        9227
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic             1477.149    1810.161
##   Degrees of freedom                                76          76
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.827
##   Shift parameter                                           24.571
##     for simple second-order correction (WLSMV)
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic           237248.778   94697.365
##   Degrees of freedom                                91          91
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.994       0.982
##   Tucker-Lewis Index (TLI)                       0.993       0.978
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.050       0.056
##   90 Percent Confidence Interval          0.048  0.053       0.054  0.058
##   P-value RMSEA <= 0.05                          0.354       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.061       0.061
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           3.170       3.170
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_f       0.766    0.009   88.419    0.000    0.766    0.766
##     GotBully2_f       0.762    0.009   86.542    0.000    0.762    0.762
##     GotBully3_f       0.801    0.009   87.196    0.000    0.801    0.801
##     GotBully4_f       0.782    0.008   99.315    0.000    0.782    0.782
##     GotBully5_f       0.818    0.009   92.901    0.000    0.818    0.818
##     GotBully6_f       0.849    0.009   90.780    0.000    0.849    0.849
##     GotBully7_f       0.752    0.009   80.652    0.000    0.752    0.752
##     GotBully8_f       0.866    0.009   98.981    0.000    0.866    0.866
##     GotBully9_f       0.895    0.010   93.624    0.000    0.895    0.895
##   alcohol =~                                                            
##     Alc1_f            0.843    0.006  142.809    0.000    0.851    0.851
##     Alc2_f            0.697    0.010   72.353    0.000    0.704    0.704
##     Alc3_f            0.937    0.004  262.302    0.000    0.946    0.946
##     Alc4_f            0.907    0.004  219.300    0.000    0.915    0.915
##     Alc5_f            0.934    0.004  262.119    0.000    0.942    0.942
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   alcohol ~                                                             
##     gotBully          0.138    0.018    7.639    0.000    0.136    0.136
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_f       0.000                               0.000    0.000
##    .GotBully2_f       0.000                               0.000    0.000
##    .GotBully3_f       0.000                               0.000    0.000
##    .GotBully4_f       0.000                               0.000    0.000
##    .GotBully5_f       0.000                               0.000    0.000
##    .GotBully6_f       0.000                               0.000    0.000
##    .GotBully7_f       0.000                               0.000    0.000
##    .GotBully8_f       0.000                               0.000    0.000
##    .GotBully9_f       0.000                               0.000    0.000
##    .Alc1_f            0.000                               0.000    0.000
##    .Alc2_f            0.000                               0.000    0.000
##    .Alc3_f            0.000                               0.000    0.000
##    .Alc4_f            0.000                               0.000    0.000
##    .Alc5_f            0.000                               0.000    0.000
##     gotBully          0.000                               0.000    0.000
##    .alcohol           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f|t1    0.436    0.015   28.568    0.000    0.436    0.436
##     GotBully1_f|t2    1.046    0.018   57.874    0.000    1.046    1.046
##     GotBully1_f|t3    1.261    0.020   63.382    0.000    1.261    1.261
##     GotBully1_f|t4    1.529    0.023   66.266    0.000    1.529    1.529
##     GotBully2_f|t1    0.616    0.016   39.007    0.000    0.616    0.616
##     GotBully2_f|t2    1.197    0.019   62.018    0.000    1.197    1.197
##     GotBully2_f|t3    1.423    0.022   65.642    0.000    1.423    1.423
##     GotBully2_f|t4    1.738    0.027   65.580    0.000    1.738    1.738
##     GotBully3_f|t1    1.084    0.018   59.030    0.000    1.084    1.084
##     GotBully3_f|t2    1.516    0.023   66.228    0.000    1.516    1.516
##     GotBully3_f|t3    1.732    0.026   65.636    0.000    1.732    1.732
##     GotBully3_f|t4    1.989    0.032   61.817    0.000    1.989    1.989
##     GotBully4_f|t1    0.425    0.015   27.871    0.000    0.425    0.425
##     GotBully4_f|t2    1.109    0.019   59.767    0.000    1.109    1.109
##     GotBully4_f|t3    1.395    0.021   65.374    0.000    1.395    1.395
##     GotBully4_f|t4    1.663    0.025   66.107    0.000    1.663    1.663
##     GotBully5_f|t1    1.113    0.019   59.876    0.000    1.113    1.113
##     GotBully5_f|t2    1.515    0.023   66.224    0.000    1.515    1.515
##     GotBully5_f|t3    1.708    0.026   65.831    0.000    1.708    1.708
##     GotBully5_f|t4    1.964    0.032   62.308    0.000    1.964    1.964
##     GotBully6_f|t1    1.340    0.021   64.681    0.000    1.340    1.340
##     GotBully6_f|t2    1.692    0.026   65.944    0.000    1.692    1.692
##     GotBully6_f|t3    1.889    0.030   63.662    0.000    1.889    1.889
##     GotBully6_f|t4    2.133    0.036   58.462    0.000    2.133    2.133
##     GotBully7_f|t1    0.678    0.016   42.295    0.000    0.678    0.678
##     GotBully7_f|t2    1.156    0.019   61.043    0.000    1.156    1.156
##     GotBully7_f|t3    1.406    0.021   65.480    0.000    1.406    1.406
##     GotBully7_f|t4    1.699    0.026   65.895    0.000    1.699    1.699
##     GotBully8_f|t1    1.402    0.021   65.442    0.000    1.402    1.402
##     GotBully8_f|t2    1.796    0.028   64.974    0.000    1.796    1.796
##     GotBully8_f|t3    2.020    0.033   61.162    0.000    2.020    2.020
##     GotBully8_f|t4    2.226    0.040   55.943    0.000    2.226    2.226
##     GotBully9_f|t1    1.541    0.023   66.295    0.000    1.541    1.541
##     GotBully9_f|t2    1.875    0.029   63.890    0.000    1.875    1.875
##     GotBully9_f|t3    2.050    0.034   60.487    0.000    2.050    2.050
##     GotBully9_f|t4    2.239    0.040   55.585    0.000    2.239    2.239
##     Alc1_f|t1         0.700    0.016   43.374    0.000    0.700    0.700
##     Alc1_f|t2         1.384    0.021   65.253    0.000    1.384    1.384
##     Alc1_f|t3         1.742    0.027   65.552    0.000    1.742    1.742
##     Alc1_f|t4         2.372    0.046   51.578    0.000    2.372    2.372
##     Alc2_f|t1         0.668    0.016   41.730    0.000    0.668    0.668
##     Alc2_f|t2         1.599    0.024   66.312    0.000    1.599    1.599
##     Alc2_f|t3         1.948    0.031   62.624    0.000    1.948    1.948
##     Alc2_f|t4         2.455    0.050   48.926    0.000    2.455    2.455
##     Alc3_f|t1         0.748    0.016   45.785    0.000    0.748    0.748
##     Alc3_f|t2         1.298    0.020   64.042    0.000    1.298    1.298
##     Alc3_f|t3         1.696    0.026   65.915    0.000    1.696    1.696
##     Alc3_f|t4         2.372    0.046   51.578    0.000    2.372    2.372
##     Alc4_f|t1         0.510    0.015   33.017    0.000    0.510    0.510
##     Alc4_f|t2         1.161    0.019   61.164    0.000    1.161    1.161
##     Alc4_f|t3         1.652    0.025   66.158    0.000    1.652    1.652
##     Alc4_f|t4         2.274    0.042   54.557    0.000    2.274    2.274
##     Alc5_f|t1         0.587    0.016   37.409    0.000    0.587    0.587
##     Alc5_f|t2         1.226    0.020   62.672    0.000    1.226    1.226
##     Alc5_f|t3         1.646    0.025   66.186    0.000    1.646    1.646
##     Alc5_f|t4         2.274    0.042   54.557    0.000    2.274    2.274
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##    .alcohol           1.000                               0.981    0.981
##    .GotBully1_f       0.413                               0.413    0.413
##    .GotBully2_f       0.420                               0.420    0.420
##    .GotBully3_f       0.359                               0.359    0.359
##    .GotBully4_f       0.388                               0.388    0.388
##    .GotBully5_f       0.331                               0.331    0.331
##    .GotBully6_f       0.279                               0.279    0.279
##    .GotBully7_f       0.434                               0.434    0.434
##    .GotBully8_f       0.250                               0.250    0.250
##    .GotBully9_f       0.199                               0.199    0.199
##    .Alc1_f            0.276                               0.276    0.276
##    .Alc2_f            0.505                               0.505    0.505
##    .Alc3_f            0.105                               0.105    0.105
##    .Alc4_f            0.162                               0.162    0.162
##    .Alc5_f            0.112                               0.112    0.112
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f       1.000                               1.000    1.000
##     GotBully2_f       1.000                               1.000    1.000
##     GotBully3_f       1.000                               1.000    1.000
##     GotBully4_f       1.000                               1.000    1.000
##     GotBully5_f       1.000                               1.000    1.000
##     GotBully6_f       1.000                               1.000    1.000
##     GotBully7_f       1.000                               1.000    1.000
##     GotBully8_f       1.000                               1.000    1.000
##     GotBully9_f       1.000                               1.000    1.000
##     Alc1_f            1.000                               1.000    1.000
##     Alc2_f            1.000                               1.000    1.000
##     Alc3_f            1.000                               1.000    1.000
##     Alc4_f            1.000                               1.000    1.000
##     Alc5_f            1.000                               1.000    1.000
####--------------------------------------------####
#### Section-4: A Three-Factor Structural Model ####
#### Depression as a potential Mediator between #### 
#### Got Bullied and Alcohol Use                ####
####--------------------------------------------####

## The Continuous Treatment (ML) of the Indirect-Effect (Mediation) Model
## The Variables for this Model Are Coded as Integers

model.indirect.con <- '
## the measurement model

gotBully =~ NA*GotBully1_i + GotBully2_i + GotBully3_i
             + GotBully4_i + GotBully5_i + GotBully6_i 
             + GotBully7_i + GotBully8_i + GotBully9_i
gotBully ~~ 1*gotBully

depress =~ NA*Depress1_i + Depress2_i + Depress3_i
         + Depress4_i + Depress5_i + Depress6_i
depress ~~ 1*depress

alcohol =~ NA*Alc1_i + Alc2_i + Alc3_i + Alc4_i + Alc5_i
alcohol ~~ 1*alcohol

## the structural model
# direct effect (the c path)
alcohol ~ c*gotBully
# mediator paths (the a and b path)
depress ~ a*gotBully # the a path - IV predicting ME
alcohol ~ b*depress  # the b path - ME predicting DV

# indirect effect (a*b)
# := operator defines new parameters
ab := a*b

# total effect
total := c + (a*b)
'

## verbose = FALSE will not display the bootsrap iterations on screen
fit.indirect.ML <- sem(model = model.indirect.con, data = hbsc,
                       mimic = "Mplus", estimator = "ML",
                       se = "bootstrap", verbose = TRUE, bootstrap = 10)
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   7489
## 
## estimation saturated H1 model -- start EM steps
##   EM iteration:    0  fx =    16.0101850496 
##   EM iteration:    1  fx =     8.5835335721  delta par =  0.81853193 
##   EM iteration:    2  fx =     8.4224092506  delta par =  0.09187098 
##   EM iteration:    3  fx =     8.4176873525  delta par =  0.01516392 
##   EM iteration:    4  fx =     8.4175401891  delta par =  0.00250352 
##   EM iteration:    5  fx =     8.4175355743  delta par =  0.00041360 
##   EM iteration:    6  fx =     8.4175354274  delta par =  0.00006837 
##   EM iteration:    7  fx =     8.4175354226  delta par =  0.00001177 
##   EM iteration:    8  fx =     8.4175354224  delta par =  0.00000230 
##   EM iteration:    9  fx =     8.4175354224  delta par =  0.00000045 
## estimated Sigma and Mu (H1):
## 
## Sigma:
##               [,1]          [,2]         [,3]         [,4]         [,5]
##  [1,]  1.348647785  0.6612443949  0.464785236  0.656071818  0.413377976
##  [2,]  0.661244395  1.0540731421  0.374926716  0.592741274  0.323317874
##  [3,]  0.464785236  0.3749267163  0.667807831  0.390818507  0.335474159
##  [4,]  0.656071818  0.5927412741  0.390818507  1.146843296  0.355573103
##  [5,]  0.413377976  0.3233178740  0.335474159  0.355573103  0.681063468
##  [6,]  0.282707430  0.2651596330  0.275824857  0.278359218  0.335082137
##  [7,]  0.567049577  0.4547644093  0.354357488  0.570825286  0.355781609
##  [8,]  0.223334152  0.2323557471  0.220735999  0.261796625  0.231396007
##  [9,]  0.191567821  0.1983309056  0.204406849  0.234535584  0.214200407
## [10,] -0.020158280 -0.0179378133 -0.018770091 -0.008353479 -0.026219612
## [11,] -0.047620070 -0.0265061719 -0.011467909 -0.025048300 -0.025489338
## [12,] -0.022226387 -0.0146624161 -0.001372837 -0.012654019 -0.015615102
## [13,] -0.029294269 -0.0173406483 -0.011649149 -0.028194467 -0.016149362
## [14,] -0.022120444 -0.0235671222 -0.014818349 -0.044632066 -0.008982916
## [15,] -0.005897136 -0.0099786620 -0.010899944 -0.016624002 -0.014645763
## [16,]  0.001177070  0.0044490535  0.049913610  0.050030200  0.060178240
## [17,]  0.023915105  0.0482588227  0.045424469  0.063751034  0.063246840
## [18,] -0.013198920  0.0032996108  0.038115093  0.066927946  0.047418916
## [19,]  0.002725261  0.0003768023  0.027163696  0.083386732  0.056903140
## [20,] -0.003617966  0.0039027269  0.031103428  0.071303398  0.051255218
##                [,6]         [,7]          [,8]         [,9]        [,10]
##  [1,]  0.2827074298  0.567049577  0.2233341519  0.191567821 -0.020158280
##  [2,]  0.2651596330  0.454764409  0.2323557471  0.198330906 -0.017937813
##  [3,]  0.2758248571  0.354357488  0.2207359994  0.204406849 -0.018770091
##  [4,]  0.2783592179  0.570825286  0.2617966251  0.234535584 -0.008353479
##  [5,]  0.3350821372  0.355781609  0.2313960072  0.214200407 -0.026219612
##  [6,]  0.4741660802  0.281833806  0.2260329434  0.215881877 -0.016550413
##  [7,]  0.2818338056  1.120255166  0.2481343622  0.225008134 -0.017543520
##  [8,]  0.2260329434  0.248134362  0.3930871483  0.245351683 -0.005199744
##  [9,]  0.2158818772  0.225008134  0.2453516834  0.346937361 -0.019282587
## [10,] -0.0165504128 -0.017543520 -0.0051997438 -0.019282587  1.240115510
## [11,] -0.0066124462 -0.019043331  0.0003112236 -0.014413632  0.614929620
## [12,] -0.0168210170 -0.006186408 -0.0057019624 -0.015989458  0.681137886
## [13,] -0.0007283239 -0.025344347 -0.0046852249 -0.015422393  0.651983626
## [14,]  0.0095146846 -0.019705481 -0.0055299280  0.001743887  0.527250969
## [15,] -0.0026171476 -0.002074906 -0.0064642431 -0.003693630  0.523132157
## [16,]  0.0442603615  0.086560249  0.0485916313  0.052072086 -0.004529692
## [17,]  0.0586844484  0.089615011  0.0571185242  0.056208890 -0.002811206
## [18,]  0.0493856991  0.090903044  0.0574493202  0.060389578 -0.010946659
## [19,]  0.0483746261  0.114071212  0.0569816049  0.057422663  0.001359820
## [20,]  0.0504321146  0.109503246  0.0592129209  0.056144375  0.008075413
##               [,11]         [,12]         [,13]        [,14]        [,15]
##  [1,] -0.0476200697 -0.0222263867 -0.0292942691 -0.022120444 -0.005897136
##  [2,] -0.0265061719 -0.0146624161 -0.0173406483 -0.023567122 -0.009978662
##  [3,] -0.0114679095 -0.0013728367 -0.0116491490 -0.014818349 -0.010899944
##  [4,] -0.0250483004 -0.0126540192 -0.0281944674 -0.044632066 -0.016624002
##  [5,] -0.0254893377 -0.0156151016 -0.0161493617 -0.008982916 -0.014645763
##  [6,] -0.0066124462 -0.0168210170 -0.0007283239  0.009514685 -0.002617148
##  [7,] -0.0190433311 -0.0061864076 -0.0253443475 -0.019705481 -0.002074906
##  [8,]  0.0003112236 -0.0057019624 -0.0046852249 -0.005529928 -0.006464243
##  [9,] -0.0144136317 -0.0159894580 -0.0154223930  0.001743887 -0.003693630
## [10,]  0.6149296201  0.6811378863  0.6519836263  0.527250969  0.523132157
## [11,]  1.2460079652  0.5381448059  0.5639284675  0.527031202  0.543593663
## [12,]  0.5381448059  1.4806555736  0.7002763548  0.557116572  0.643638650
## [13,]  0.5639284675  0.7002763548  1.7702796564  0.841863837  0.668673705
## [14,]  0.5270312017  0.5571165724  0.8418638374  1.846480828  0.667031260
## [15,]  0.5435936625  0.6436386505  0.6686737050  0.667031260  1.798776740
## [16,] -0.0057092056 -0.0027937279  0.0091542450  0.004144423  0.010287652
## [17,]  0.0012818862 -0.0032366840  0.0005159038  0.004622549  0.007581464
## [18,] -0.0076661063 -0.0148973627  0.0040813834 -0.005235981 -0.002243470
## [19,]  0.0065573925  0.0009764599  0.0064313755  0.002288031  0.022892343
## [20,]  0.0082487079 -0.0034238662  0.0142779906  0.002029729  0.013799987
##              [,16]         [,17]        [,18]        [,19]        [,20]
##  [1,]  0.001177070  0.0239151052 -0.013198920 0.0027252609 -0.003617966
##  [2,]  0.004449053  0.0482588227  0.003299611 0.0003768023  0.003902727
##  [3,]  0.049913610  0.0454244686  0.038115093 0.0271636958  0.031103428
##  [4,]  0.050030200  0.0637510339  0.066927946 0.0833867316  0.071303398
##  [5,]  0.060178240  0.0632468405  0.047418916 0.0569031398  0.051255218
##  [6,]  0.044260362  0.0586844484  0.049385699 0.0483746261  0.050432115
##  [7,]  0.086560249  0.0896150105  0.090903044 0.1140712124  0.109503246
##  [8,]  0.048591631  0.0571185242  0.057449320 0.0569816049  0.059212921
##  [9,]  0.052072086  0.0562088900  0.060389578 0.0574226627  0.056144375
## [10,] -0.004529692 -0.0028112063 -0.010946659 0.0013598196  0.008075413
## [11,] -0.005709206  0.0012818862 -0.007666106 0.0065573925  0.008248708
## [12,] -0.002793728 -0.0032366840 -0.014897363 0.0009764599 -0.003423866
## [13,]  0.009154245  0.0005159038  0.004081383 0.0064313755  0.014277991
## [14,]  0.004144423  0.0046225488 -0.005235981 0.0022880315  0.002029729
## [15,]  0.010287652  0.0075814643 -0.002243470 0.0228923428  0.013799987
## [16,]  0.600692486  0.2747954221  0.435796230 0.4208187467  0.437484620
## [17,]  0.274795422  0.4768761310  0.291767191 0.2900336240  0.305564370
## [18,]  0.435796230  0.2917671914  0.645787232 0.5233723751  0.536263647
## [19,]  0.420818747  0.2900336240  0.523372375 0.7561875171  0.568341520
## [20,]  0.437484620  0.3055643698  0.536263647 0.5683415202  0.714177222
## 
## Mu:
##  [1] 0.6639093 0.5130381 0.2814933 0.6088566 0.2776411 0.1889669 0.5094545
##  [8] 0.1591199 0.1298735 2.5951270 2.2315175 3.1048608 2.7506438 2.4837312
## [15] 2.3752808 2.3546066 2.3268822 2.3584999 2.4686215 2.4253659
## 
## estimation saturated H1 model -- end
## 
## Quasi-Newton steps using NLMINB:
## Objective function  = 1.2369394636385671
## Objective function  =                Inf
## Objective function  = 1.1114621719120255
## Objective function  = 0.8904262513281544
## Objective function  =                Inf
## Objective function  = 1.5355984914003225
## Objective function  = 0.8206908981440808
## Objective function  = 0.7246917304603961
## Objective function  = 0.6762196469390220
## Objective function  = 0.5597239457339871
## Objective function  = 0.8458274928391765
## Objective function  = 0.5454052383944701
## Objective function  = 0.5114993454624628
## Objective function  = 0.5013579753533532
## Objective function  = 0.4772543852832980
## Objective function  = 0.4803062546886245
## Objective function  = 0.4712857108391519
## Objective function  = 0.4631933205011221
## Objective function  = 0.4475351990961274
## Objective function  = 0.4270170584534769
## Objective function  = 0.4173760763594023
## Objective function  = 0.3895696431122015
## Objective function  = 0.4849044035586934
## Objective function  = 0.3792603661456360
## Objective function  = 0.3496990470089516
## Objective function  = 0.4189794353833713
## Objective function  = 0.3343492601984668
## Objective function  = 0.3275421644749690
## Objective function  = 0.3245741990539956
## Objective function  = 0.3201386195945810
## Objective function  = 0.3185234453248427
## Objective function  = 0.3124835486741135
## Objective function  = 0.3073475774833794
## Objective function  = 0.3060613845439581
## Objective function  = 0.3057813498127429
## Objective function  = 0.3053442790109511
## Objective function  = 0.3042562978855106
## Objective function  = 0.3049496042039630
## Objective function  = 0.3038735184470696
## Objective function  = 0.3041314089508367
## Objective function  = 0.3038388714351603
## Objective function  = 0.3038264999696167
## Objective function  = 0.3038112941432729
## Objective function  = 0.3038038480452467
## Objective function  = 0.3037986089248799
## Objective function  = 0.3038009278393590
## Objective function  = 0.3037941742007462
## Objective function  = 0.3037937444523742
## Objective function  = 0.3037943339261568
## Objective function  = 0.3037927609799480
## Objective function  = 0.3037925990722634
## Objective function  = 0.3037922131067257
## Objective function  = 0.3037922231474468
## Objective function  = 0.3037920596484724
## Objective function  = 0.3037919946021921
## Objective function  = 0.3037919778380491
## Objective function  = 0.3037919499176001
## Objective function  = 0.3037919390166426
## Objective function  = 0.3037919408153167
## Objective function  = 0.3037919313379485
## Objective function  = 0.3037919293624363
## Objective function  = 0.3037919279045971
## Objective function  = 0.3037919271861362
## Objective function  = 0.3037919262435214
## Objective function  = 0.3037919262988318
## Objective function  = 0.3037919261366486
## Objective function  = 0.3037919261072721
## Objective function  = 0.3037919260840605
## Objective function  = 0.3037919260837665
## Objective function  = 0.3037919260837665
## convergence status (0=ok):  0 
## nlminb message says:  relative convergence (4) 
## number of iterations:  51 
## number of function evaluations [objective, gradient]:  69 52 
## Computing VCOV for se = bootstrap ...  ... bootstrap draw number:    1   OK -- niter =   38  fx =    0.323563670 
##   ... bootstrap draw number:    2   OK -- niter =   39  fx =    0.320683188 
##   ... bootstrap draw number:    3   OK -- niter =   39  fx =    0.285763277 
##   ... bootstrap draw number:    4   OK -- niter =   41  fx =    0.315717522 
##   ... bootstrap draw number:    5   OK -- niter =   44  fx =    0.307472990 
##   ... bootstrap draw number:    6   OK -- niter =   39  fx =    0.303556909 
##   ... bootstrap draw number:    7   OK -- niter =   43  fx =    0.306022572 
##   ... bootstrap draw number:    8   OK -- niter =   41  fx =    0.332700638 
##   ... bootstrap draw number:    9   OK -- niter =   40  fx =    0.310919412 
##   ... bootstrap draw number:   10   OK -- niter =   40  fx =    0.345218173 
## Number of successful bootstrap draws: 10 
##  done.
## Computing TEST for test = standard ... done.
summary(fit.indirect.ML, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  51 iterations
## 
##                                                   Used       Total
##   Number of observations                          9226        9227
## 
##   Number of missing patterns                       144
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic             5605.569
##   Degrees of freedom                               167
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            70049.784
##   Degrees of freedom                               190
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.922
##   Tucker-Lewis Index (TLI)                       0.911
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -195609.297
##   Loglikelihood unrestricted model (H1)     -192806.513
## 
##   Number of free parameters                         63
##   Akaike (AIC)                              391344.594
##   Bayesian (BIC)                            391793.770
##   Sample-size adjusted Bayesian (BIC)       391593.566
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.059
##   90 Percent Confidence Interval          0.058  0.061
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.039
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                            Bootstrap
##   Number of requested bootstrap draws               10
##   Number of successful bootstrap draws              10
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_i       0.738    0.020   36.224    0.000    0.738    0.636
##     GotBully2_i       0.652    0.015   43.979    0.000    0.652    0.635
##     GotBully3_i       0.565    0.009   62.198    0.000    0.565    0.691
##     GotBully4_i       0.711    0.010   73.024    0.000    0.711    0.664
##     GotBully5_i       0.568    0.010   55.803    0.000    0.568    0.689
##     GotBully6_i       0.478    0.018   26.471    0.000    0.478    0.695
##     GotBully7_i       0.659    0.016   40.269    0.000    0.659    0.622
##     GotBully8_i       0.415    0.015   27.458    0.000    0.415    0.664
##     GotBully9_i       0.380    0.018   20.553    0.000    0.380    0.647
##   depress =~                                                            
##     Depress1_i        0.776    0.012   64.828    0.000    0.776    0.697
##     Depress2_i        0.703    0.015   48.427    0.000    0.703    0.630
##     Depress3_i        0.808    0.007  115.089    0.000    0.808    0.664
##     Depress4_i        0.879    0.009   92.838    0.000    0.879    0.661
##     Depress5_i        0.778    0.011   69.644    0.000    0.779    0.573
##     Depress6_i        0.760    0.014   53.612    0.000    0.761    0.567
##   alcohol =~                                                            
##     Alc1_i            0.588    0.012   48.322    0.000    0.593    0.765
##     Alc2_i            0.408    0.013   32.620    0.000    0.411    0.596
##     Alc3_i            0.709    0.011   62.460    0.000    0.715    0.890
##     Alc4_i            0.730    0.009   85.618    0.000    0.736    0.846
##     Alc5_i            0.748    0.011   65.792    0.000    0.754    0.892
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   alcohol ~                                                             
##     gotBully   (c)    0.128    0.017    7.612    0.000    0.127    0.127
##   depress ~                                                             
##     gotBully   (a)   -0.032    0.008   -4.069    0.000   -0.032   -0.032
##   alcohol ~                                                             
##     depress    (b)    0.006    0.011    0.548    0.584    0.006    0.006
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_i       0.660    0.011   60.623    0.000    0.660    0.568
##    .GotBully2_i       0.510    0.013   39.102    0.000    0.510    0.497
##    .GotBully3_i       0.280    0.007   39.411    0.000    0.280    0.343
##    .GotBully4_i       0.609    0.009   66.624    0.000    0.609    0.569
##    .GotBully5_i       0.278    0.006   46.982    0.000    0.278    0.337
##    .GotBully6_i       0.189    0.005   35.318    0.000    0.189    0.275
##    .GotBully7_i       0.512    0.009   55.766    0.000    0.512    0.484
##    .GotBully8_i       0.160    0.006   27.735    0.000    0.160    0.256
##    .GotBully9_i       0.131    0.005   27.903    0.000    0.131    0.223
##    .Depress1_i        2.595    0.008  315.629    0.000    2.595    2.330
##    .Depress2_i        2.231    0.014  159.666    0.000    2.231    1.999
##    .Depress3_i        3.105    0.013  230.807    0.000    3.105    2.551
##    .Depress4_i        2.751    0.013  216.225    0.000    2.751    2.067
##    .Depress5_i        2.484    0.012  200.322    0.000    2.484    1.828
##    .Depress6_i        2.376    0.009  276.795    0.000    2.376    1.771
##    .Alc1_i            2.355    0.006  364.913    0.000    2.355    3.038
##    .Alc2_i            2.327    0.007  343.750    0.000    2.327    3.370
##    .Alc3_i            2.359    0.007  335.399    0.000    2.359    2.935
##    .Alc4_i            2.469    0.007  357.539    0.000    2.469    2.839
##    .Alc5_i            2.426    0.008  302.442    0.000    2.426    2.870
##     gotBully          0.000                               0.000    0.000
##    .depress           0.000                               0.000    0.000
##    .alcohol           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##    .depress           1.000                               0.999    0.999
##    .alcohol           1.000                               0.984    0.984
##    .GotBully1_i       0.804    0.021   37.589    0.000    0.804    0.596
##    .GotBully2_i       0.629    0.021   30.464    0.000    0.629    0.597
##    .GotBully3_i       0.348    0.014   24.902    0.000    0.348    0.522
##    .GotBully4_i       0.640    0.023   27.769    0.000    0.640    0.559
##    .GotBully5_i       0.358    0.018   20.081    0.000    0.358    0.526
##    .GotBully6_i       0.244    0.013   19.254    0.000    0.244    0.516
##    .GotBully7_i       0.687    0.021   31.974    0.000    0.687    0.613
##    .GotBully8_i       0.219    0.010   21.895    0.000    0.219    0.560
##    .GotBully9_i       0.200    0.008   26.669    0.000    0.200    0.581
##    .Depress1_i        0.637    0.014   45.616    0.000    0.637    0.514
##    .Depress2_i        0.752    0.012   63.271    0.000    0.752    0.603
##    .Depress3_i        0.827    0.023   36.737    0.000    0.827    0.559
##    .Depress4_i        0.997    0.019   52.530    0.000    0.997    0.563
##    .Depress5_i        1.240    0.021   59.665    0.000    1.240    0.672
##    .Depress6_i        1.220    0.028   43.874    0.000    1.220    0.678
##    .Alc1_i            0.249    0.008   32.761    0.000    0.249    0.414
##    .Alc2_i            0.308    0.009   35.811    0.000    0.308    0.645
##    .Alc3_i            0.135    0.006   22.435    0.000    0.135    0.208
##    .Alc4_i            0.215    0.012   17.710    0.000    0.215    0.284
##    .Alc5_i            0.146    0.007   19.533    0.000    0.146    0.204
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ab               -0.000    0.000   -0.399    0.690   -0.000   -0.000
##     total             0.128    0.018    7.134    0.000    0.126    0.126
## The Categorical Treatment (DWLS) of the Indirect-Effect (Mediation) Model
## The Variables for this Model Are Coded as Factors

model.indirect.cat <- '
## the measurement model

gotBully =~ NA*GotBully1_f + GotBully2_f + GotBully3_f
             + GotBully4_f + GotBully5_f + GotBully6_f 
             + GotBully7_f + GotBully8_f + GotBully9_f
gotBully ~~ 1*gotBully

depress =~ NA*Depress1_f + Depress2_f + Depress3_f
            + Depress4_f + Depress5_f + Depress6_f
depress ~~ 1*depress

alcohol =~ NA*Alc1_f + Alc2_f + Alc3_f + Alc4_f + Alc5_f
alcohol ~~ 1*alcohol

## the structural model

## direct effect (the c path)
alcohol ~ c*gotBully

## mediator paths (the a and b path)
depress ~ a*gotBully # the a path - IV predicting ME
alcohol ~ b*depress  # the b path - ME predicting DV

## indirect effect (a*b)
## := operator defines new parameters
ab := a*b

## total effect
total := c + (a*b)
'

fit.indirect.DWLS <-
    sem(model = model.indirect.cat, data = hbsc, mimic = "Mplus",
        estimator = "DWLS", se = "bootstrap", verbose = TRUE,
        bootstrap = 10,
        ordered = c("GotBully1_f", "GotBully2_f", "GotBully3_f",
                    "GotBully4_f", "GotBully5_f", "GotBully6_f",
                    "GotBully7_f", "GotBully8_f", "GotBully9_f",
                    "Depress1_f", "Depress2_f", "Depress3_f",
                    "Depress4_f", "Depress5_f", "Depress6_f",
                    "Alc1_f", "Alc2_f", "Alc3_f", "Alc4_f", "Alc5_f"))
## Estimating sample thresholds and correlations ...
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc1_f
## x GotBully5_f
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc2_f
## x GotBully6_f
## Warning in pc_cor_TS(fit.y1 = UNI[[i]], fit.y2 = UNI[[j]], method =
## optim.method, : lavaan WARNING: empty cell(s) in bivariate table of Alc3_f
## x Alc1_f
## done
## Quasi-Newton steps using NLMINB:
## Objective function  = 3.4744358632854544
## Objective function  = 5.2715188376976485
## Objective function  = 0.9339952795637124
## Objective function  = 1.1741833689023096
## Objective function  = 0.4965823898158700
## Objective function  = 0.3105534612551779
## Objective function  = 0.2231495606575221
## Objective function  = 0.2370709720779824
## Objective function  = 0.1902542238851119
## Objective function  = 0.1952162422350136
## Objective function  = 0.1897729257393825
## Objective function  = 0.1861996616330555
## Objective function  = 0.1853975415199050
## Objective function  = 0.1866419404050293
## Objective function  = 0.1851219740255428
## Objective function  = 0.1850996320939146
## Objective function  = 0.1851606317733811
## Objective function  = 0.1850383775620663
## Objective function  = 0.1850202796351650
## Objective function  = 0.1850270548246426
## Objective function  = 0.1850094994058001
## Objective function  = 0.1850062243637064
## Objective function  = 0.1850077079090387
## Objective function  = 0.1850062602051931
## Objective function  = 0.1850057917590691
## Objective function  = 0.1850054005111328
## Objective function  = 0.1850053224833825
## Objective function  = 0.1850052644029618
## Objective function  = 0.1850052944855754
## Objective function  = 0.1850052416883415
## Objective function  = 0.1850052281783777
## Objective function  = 0.1850052336814881
## Objective function  = 0.1850052244155190
## Objective function  = 0.1850052239940537
## Objective function  = 0.1850052237051723
## Objective function  = 0.1850052235355862
## Objective function  = 0.1850052233625344
## Objective function  = 0.1850052234164415
## Objective function  = 0.1850052233048558
## Objective function  = 0.1850052232940274
## Objective function  = 0.1850052232942344
## Objective function  = 0.1850052232940274
## convergence status (0=ok):  0 
## nlminb message says:  relative convergence (4) 
## number of iterations:  28 
## number of function evaluations [objective, gradient]:  41 28 
## Computing VCOV for se = bootstrap ...  ... bootstrap draw number:    1   OK -- niter =   31  fx =    0.182878577 
##   ... bootstrap draw number:    2   OK -- niter =   30  fx =    0.216170672 
##   ... bootstrap draw number:    3   OK -- niter =   34  fx =    0.211663918 
##   ... bootstrap draw number:    4   OK -- niter =   32  fx =    0.218984143 
##   ... bootstrap draw number:    5   OK -- niter =   32  fx =    0.173710327 
##   ... bootstrap draw number:    6   OK -- niter =   31  fx =    0.205184150 
##   ... bootstrap draw number:    7   OK -- niter =   29  fx =    0.207614464 
##   ... bootstrap draw number:    8   OK -- niter =   27  fx =    0.197489822 
##   ... bootstrap draw number:    9   OK -- niter =   27  fx =    0.208924680 
##   ... bootstrap draw number:   10   OK -- niter =   29  fx =    0.180718442 
## Number of successful bootstrap draws: 10 
##  done.
## Computing TEST for test = standard ... done.
summary(fit.indirect.DWLS, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  28 iterations
## 
##                                                   Used       Total
##   Number of observations                          7118        9227
## 
##   Estimator                                       DWLS
##   Minimum Function Test Statistic             2633.734
##   Degrees of freedom                               167
##   P-value (Chi-square)                           0.000
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic           281854.962
##   Degrees of freedom                               190
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.991
##   Tucker-Lewis Index (TLI)                       0.990
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.046
##   90 Percent Confidence Interval          0.044  0.047
##   P-value RMSEA <= 0.05                          1.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.056
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           3.123
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                            Bootstrap
##   Number of requested bootstrap draws               10
##   Number of successful bootstrap draws              10
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   gotBully =~                                                           
##     GotBully1_f       0.770    0.012   63.455    0.000    0.770    0.770
##     GotBully2_f       0.768    0.012   66.381    0.000    0.768    0.768
##     GotBully3_f       0.788    0.016   50.203    0.000    0.788    0.788
##     GotBully4_f       0.798    0.007  108.918    0.000    0.798    0.798
##     GotBully5_f       0.811    0.011   77.005    0.000    0.811    0.811
##     GotBully6_f       0.833    0.011   73.890    0.000    0.833    0.833
##     GotBully7_f       0.770    0.012   65.382    0.000    0.770    0.770
##     GotBully8_f       0.858    0.015   55.738    0.000    0.858    0.858
##     GotBully9_f       0.883    0.019   46.673    0.000    0.883    0.883
##   depress =~                                                            
##     Depress1_f        0.675    0.011   61.857    0.000    0.735    0.735
##     Depress2_f        0.606    0.013   47.642    0.000    0.659    0.659
##     Depress3_f        0.695    0.010   66.699    0.000    0.756    0.756
##     Depress4_f        0.663    0.011   57.899    0.000    0.721    0.721
##     Depress5_f        0.583    0.012   50.001    0.000    0.634    0.634
##     Depress6_f        0.582    0.008   68.869    0.000    0.633    0.633
##   alcohol =~                                                            
##     Alc1_f            0.806    0.009   91.343    0.000    0.847    0.847
##     Alc2_f            0.667    0.017   38.288    0.000    0.701    0.701
##     Alc3_f            0.900    0.004  214.320    0.000    0.946    0.946
##     Alc4_f            0.871    0.007  119.178    0.000    0.916    0.916
##     Alc5_f            0.897    0.005  167.267    0.000    0.943    0.943
## 
## Regressions:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   alcohol ~                                                             
##     gotBully   (c)    0.014    0.027    0.532    0.594    0.014    0.014
##   depress ~                                                             
##     gotBully   (a)    0.428    0.022   19.572    0.000    0.394    0.394
##   alcohol ~                                                             
##     depress    (b)    0.292    0.019   15.292    0.000    0.302    0.302
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .GotBully1_f       0.000                               0.000    0.000
##    .GotBully2_f       0.000                               0.000    0.000
##    .GotBully3_f       0.000                               0.000    0.000
##    .GotBully4_f       0.000                               0.000    0.000
##    .GotBully5_f       0.000                               0.000    0.000
##    .GotBully6_f       0.000                               0.000    0.000
##    .GotBully7_f       0.000                               0.000    0.000
##    .GotBully8_f       0.000                               0.000    0.000
##    .GotBully9_f       0.000                               0.000    0.000
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##    .Alc1_f            0.000                               0.000    0.000
##    .Alc2_f            0.000                               0.000    0.000
##    .Alc3_f            0.000                               0.000    0.000
##    .Alc4_f            0.000                               0.000    0.000
##    .Alc5_f            0.000                               0.000    0.000
##     gotBully          0.000                               0.000    0.000
##    .depress           0.000                               0.000    0.000
##    .alcohol           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f|t1    0.435    0.015   29.086    0.000    0.435    0.435
##     GotBully1_f|t2    1.046    0.018   58.550    0.000    1.046    1.046
##     GotBully1_f|t3    1.262    0.022   57.812    0.000    1.262    1.262
##     GotBully1_f|t4    1.528    0.020   75.165    0.000    1.528    1.528
##     GotBully2_f|t1    0.618    0.013   46.304    0.000    0.618    0.618
##     GotBully2_f|t2    1.198    0.017   69.725    0.000    1.198    1.198
##     GotBully2_f|t3    1.422    0.030   48.169    0.000    1.422    1.422
##     GotBully2_f|t4    1.736    0.037   46.586    0.000    1.736    1.736
##     GotBully3_f|t1    1.088    0.010  112.983    0.000    1.088    1.088
##     GotBully3_f|t2    1.518    0.017   90.037    0.000    1.518    1.518
##     GotBully3_f|t3    1.734    0.024   73.454    0.000    1.734    1.734
##     GotBully3_f|t4    1.987    0.045   43.913    0.000    1.987    1.987
##     GotBully4_f|t1    0.425    0.016   26.647    0.000    0.425    0.425
##     GotBully4_f|t2    1.111    0.021   53.522    0.000    1.111    1.111
##     GotBully4_f|t3    1.399    0.015   92.414    0.000    1.399    1.399
##     GotBully4_f|t4    1.664    0.024   70.290    0.000    1.664    1.664
##     GotBully5_f|t1    1.119    0.015   72.627    0.000    1.119    1.119
##     GotBully5_f|t2    1.520    0.023   66.549    0.000    1.520    1.520
##     GotBully5_f|t3    1.711    0.025   67.332    0.000    1.711    1.711
##     GotBully5_f|t4    1.965    0.034   57.182    0.000    1.965    1.965
##     GotBully6_f|t1    1.340    0.019   69.151    0.000    1.340    1.340
##     GotBully6_f|t2    1.696    0.025   67.799    0.000    1.696    1.696
##     GotBully6_f|t3    1.890    0.031   61.337    0.000    1.890    1.890
##     GotBully6_f|t4    2.134    0.043   50.142    0.000    2.134    2.134
##     GotBully7_f|t1    0.677    0.015   45.133    0.000    0.677    0.677
##     GotBully7_f|t2    1.155    0.022   53.115    0.000    1.155    1.155
##     GotBully7_f|t3    1.405    0.023   62.438    0.000    1.405    1.405
##     GotBully7_f|t4    1.696    0.027   61.945    0.000    1.696    1.696
##     GotBully8_f|t1    1.404    0.019   73.617    0.000    1.404    1.404
##     GotBully8_f|t2    1.800    0.029   61.640    0.000    1.800    1.800
##     GotBully8_f|t3    2.027    0.035   57.823    0.000    2.027    2.027
##     GotBully8_f|t4    2.237    0.049   45.349    0.000    2.237    2.237
##     GotBully9_f|t1    1.544    0.027   57.875    0.000    1.544    1.544
##     GotBully9_f|t2    1.878    0.036   51.763    0.000    1.878    1.878
##     GotBully9_f|t3    2.058    0.031   66.164    0.000    2.058    2.058
##     GotBully9_f|t4    2.241    0.043   52.205    0.000    2.241    2.241
##     Depress1_f|t1    -0.666    0.018  -36.981    0.000   -0.666   -0.666
##     Depress1_f|t2     0.095    0.013    7.098    0.000    0.095    0.095
##     Depress1_f|t3     1.004    0.016   64.308    0.000    1.004    1.004
##     Depress1_f|t4     1.723    0.024   72.520    0.000    1.723    1.723
##     Depress2_f|t1    -1.046    0.013  -78.910    0.000   -1.046   -1.046
##     Depress2_f|t2    -0.295    0.013  -22.755    0.000   -0.295   -0.295
##     Depress2_f|t3     0.688    0.011   65.060    0.000    0.688    0.688
##     Depress2_f|t4     1.532    0.025   62.112    0.000    1.532    1.532
##     Depress3_f|t1     0.142    0.023    6.281    0.000    0.142    0.142
##     Depress3_f|t2     0.607    0.023   26.224    0.000    0.607    0.607
##     Depress3_f|t3     1.137    0.018   61.763    0.000    1.137    1.137
##     Depress3_f|t4     1.612    0.023   70.325    0.000    1.612    1.612
##     Depress4_f|t1    -0.174    0.017  -10.246    0.000   -0.174   -0.174
##     Depress4_f|t2     0.228    0.023    9.923    0.000    0.228    0.228
##     Depress4_f|t3     0.841    0.018   47.943    0.000    0.841    0.841
##     Depress4_f|t4     1.433    0.023   61.536    0.000    1.433    1.433
##     Depress5_f|t1    -0.456    0.022  -21.033    0.000   -0.456   -0.456
##     Depress5_f|t2     0.033    0.016    2.069    0.039    0.033    0.033
##     Depress5_f|t3     0.665    0.014   46.007    0.000    0.665    0.665
##     Depress5_f|t4     1.248    0.016   76.414    0.000    1.248    1.248
##     Depress6_f|t1    -0.618    0.019  -31.798    0.000   -0.618   -0.618
##     Depress6_f|t2    -0.055    0.013   -4.228    0.000   -0.055   -0.055
##     Depress6_f|t3     0.618    0.011   54.540    0.000    0.618    0.618
##     Depress6_f|t4     1.179    0.014   86.694    0.000    1.179    1.179
##     Alc1_f|t1         0.699    0.011   63.940    0.000    0.699    0.699
##     Alc1_f|t2         1.384    0.020   67.612    0.000    1.384    1.384
##     Alc1_f|t3         1.745    0.020   85.877    0.000    1.745    1.745
##     Alc1_f|t4         2.396    0.038   62.680    0.000    2.396    2.396
##     Alc2_f|t1         0.668    0.019   36.049    0.000    0.668    0.668
##     Alc2_f|t2         1.601    0.026   62.633    0.000    1.601    1.601
##     Alc2_f|t3         1.955    0.024   79.866    0.000    1.955    1.955
##     Alc2_f|t4         2.478    0.061   40.401    0.000    2.478    2.478
##     Alc3_f|t1         0.746    0.017   44.984    0.000    0.746    0.746
##     Alc3_f|t2         1.297    0.012  103.942    0.000    1.297    1.297
##     Alc3_f|t3         1.696    0.022   76.934    0.000    1.696    1.696
##     Alc3_f|t4         2.384    0.049   49.132    0.000    2.384    2.384
##     Alc4_f|t1         0.507    0.013   40.009    0.000    0.507    0.507
##     Alc4_f|t2         1.159    0.013   88.145    0.000    1.159    1.159
##     Alc4_f|t3         1.653    0.019   89.039    0.000    1.653    1.653
##     Alc4_f|t4         2.292    0.035   65.058    0.000    2.292    2.292
##     Alc5_f|t1         0.585    0.016   35.871    0.000    0.585    0.585
##     Alc5_f|t2         1.225    0.013   96.120    0.000    1.225    1.225
##     Alc5_f|t3         1.645    0.018   89.975    0.000    1.645    1.645
##     Alc5_f|t4         2.282    0.028   81.501    0.000    2.282    2.282
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     gotBully          1.000                               1.000    1.000
##    .depress           1.000                               0.845    0.845
##    .alcohol           1.000                               0.905    0.905
##    .GotBully1_f       0.407                               0.407    0.407
##    .GotBully2_f       0.411                               0.411    0.411
##    .GotBully3_f       0.380                               0.380    0.380
##    .GotBully4_f       0.363                               0.363    0.363
##    .GotBully5_f       0.342                               0.342    0.342
##    .GotBully6_f       0.306                               0.306    0.306
##    .GotBully7_f       0.406                               0.406    0.406
##    .GotBully8_f       0.264                               0.264    0.264
##    .GotBully9_f       0.221                               0.221    0.221
##    .Depress1_f        0.460                               0.460    0.460
##    .Depress2_f        0.565                               0.565    0.565
##    .Depress3_f        0.428                               0.428    0.428
##    .Depress4_f        0.480                               0.480    0.480
##    .Depress5_f        0.598                               0.598    0.598
##    .Depress6_f        0.599                               0.599    0.599
##    .Alc1_f            0.282                               0.282    0.282
##    .Alc2_f            0.509                               0.509    0.509
##    .Alc3_f            0.106                               0.106    0.106
##    .Alc4_f            0.161                               0.161    0.161
##    .Alc5_f            0.110                               0.110    0.110
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     GotBully1_f       1.000                               1.000    1.000
##     GotBully2_f       1.000                               1.000    1.000
##     GotBully3_f       1.000                               1.000    1.000
##     GotBully4_f       1.000                               1.000    1.000
##     GotBully5_f       1.000                               1.000    1.000
##     GotBully6_f       1.000                               1.000    1.000
##     GotBully7_f       1.000                               1.000    1.000
##     GotBully8_f       1.000                               1.000    1.000
##     GotBully9_f       1.000                               1.000    1.000
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
##     Alc1_f            1.000                               1.000    1.000
##     Alc2_f            1.000                               1.000    1.000
##     Alc3_f            1.000                               1.000    1.000
##     Alc4_f            1.000                               1.000    1.000
##     Alc5_f            1.000                               1.000    1.000
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ab                0.125    0.010   11.968    0.000    0.119    0.119
##     total             0.139    0.020    7.119    0.000    0.133    0.133
####-------------------------------------------------------------####
#### Section-5: One- Factort Two-Group Measurement Invariance    ####
#### A One-Factor (Depression) CFA Model between Grade 6 and 7   ####
####-------------------------------------------------------------####

## Creating a Dataset only Containing Observations from Grade 6 and 7
dat.inva <- hbsc[hbsc$Grade %in% c("Grade_6", "Grade_7"), ]
dim(dat.inva)
## [1] 4284   90
## The Continous Treatment (ML) of the Items Coded as Interger Variables

## 1. Configural Invariance Test (ML)
model.config.ML <- '
depress =~ Depress1_i + Depress2_i + Depress3_i + Depress4_i
           + Depress5_i + Depress6_i
'

fit.config.ML <- cfa(model = model.config.ML, data = dat.inva,
                     mimic = "Mplus", estimator = "ML",
                     std.lv = TRUE, group = "Grade")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   49 52 132 202 251 354 415 456 634 637 670 688 713 811 1027 1099 1176 1187 1208 1545 1553 1579 1601 1653 1665 1747 1792 1806 1845
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   22 105 115 216 232 291 343 369 836 858 1038 1082 1085 1129 1144 1147 1185 1275 1316 1322 1328 1397 1406 1706 1722 1806 1860 1879 1906 1907 2013 2089 2106 2127 2291 2379
summary(fit.config.ML, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  28 iterations
## 
##                                                   Used       Total
##   Number of observations per group         
##   Grade_7                                         1851        1880
##   Grade_6                                         2368        2404
## 
##   Number of missing patterns per group     
##   Grade_7                                           11
##   Grade_6                                           17
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              268.115
##   Degrees of freedom                                29
##   P-value (Chi-square)                           0.000
## 
## Chi-square for each group:
## 
##   Grade_7                                      113.963
##   Grade_6                                      154.152
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             6441.145
##   Degrees of freedom                                30
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.963
##   Tucker-Lewis Index (TLI)                       0.961
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -38132.707
##   Loglikelihood unrestricted model (H1)     -37998.649
## 
##   Number of free parameters                         25
##   Akaike (AIC)                               76315.413
##   Bayesian (BIC)                             76474.097
##   Sample-size adjusted Bayesian (BIC)        76394.658
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.063
##   90 Percent Confidence Interval          0.056  0.069
##   P-value RMSEA <= 0.05                          0.001
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.033
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## 
## Group 1 [Grade_7]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.783    0.017   46.428    0.000    0.783    0.701
##     Dprss2_ (.p2.)    0.696    0.017   40.458    0.000    0.696    0.621
##     Dprss3_ (.p3.)    0.801    0.019   42.881    0.000    0.801    0.662
##     Dprss4_ (.p4.)    0.889    0.020   43.620    0.000    0.889    0.664
##     Dprss5_ (.p5.)    0.781    0.021   36.345    0.000    0.781    0.580
##     Dprss6_ (.p6.)    0.756    0.021   35.681    0.000    0.756    0.574
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Dprss1_ (.14.)    2.568    0.023  111.811    0.000    2.568    2.299
##    .Dprss2_ (.15.)    2.207    0.022  100.879    0.000    2.207    1.968
##    .Dprss3_ (.16.)    3.098    0.024  127.152    0.000    3.098    2.563
##    .Dprss4_ (.17.)    2.727    0.027  101.467    0.000    2.727    2.037
##    .Dprss5_ (.18.)    2.493    0.026   96.404    0.000    2.493    1.850
##    .Dprss6_ (.19.)    2.362    0.025   93.399    0.000    2.362    1.795
##     depress           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        0.635    0.027   23.751    0.000    0.635    0.509
##    .Depress2_i        0.772    0.029   26.205    0.000    0.772    0.614
##    .Depress3_i        0.820    0.033   24.970    0.000    0.820    0.561
##    .Depress4_i        1.003    0.040   25.028    0.000    1.003    0.559
##    .Depress5_i        1.205    0.045   26.807    0.000    1.205    0.664
##    .Depress6_i        1.160    0.043   26.933    0.000    1.160    0.670
##     depress           1.000                               1.000    1.000
## 
## 
## Group 2 [Grade_6]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.783    0.017   46.428    0.000    0.783    0.700
##     Dprss2_ (.p2.)    0.696    0.017   40.458    0.000    0.696    0.629
##     Dprss3_ (.p3.)    0.801    0.019   42.881    0.000    0.801    0.651
##     Dprss4_ (.p4.)    0.889    0.020   43.620    0.000    0.889    0.670
##     Dprss5_ (.p5.)    0.781    0.021   36.345    0.000    0.781    0.572
##     Dprss6_ (.p6.)    0.756    0.021   35.681    0.000    0.756    0.555
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Dprss1_ (.14.)    2.568    0.023  111.811    0.000    2.568    2.297
##    .Dprss2_ (.15.)    2.207    0.022  100.879    0.000    2.207    1.994
##    .Dprss3_ (.16.)    3.098    0.024  127.152    0.000    3.098    2.518
##    .Dprss4_ (.17.)    2.727    0.027  101.467    0.000    2.727    2.056
##    .Dprss5_ (.18.)    2.493    0.026   96.404    0.000    2.493    1.825
##    .Dprss6_ (.19.)    2.362    0.025   93.399    0.000    2.362    1.733
##     depress           0.014    0.035    0.391    0.696    0.014    0.014
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        0.638    0.024   26.639    0.000    0.638    0.510
##    .Depress2_i        0.740    0.025   29.102    0.000    0.740    0.604
##    .Depress3_i        0.873    0.030   28.629    0.000    0.873    0.577
##    .Depress4_i        0.969    0.035   27.577    0.000    0.969    0.551
##    .Depress5_i        1.256    0.041   30.302    0.000    1.256    0.673
##    .Depress6_i        1.285    0.042   30.949    0.000    1.285    0.692
##     depress           1.000                               1.000    1.000
## 2. Metric (Weak) Invariance Test (ML)
model.metric.ML <-'
depress =~ Depress1_i + Depress2_i + Depress3_i + Depress4_i
           + Depress5_i + Depress6_i
depress ~~ c(1, NA)*depress'

fit.metric.ML <- cfa(model = model.config.ML, data = dat.inva,
                     mimic = "Mplus", estimator = "ML",
                     std.lv = TRUE, group = "Grade",
                     group.equal = "loadings")
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   49 52 132 202 251 354 415 456 634 637 670 688 713 811 1027 1099 1176 1187 1208 1545 1553 1579 1601 1653 1665 1747 1792 1806 1845

## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   22 105 115 216 232 291 343 369 836 858 1038 1082 1085 1129 1144 1147 1185 1275 1316 1322 1328 1397 1406 1706 1722 1806 1860 1879 1906 1907 2013 2089 2106 2127 2291 2379
summary(fit.metric.ML, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  32 iterations
## 
##                                                   Used       Total
##   Number of observations per group         
##   Grade_7                                         1851        1880
##   Grade_6                                         2368        2404
## 
##   Number of missing patterns per group     
##   Grade_7                                           11
##   Grade_6                                           17
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              265.787
##   Degrees of freedom                                24
##   P-value (Chi-square)                           0.000
## 
## Chi-square for each group:
## 
##   Grade_7                                      112.708
##   Grade_6                                      153.079
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             6441.145
##   Degrees of freedom                                30
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.962
##   Tucker-Lewis Index (TLI)                       0.953
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -38131.543
##   Loglikelihood unrestricted model (H1)     -37998.649
## 
##   Number of free parameters                         30
##   Akaike (AIC)                               76323.085
##   Bayesian (BIC)                             76513.506
##   Sample-size adjusted Bayesian (BIC)        76418.178
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.069
##   90 Percent Confidence Interval          0.062  0.077
##   P-value RMSEA <= 0.05                          0.000
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.032
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## 
## Group 1 [Grade_7]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.783    0.017   46.426    0.000    0.783    0.701
##     Dprss2_ (.p2.)    0.696    0.017   40.460    0.000    0.696    0.621
##     Dprss3_ (.p3.)    0.801    0.019   42.882    0.000    0.801    0.662
##     Dprss4_ (.p4.)    0.889    0.020   43.629    0.000    0.889    0.664
##     Dprss5_ (.p5.)    0.782    0.021   36.353    0.000    0.782    0.580
##     Dprss6_ (.p6.)    0.756    0.021   35.678    0.000    0.756    0.574
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        2.567    0.026   98.817    0.000    2.567    2.298
##    .Depress2_i        2.213    0.026   84.847    0.000    2.213    1.973
##    .Depress3_i        3.082    0.028  109.603    0.000    3.082    2.551
##    .Depress4_i        2.739    0.031   87.749    0.000    2.739    2.045
##    .Depress5_i        2.506    0.031   79.703    0.000    2.506    1.859
##    .Depress6_i        2.352    0.031   76.764    0.000    2.352    1.788
##     depress           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        0.635    0.027   23.753    0.000    0.635    0.509
##    .Depress2_i        0.772    0.029   26.205    0.000    0.772    0.614
##    .Depress3_i        0.820    0.033   24.974    0.000    0.820    0.561
##    .Depress4_i        1.003    0.040   25.027    0.000    1.003    0.559
##    .Depress5_i        1.205    0.045   26.808    0.000    1.205    0.664
##    .Depress6_i        1.160    0.043   26.935    0.000    1.160    0.670
##     depress           1.000                               1.000    1.000
## 
## 
## Group 2 [Grade_6]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.783    0.017   46.426    0.000    0.783    0.700
##     Dprss2_ (.p2.)    0.696    0.017   40.460    0.000    0.696    0.629
##     Dprss3_ (.p3.)    0.801    0.019   42.882    0.000    0.801    0.651
##     Dprss4_ (.p4.)    0.889    0.020   43.629    0.000    0.889    0.670
##     Dprss5_ (.p5.)    0.782    0.021   36.353    0.000    0.782    0.572
##     Dprss6_ (.p6.)    0.756    0.021   35.678    0.000    0.756    0.555
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        2.580    0.023  112.171    0.000    2.580    2.307
##    .Depress2_i        2.212    0.023   97.047    0.000    2.212    1.998
##    .Depress3_i        3.122    0.025  123.223    0.000    3.122    2.537
##    .Depress4_i        2.731    0.027   99.954    0.000    2.731    2.059
##    .Depress5_i        2.493    0.028   88.596    0.000    2.493    1.825
##    .Depress6_i        2.381    0.028   84.920    0.000    2.381    1.747
##     depress           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        0.638    0.024   26.641    0.000    0.638    0.510
##    .Depress2_i        0.740    0.025   29.102    0.000    0.740    0.604
##    .Depress3_i        0.873    0.030   28.633    0.000    0.873    0.577
##    .Depress4_i        0.969    0.035   27.577    0.000    0.969    0.551
##    .Depress5_i        1.255    0.041   30.303    0.000    1.255    0.673
##    .Depress6_i        1.285    0.042   30.951    0.000    1.285    0.692
##     depress           1.000                               1.000    1.000
lavTestLRT(fit.config.ML, fit.metric.ML)
## Chi Square Difference Test
## 
##               Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.metric.ML 24 76323 76514 265.79                              
## fit.config.ML 29 76315 76474 268.11     2.3283       5     0.8021
## 3. Scalar (Strong) Invariance Test (ML)
model.scalar.ML <- '
depress =~ Depress1_i + Depress2_i  + Depress3_i + Depress4_i
           + Depress5_i + Depress6_i
depress ~~ (1, NA)*depress
depress ~ c(0, NA)*1
'

fit.scalar.ML <- cfa(model = model.config.ML, data = dat.inva,
                     mimic = "Mplus", estimator = "ML",
                     std.lv = TRUE, group = "Grade",
                     group.equal = c("loadings", "intercepts"))
## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   49 52 132 202 251 354 415 456 634 637 670 688 713 811 1027 1099 1176 1187 1208 1545 1553 1579 1601 1653 1665 1747 1792 1806 1845

## Warning in lav_data_full(data = data, group = group, group.label = group.label, : lavaan WARNING: some cases are empty and will be ignored:
##   22 105 115 216 232 291 343 369 836 858 1038 1082 1085 1129 1144 1147 1185 1275 1316 1322 1328 1397 1406 1706 1722 1806 1860 1879 1906 1907 2013 2089 2106 2127 2291 2379
summary(fit.scalar.ML, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  28 iterations
## 
##                                                   Used       Total
##   Number of observations per group         
##   Grade_7                                         1851        1880
##   Grade_6                                         2368        2404
## 
##   Number of missing patterns per group     
##   Grade_7                                           11
##   Grade_6                                           17
## 
##   Estimator                                         ML
##   Minimum Function Test Statistic              268.115
##   Degrees of freedom                                29
##   P-value (Chi-square)                           0.000
## 
## Chi-square for each group:
## 
##   Grade_7                                      113.963
##   Grade_6                                      154.152
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic             6441.145
##   Degrees of freedom                                30
##   P-value                                        0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.963
##   Tucker-Lewis Index (TLI)                       0.961
## 
## Loglikelihood and Information Criteria:
## 
##   Loglikelihood user model (H0)             -38132.707
##   Loglikelihood unrestricted model (H1)     -37998.649
## 
##   Number of free parameters                         25
##   Akaike (AIC)                               76315.413
##   Bayesian (BIC)                             76474.097
##   Sample-size adjusted Bayesian (BIC)        76394.658
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.063
##   90 Percent Confidence Interval          0.056  0.069
##   P-value RMSEA <= 0.05                          0.001
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.033
## 
## Parameter Estimates:
## 
##   Information                                 Observed
##   Standard Errors                             Standard
## 
## 
## Group 1 [Grade_7]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.783    0.017   46.428    0.000    0.783    0.701
##     Dprss2_ (.p2.)    0.696    0.017   40.458    0.000    0.696    0.621
##     Dprss3_ (.p3.)    0.801    0.019   42.881    0.000    0.801    0.662
##     Dprss4_ (.p4.)    0.889    0.020   43.620    0.000    0.889    0.664
##     Dprss5_ (.p5.)    0.781    0.021   36.345    0.000    0.781    0.580
##     Dprss6_ (.p6.)    0.756    0.021   35.681    0.000    0.756    0.574
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Dprss1_ (.14.)    2.568    0.023  111.811    0.000    2.568    2.299
##    .Dprss2_ (.15.)    2.207    0.022  100.879    0.000    2.207    1.968
##    .Dprss3_ (.16.)    3.098    0.024  127.152    0.000    3.098    2.563
##    .Dprss4_ (.17.)    2.727    0.027  101.467    0.000    2.727    2.037
##    .Dprss5_ (.18.)    2.493    0.026   96.404    0.000    2.493    1.850
##    .Dprss6_ (.19.)    2.362    0.025   93.399    0.000    2.362    1.795
##     depress           0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        0.635    0.027   23.751    0.000    0.635    0.509
##    .Depress2_i        0.772    0.029   26.205    0.000    0.772    0.614
##    .Depress3_i        0.820    0.033   24.970    0.000    0.820    0.561
##    .Depress4_i        1.003    0.040   25.028    0.000    1.003    0.559
##    .Depress5_i        1.205    0.045   26.807    0.000    1.205    0.664
##    .Depress6_i        1.160    0.043   26.933    0.000    1.160    0.670
##     depress           1.000                               1.000    1.000
## 
## 
## Group 2 [Grade_6]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.783    0.017   46.428    0.000    0.783    0.700
##     Dprss2_ (.p2.)    0.696    0.017   40.458    0.000    0.696    0.629
##     Dprss3_ (.p3.)    0.801    0.019   42.881    0.000    0.801    0.651
##     Dprss4_ (.p4.)    0.889    0.020   43.620    0.000    0.889    0.670
##     Dprss5_ (.p5.)    0.781    0.021   36.345    0.000    0.781    0.572
##     Dprss6_ (.p6.)    0.756    0.021   35.681    0.000    0.756    0.555
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Dprss1_ (.14.)    2.568    0.023  111.811    0.000    2.568    2.297
##    .Dprss2_ (.15.)    2.207    0.022  100.879    0.000    2.207    1.994
##    .Dprss3_ (.16.)    3.098    0.024  127.152    0.000    3.098    2.518
##    .Dprss4_ (.17.)    2.727    0.027  101.467    0.000    2.727    2.056
##    .Dprss5_ (.18.)    2.493    0.026   96.404    0.000    2.493    1.825
##    .Dprss6_ (.19.)    2.362    0.025   93.399    0.000    2.362    1.733
##     depress           0.014    0.035    0.391    0.696    0.014    0.014
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_i        0.638    0.024   26.639    0.000    0.638    0.510
##    .Depress2_i        0.740    0.025   29.102    0.000    0.740    0.604
##    .Depress3_i        0.873    0.030   28.629    0.000    0.873    0.577
##    .Depress4_i        0.969    0.035   27.577    0.000    0.969    0.551
##    .Depress5_i        1.256    0.041   30.302    0.000    1.256    0.673
##    .Depress6_i        1.285    0.042   30.949    0.000    1.285    0.692
##     depress           1.000                               1.000    1.000
lavTestLRT(fit.metric.ML, fit.scalar.ML)
## Chi Square Difference Test
## 
##               Df   AIC   BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.metric.ML 24 76323 76514 265.79                              
## fit.scalar.ML 29 76315 76474 268.11     2.3283       5     0.8021
## The Categorical Treatment (WLSMV) of the Items Coded as Factor Variables
## 1. Configural Invariance Test (WLSMV)
model.config.WLSMV <- '
depress =~ Depress1_f + Depress2_f + Depress3_f
           + Depress4_f + Depress5_f + Depress6_f
'

fit.config.WLSMV <- cfa(model = model.config.WLSMV, data = dat.inva,
                        mimic = "Mplus", estimator = "WLSMV",
                        std.lv = TRUE, group = "Grade",
                        ordered = c("Depress1_f", "Depress2_f",
                                    "Depress3_f", "Depress4_f",
                                    "Depress5_f", "Depress6_f"))

summary(fit.config.WLSMV, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  22 iterations
## 
##                                                   Used       Total
##   Number of observations per group         
##   Grade_7                                         1811        1880
##   Grade_6                                         2292        2404
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              210.489     276.702
##   Degrees of freedom                                41          41
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.764
##   Shift parameter for each group:
##     Grade_7                                                  0.600
##     Grade_6                                                  0.760
##     for simple second-order correction (WLSMV)
## 
## Chi-square for each group:
## 
##   Grade_7                                       85.291     112.170
##   Grade_6                                      125.198     164.532
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            16164.928   11074.106
##   Degrees of freedom                                30          30
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.989       0.979
##   Tucker-Lewis Index (TLI)                       0.992       0.984
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.045       0.053
##   90 Percent Confidence Interval          0.039  0.051       0.047  0.059
##   P-value RMSEA <= 0.05                          0.914       0.198
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.036       0.036
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           2.323       2.323
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## 
## Group 1 [Grade_7]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.706    0.012   57.211    0.000    0.706    0.706
##     Dprss2_ (.p2.)    0.662    0.013   52.099    0.000    0.662    0.662
##     Dprss3_ (.p3.)    0.764    0.014   54.299    0.000    0.764    0.764
##     Dprss4_ (.p4.)    0.734    0.013   54.902    0.000    0.734    0.734
##     Dprss5_ (.p5.)    0.611    0.015   40.407    0.000    0.611    0.611
##     Dprss6_ (.p6.)    0.602    0.015   41.143    0.000    0.602    0.602
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##     depress           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Dpr1_|1 (.p7.)   -0.565    0.026  -21.510    0.000   -0.565   -0.565
##     Dpr1_|2 (.p8.)    0.126    0.024    5.190    0.000    0.126    0.126
##     Dpr1_|3 (.p9.)    1.082    0.030   36.172    0.000    1.082    1.082
##     Dpr1_|4 (.10.)    1.768    0.042   42.022    0.000    1.768    1.768
##     Dpr2_|1 (.11.)   -0.886    0.028  -31.287    0.000   -0.886   -0.886
##     Dpr2_|2 (.12.)   -0.201    0.024   -8.287    0.000   -0.201   -0.201
##     Dpr2_|3 (.13.)    0.741    0.026   27.969    0.000    0.741    0.741
##     Dpr2_|4 (.14.)    1.523    0.036   41.830    0.000    1.523    1.523
##     Dpr3_|1 (.15.)    0.290    0.025   11.450    0.000    0.290    0.290
##     Dpr3_|2 (.16.)    0.679    0.027   25.325    0.000    0.679    0.679
##     Dpr3_|3 (.17.)    1.200    0.032   37.683    0.000    1.200    1.200
##     Dpr3_|4 (.18.)    1.658    0.040   41.070    0.000    1.658    1.658
##     Dpr4_|1 (.19.)   -0.115    0.025   -4.549    0.000   -0.115   -0.115
##     Dpr4_|2 (.20.)    0.257    0.025   10.198    0.000    0.257    0.257
##     Dpr4_|3 (.21.)    0.907    0.028   31.921    0.000    0.907    0.907
##     Dpr4_|4 (.22.)    1.470    0.036   40.633    0.000    1.470    1.470
##     Dpr5_|1 (.23.)   -0.380    0.025  -15.342    0.000   -0.380   -0.380
##     Dpr5_|2 (.24.)    0.068    0.023    2.926    0.003    0.068    0.068
##     Dpr5_|3 (.25.)    0.675    0.026   25.926    0.000    0.675    0.675
##     Dpr5_|4 (.26.)    1.246    0.033   37.568    0.000    1.246    1.246
##     Dpr6_|1 (.27.)   -0.442    0.025  -17.621    0.000   -0.442   -0.442
##     Dpr6_|2 (.28.)    0.082    0.023    3.477    0.001    0.082    0.082
##     Dpr6_|3 (.29.)    0.750    0.027   28.107    0.000    0.750    0.750
##     Dpr6_|4 (.30.)    1.273    0.033   38.449    0.000    1.273    1.273
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.501                               0.501    0.501
##    .Depress2_f        0.562                               0.562    0.562
##    .Depress3_f        0.416                               0.416    0.416
##    .Depress4_f        0.461                               0.461    0.461
##    .Depress5_f        0.627                               0.627    0.627
##    .Depress6_f        0.638                               0.638    0.638
##     depress           1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
## 
## 
## Group 2 [Grade_6]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.706    0.012   57.211    0.000    0.706    0.715
##     Dprss2_ (.p2.)    0.662    0.013   52.099    0.000    0.662    0.648
##     Dprss3_ (.p3.)    0.764    0.014   54.299    0.000    0.764    0.732
##     Dprss4_ (.p4.)    0.734    0.013   54.902    0.000    0.734    0.700
##     Dprss5_ (.p5.)    0.611    0.015   40.407    0.000    0.611    0.595
##     Dprss6_ (.p6.)    0.602    0.015   41.143    0.000    0.602    0.581
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##     depress          -0.013    0.037   -0.364    0.716   -0.013   -0.013
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Dpr1_|1 (.p7.)   -0.565    0.026  -21.510    0.000   -0.565   -0.572
##     Dpr1_|2 (.p8.)    0.126    0.024    5.190    0.000    0.126    0.128
##     Dpr1_|3 (.p9.)    1.082    0.030   36.172    0.000    1.082    1.096
##     Dpr1_|4 (.10.)    1.768    0.042   42.022    0.000    1.768    1.791
##     Dpr2_|1 (.11.)   -0.886    0.028  -31.287    0.000   -0.886   -0.867
##     Dpr2_|2 (.12.)   -0.201    0.024   -8.287    0.000   -0.201   -0.196
##     Dpr2_|3 (.13.)    0.741    0.026   27.969    0.000    0.741    0.725
##     Dpr2_|4 (.14.)    1.523    0.036   41.830    0.000    1.523    1.491
##     Dpr3_|1 (.15.)    0.290    0.025   11.450    0.000    0.290    0.278
##     Dpr3_|2 (.16.)    0.679    0.027   25.325    0.000    0.679    0.651
##     Dpr3_|3 (.17.)    1.200    0.032   37.683    0.000    1.200    1.149
##     Dpr3_|4 (.18.)    1.658    0.040   41.070    0.000    1.658    1.589
##     Dpr4_|1 (.19.)   -0.115    0.025   -4.549    0.000   -0.115   -0.109
##     Dpr4_|2 (.20.)    0.257    0.025   10.198    0.000    0.257    0.245
##     Dpr4_|3 (.21.)    0.907    0.028   31.921    0.000    0.907    0.864
##     Dpr4_|4 (.22.)    1.470    0.036   40.633    0.000    1.470    1.401
##     Dpr5_|1 (.23.)   -0.380    0.025  -15.342    0.000   -0.380   -0.370
##     Dpr5_|2 (.24.)    0.068    0.023    2.926    0.003    0.068    0.067
##     Dpr5_|3 (.25.)    0.675    0.026   25.926    0.000    0.675    0.657
##     Dpr5_|4 (.26.)    1.246    0.033   37.568    0.000    1.246    1.213
##     Dpr6_|1 (.27.)   -0.442    0.025  -17.621    0.000   -0.442   -0.427
##     Dpr6_|2 (.28.)    0.082    0.023    3.477    0.001    0.082    0.079
##     Dpr6_|3 (.29.)    0.750    0.027   28.107    0.000    0.750    0.725
##     Dpr6_|4 (.30.)    1.273    0.033   38.449    0.000    1.273    1.230
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.476                               0.476    0.488
##    .Depress2_f        0.605                               0.605    0.580
##    .Depress3_f        0.506                               0.506    0.464
##    .Depress4_f        0.562                               0.562    0.510
##    .Depress5_f        0.682                               0.682    0.646
##    .Depress6_f        0.709                               0.709    0.662
##     depress           1.000                               1.000    1.000
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        1.013    0.018   56.739    0.000    1.013    1.000
##     Depress2_f        0.979    0.018   55.918    0.000    0.979    1.000
##     Depress3_f        0.958    0.019   49.293    0.000    0.958    1.000
##     Depress4_f        0.953    0.020   48.613    0.000    0.953    1.000
##     Depress5_f        0.973    0.024   40.348    0.000    0.973    1.000
##     Depress6_f        0.966    0.023   41.212    0.000    0.966    1.000
## 2. Metric (Weak) Invariance Test (WLSMV)
model.metric.WLSMV <- '
depress =~ Depress1_f + Depress2_f + Depress3_f
           + Depress4_f + Depress5_f + Depress6_f
depress ~~ c(1, NA)*depress'

fit.metric.WLSMV <- cfa(model = model.metric.WLSMV, data = dat.inva,
                        mimic = "Mplus", estimator = "WLSMV",
                        std.lv = TRUE, group = "Grade",
                        ordered = c("Depress1_f", "Depress2_f",
                                    "Depress3_f", "Depress4_f",
                                    "Depress5_f", "Depress6_f"),
                        group.equal = "loadings")

summary(fit.metric.WLSMV, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after   9 iterations
## 
##                                                   Used       Total
##   Number of observations per group         
##   Grade_7                                         1811        1880
##   Grade_6                                         2292        2404
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              188.866     306.223
##   Degrees of freedom                                23          23
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.614
##   Shift parameter for each group:
##     Grade_7                                                 -0.654
##     Grade_6                                                 -0.827
##     for simple second-order correction (WLSMV)
## 
## Chi-square for each group:
## 
##   Grade_7                                       73.253     118.692
##   Grade_6                                      115.613     187.532
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            16164.928   11074.106
##   Degrees of freedom                                30          30
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.990       0.974
##   Tucker-Lewis Index (TLI)                       0.987       0.967
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.059       0.077
##   90 Percent Confidence Interval          0.052  0.067       0.070  0.085
##   P-value RMSEA <= 0.05                          0.024       0.000
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.036       0.036
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           2.201       2.201
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## 
## Group 1 [Grade_7]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.716    0.012   57.899    0.000    0.716    0.716
##     Dprss2_ (.p2.)    0.660    0.013   52.754    0.000    0.660    0.660
##     Dprss3_ (.p3.)    0.753    0.013   56.194    0.000    0.753    0.753
##     Dprss4_ (.p4.)    0.721    0.013   57.076    0.000    0.721    0.721
##     Dprss5_ (.p5.)    0.607    0.014   43.692    0.000    0.607    0.607
##     Dprss6_ (.p6.)    0.595    0.014   42.733    0.000    0.595    0.595
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##     depress           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f|t1    -0.591    0.031  -18.823    0.000   -0.591   -0.591
##     Depress1_f|t2     0.142    0.030    4.815    0.000    0.142    0.142
##     Depress1_f|t3     1.089    0.037   29.615    0.000    1.089    1.089
##     Depress1_f|t4     1.780    0.055   32.603    0.000    1.780    1.780
##     Depress2_f|t1    -0.945    0.035  -27.179    0.000   -0.945   -0.945
##     Depress2_f|t2    -0.214    0.030   -7.207    0.000   -0.214   -0.214
##     Depress2_f|t3     0.747    0.033   22.882    0.000    0.747    0.747
##     Depress2_f|t4     1.535    0.046   33.163    0.000    1.535    1.535
##     Depress3_f|t1     0.294    0.030    9.830    0.000    0.294    0.294
##     Depress3_f|t2     0.702    0.032   21.768    0.000    0.702    0.702
##     Depress3_f|t3     1.210    0.039   31.178    0.000    1.210    1.210
##     Depress3_f|t4     1.722    0.052   32.881    0.000    1.722    1.722
##     Depress4_f|t1    -0.094    0.030   -3.171    0.002   -0.094   -0.094
##     Depress4_f|t2     0.267    0.030    8.940    0.000    0.267    0.267
##     Depress4_f|t3     0.907    0.034   26.431    0.000    0.907    0.907
##     Depress4_f|t4     1.504    0.045   33.113    0.000    1.504    1.504
##     Depress5_f|t1    -0.394    0.030  -13.003    0.000   -0.394   -0.394
##     Depress5_f|t2     0.070    0.029    2.373    0.018    0.070    0.070
##     Depress5_f|t3     0.697    0.032   21.633    0.000    0.697    0.697
##     Depress5_f|t4     1.279    0.040   31.871    0.000    1.279    1.279
##     Depress6_f|t1    -0.481    0.031  -15.649    0.000   -0.481   -0.481
##     Depress6_f|t2     0.069    0.029    2.326    0.020    0.069    0.069
##     Depress6_f|t3     0.727    0.032   22.393    0.000    0.727    0.727
##     Depress6_f|t4     1.230    0.039   31.398    0.000    1.230    1.230
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           1.000                               1.000    1.000
##    .Depress1_f        0.487                               0.487    0.487
##    .Depress2_f        0.565                               0.565    0.565
##    .Depress3_f        0.434                               0.434    0.434
##    .Depress4_f        0.480                               0.480    0.480
##    .Depress5_f        0.632                               0.632    0.632
##    .Depress6_f        0.646                               0.646    0.646
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
## 
## 
## Group 2 [Grade_6]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.716    0.012   57.899    0.000    0.706    0.706
##     Dprss2_ (.p2.)    0.660    0.013   52.754    0.000    0.650    0.650
##     Dprss3_ (.p3.)    0.753    0.013   56.194    0.000    0.742    0.742
##     Dprss4_ (.p4.)    0.721    0.013   57.076    0.000    0.711    0.711
##     Dprss5_ (.p5.)    0.607    0.014   43.692    0.000    0.598    0.598
##     Dprss6_ (.p6.)    0.595    0.014   42.733    0.000    0.587    0.587
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
##     depress           0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f|t1    -0.543    0.028  -19.641    0.000   -0.543   -0.543
##     Depress1_f|t2     0.125    0.026    4.760    0.000    0.125    0.125
##     Depress1_f|t3     1.100    0.033   33.493    0.000    1.100    1.100
##     Depress1_f|t4     1.791    0.049   36.607    0.000    1.791    1.791
##     Depress2_f|t1    -0.815    0.030  -27.517    0.000   -0.815   -0.815
##     Depress2_f|t2    -0.177    0.026   -6.721    0.000   -0.177   -0.177
##     Depress2_f|t3     0.729    0.029   25.246    0.000    0.729    0.729
##     Depress2_f|t4     1.490    0.040   37.216    0.000    1.490    1.490
##     Depress3_f|t1     0.285    0.027   10.720    0.000    0.285    0.285
##     Depress3_f|t2     0.642    0.028   22.727    0.000    0.642    0.642
##     Depress3_f|t3     1.151    0.034   34.287    0.000    1.151    1.151
##     Depress3_f|t4     1.557    0.042   37.328    0.000    1.557    1.557
##     Depress4_f|t1    -0.117    0.026   -4.468    0.000   -0.117   -0.117
##     Depress4_f|t2     0.246    0.026    9.305    0.000    0.246    0.246
##     Depress4_f|t3     0.874    0.030   28.970    0.000    0.874    0.874
##     Depress4_f|t4     1.386    0.038   36.737    0.000    1.386    1.386
##     Depress5_f|t1    -0.350    0.027  -13.087    0.000   -0.350   -0.350
##     Depress5_f|t2     0.073    0.026    2.798    0.005    0.073    0.073
##     Depress5_f|t3     0.647    0.028   22.888    0.000    0.647    0.647
##     Depress5_f|t4     1.197    0.034   34.915    0.000    1.197    1.197
##     Depress6_f|t1    -0.388    0.027  -14.413    0.000   -0.388   -0.388
##     Depress6_f|t2     0.097    0.026    3.717    0.000    0.097    0.097
##     Depress6_f|t3     0.752    0.029   25.878    0.000    0.752    0.752
##     Depress6_f|t4     1.275    0.036   35.813    0.000    1.275    1.275
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           0.973    0.033   29.086    0.000    1.000    1.000
##    .Depress1_f        0.501                               0.501    0.501
##    .Depress2_f        0.577                               0.577    0.577
##    .Depress3_f        0.449                               0.449    0.449
##    .Depress4_f        0.494                               0.494    0.494
##    .Depress5_f        0.642                               0.642    0.642
##    .Depress6_f        0.655                               0.655    0.655
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
lavTestLRT(fit.config.WLSMV, fit.metric.WLSMV, method = "satorra.bentler.2010", A.method = "delta") 
## Scaled Chi Square Difference Test (method = "satorra.bentler.2010")
## 
##                  Df AIC BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.metric.WLSMV 23         188.87                              
## fit.config.WLSMV 41         210.49     22.609      18     0.2061
## 3. Scalar (Strong) Invariance Test (WLSMV)
model.scalar.WLSMV <- '
depress =~ Depress1_f + Depress2_f + Depress3_f
           + Depress4_f + Depress5_f + Depress6_f
depress ~~ c(1, NA)*depress
depress ~ c(0, NA)*1
'

fit.scalar.WLSMV <- cfa(model = model.scalar.WLSMV, data = dat.inva,
                        mimic = "Mplus", estimator = "WLSMV",
                        std.lv = TRUE, group = "Grade",
                        ordered = c("Depress1_f", "Depress2_f",
                                    "Depress3_f", "Depress4_f",
                                    "Depress5_f", "Depress6_f"),
                        group.equal = c("loadings", "thresholds"))

summary(fit.scalar.WLSMV, fit.measures = TRUE, standardized = TRUE)
## lavaan (0.5-22) converged normally after  28 iterations
## 
##                                                   Used       Total
##   Number of observations per group         
##   Grade_7                                         1811        1880
##   Grade_6                                         2292        2404
## 
##   Estimator                                       DWLS      Robust
##   Minimum Function Test Statistic              201.376     330.890
##   Degrees of freedom                                40          40
##   P-value (Chi-square)                           0.000       0.000
##   Scaling correction factor                                  0.603
##   Shift parameter for each group:
##     Grade_7                                                 -1.415
##     Grade_6                                                 -1.791
##     for simple second-order correction (WLSMV)
## 
## Chi-square for each group:
## 
##   Grade_7                                       79.770     130.929
##   Grade_6                                      121.605     199.960
## 
## Model test baseline model:
## 
##   Minimum Function Test Statistic            16164.928   11074.106
##   Degrees of freedom                                30          30
##   P-value                                        0.000       0.000
## 
## User model versus baseline model:
## 
##   Comparative Fit Index (CFI)                    0.990       0.974
##   Tucker-Lewis Index (TLI)                       0.992       0.980
## 
##   Robust Comparative Fit Index (CFI)                            NA
##   Robust Tucker-Lewis Index (TLI)                               NA
## 
## Root Mean Square Error of Approximation:
## 
##   RMSEA                                          0.044       0.060
##   90 Percent Confidence Interval          0.038  0.051       0.054  0.066
##   P-value RMSEA <= 0.05                          0.933       0.004
## 
##   Robust RMSEA                                                  NA
##   90 Percent Confidence Interval                                NA     NA
## 
## Standardized Root Mean Square Residual:
## 
##   SRMR                                           0.037       0.037
## 
## Weighted Root Mean Square Residual:
## 
##   WRMR                                           2.272       2.272
## 
## Parameter Estimates:
## 
##   Information                                 Expected
##   Standard Errors                           Robust.sem
## 
## 
## Group 1 [Grade_7]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.701    0.013   52.280    0.000    0.701    0.701
##     Dprss2_ (.p2.)    0.656    0.014   47.423    0.000    0.656    0.656
##     Dprss3_ (.p3.)    0.760    0.015   51.164    0.000    0.760    0.760
##     Dprss4_ (.p4.)    0.732    0.014   52.473    0.000    0.732    0.732
##     Dprss5_ (.p5.)    0.607    0.016   38.240    0.000    0.607    0.607
##     Dprss6_ (.p6.)    0.598    0.015   38.679    0.000    0.598    0.598
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           0.000                               0.000    0.000
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Dpr1_|1 (.p9.)   -0.585    0.027  -21.695    0.000   -0.585   -0.585
##     Dpr1_|2 (.10.)    0.121    0.024    4.980    0.000    0.121    0.121
##     Dpr1_|3 (.11.)    1.096    0.032   34.565    0.000    1.096    1.096
##     Dpr1_|4 (.12.)    1.795    0.046   39.334    0.000    1.795    1.795
##     Dpr2_|1 (.13.)   -0.910    0.029  -30.915    0.000   -0.910   -0.910
##     Dpr2_|2 (.14.)   -0.212    0.024   -8.753    0.000   -0.212   -0.212
##     Dpr2_|3 (.15.)    0.746    0.027   27.438    0.000    0.746    0.746
##     Dpr2_|4 (.16.)    1.542    0.039   39.672    0.000    1.542    1.542
##     Dpr3_|1 (.17.)    0.288    0.025   11.342    0.000    0.288    0.288
##     Dpr3_|2 (.18.)    0.685    0.028   24.801    0.000    0.685    0.685
##     Dpr3_|3 (.19.)    1.216    0.034   35.484    0.000    1.216    1.216
##     Dpr3_|4 (.20.)    1.687    0.044   38.020    0.000    1.687    1.687
##     Dpr4_|1 (.21.)   -0.125    0.025   -4.969    0.000   -0.125   -0.125
##     Dpr4_|2 (.22.)    0.255    0.025   10.074    0.000    0.255    0.255
##     Dpr4_|3 (.23.)    0.919    0.030   30.907    0.000    0.919    0.919
##     Dpr4_|4 (.24.)    1.496    0.039   38.156    0.000    1.496    1.496
##     Dpr5_|1 (.25.)   -0.395    0.025  -15.910    0.000   -0.395   -0.395
##     Dpr5_|2 (.26.)    0.063    0.023    2.679    0.007    0.063    0.063
##     Dpr5_|3 (.27.)    0.682    0.027   25.606    0.000    0.682    0.682
##     Dpr5_|4 (.28.)    1.265    0.035   36.580    0.000    1.265    1.265
##     Dpr6_|1 (.29.)   -0.458    0.025  -18.074    0.000   -0.458   -0.458
##     Dpr6_|2 (.30.)    0.076    0.024    3.239    0.001    0.076    0.076
##     Dpr6_|3 (.31.)    0.757    0.027   27.632    0.000    0.757    0.757
##     Dpr6_|4 (.32.)    1.289    0.034   37.387    0.000    1.289    1.289
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           1.000                               1.000    1.000
##    .Depress1_f        0.509                               0.509    0.509
##    .Depress2_f        0.569                               0.569    0.569
##    .Depress3_f        0.423                               0.423    0.423
##    .Depress4_f        0.465                               0.465    0.465
##    .Depress5_f        0.632                               0.632    0.632
##    .Depress6_f        0.643                               0.643    0.643
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        1.000                               1.000    1.000
##     Depress2_f        1.000                               1.000    1.000
##     Depress3_f        1.000                               1.000    1.000
##     Depress4_f        1.000                               1.000    1.000
##     Depress5_f        1.000                               1.000    1.000
##     Depress6_f        1.000                               1.000    1.000
## 
## 
## Group 2 [Grade_6]:
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   depress =~                                                            
##     Dprss1_ (.p1.)    0.701    0.013   52.280    0.000    0.736    0.719
##     Dprss2_ (.p2.)    0.656    0.014   47.423    0.000    0.689    0.653
##     Dprss3_ (.p3.)    0.760    0.015   51.164    0.000    0.798    0.736
##     Dprss4_ (.p4.)    0.732    0.014   52.473    0.000    0.768    0.702
##     Dprss5_ (.p5.)    0.607    0.016   38.240    0.000    0.637    0.598
##     Dprss6_ (.p6.)    0.598    0.015   38.679    0.000    0.627    0.585
## 
## Intercepts:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress          -0.036    0.037   -0.973    0.330   -0.034   -0.034
##    .Depress1_f        0.000                               0.000    0.000
##    .Depress2_f        0.000                               0.000    0.000
##    .Depress3_f        0.000                               0.000    0.000
##    .Depress4_f        0.000                               0.000    0.000
##    .Depress5_f        0.000                               0.000    0.000
##    .Depress6_f        0.000                               0.000    0.000
## 
## Thresholds:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Dpr1_|1 (.p9.)   -0.585    0.027  -21.695    0.000   -0.585   -0.572
##     Dpr1_|2 (.10.)    0.121    0.024    4.980    0.000    0.121    0.118
##     Dpr1_|3 (.11.)    1.096    0.032   34.565    0.000    1.096    1.070
##     Dpr1_|4 (.12.)    1.795    0.046   39.334    0.000    1.795    1.754
##     Dpr2_|1 (.13.)   -0.910    0.029  -30.915    0.000   -0.910   -0.863
##     Dpr2_|2 (.14.)   -0.212    0.024   -8.753    0.000   -0.212   -0.201
##     Dpr2_|3 (.15.)    0.746    0.027   27.438    0.000    0.746    0.708
##     Dpr2_|4 (.16.)    1.542    0.039   39.672    0.000    1.542    1.462
##     Dpr3_|1 (.17.)    0.288    0.025   11.342    0.000    0.288    0.265
##     Dpr3_|2 (.18.)    0.685    0.028   24.801    0.000    0.685    0.631
##     Dpr3_|3 (.19.)    1.216    0.034   35.484    0.000    1.216    1.121
##     Dpr3_|4 (.20.)    1.687    0.044   38.020    0.000    1.687    1.556
##     Dpr4_|1 (.21.)   -0.125    0.025   -4.969    0.000   -0.125   -0.114
##     Dpr4_|2 (.22.)    0.255    0.025   10.074    0.000    0.255    0.233
##     Dpr4_|3 (.23.)    0.919    0.030   30.907    0.000    0.919    0.840
##     Dpr4_|4 (.24.)    1.496    0.039   38.156    0.000    1.496    1.368
##     Dpr5_|1 (.25.)   -0.395    0.025  -15.910    0.000   -0.395   -0.370
##     Dpr5_|2 (.26.)    0.063    0.023    2.679    0.007    0.063    0.059
##     Dpr5_|3 (.27.)    0.682    0.027   25.606    0.000    0.682    0.639
##     Dpr5_|4 (.28.)    1.265    0.035   36.580    0.000    1.265    1.187
##     Dpr6_|1 (.29.)   -0.458    0.025  -18.074    0.000   -0.458   -0.427
##     Dpr6_|2 (.30.)    0.076    0.024    3.239    0.001    0.076    0.071
##     Dpr6_|3 (.31.)    0.757    0.027   27.632    0.000    0.757    0.706
##     Dpr6_|4 (.32.)    1.289    0.034   37.387    0.000    1.289    1.203
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     depress           1.102    0.073   15.043    0.000    1.000    1.000
##    .Depress1_f        0.506                               0.506    0.483
##    .Depress2_f        0.637                               0.637    0.573
##    .Depress3_f        0.540                               0.540    0.459
##    .Depress4_f        0.607                               0.607    0.507
##    .Depress5_f        0.730                               0.730    0.643
##    .Depress6_f        0.755                               0.755    0.657
## 
## Scales y*:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     Depress1_f        0.977    0.025   39.059    0.000    0.977    1.000
##     Depress2_f        0.948    0.023   41.419    0.000    0.948    1.000
##     Depress3_f        0.922    0.026   35.114    0.000    0.922    1.000
##     Depress4_f        0.914    0.025   36.812    0.000    0.914    1.000
##     Depress5_f        0.938    0.026   35.440    0.000    0.938    1.000
##     Depress6_f        0.933    0.026   35.862    0.000    0.933    1.000
lavTestLRT(fit.metric.WLSMV, fit.scalar.WLSMV, method = "satorra.bentler.2010", A.method = "delta")
## Scaled Chi Square Difference Test (method = "satorra.bentler.2010")
## 
##                  Df AIC BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.metric.WLSMV 23         188.87                              
## fit.scalar.WLSMV 40         201.38     21.469      17      0.206
## 4. Metric and Scalar Combined Test (WLSMV)

lavTestLRT(fit.config.WLSMV, fit.scalar.WLSMV, method = "satorra.bentler.2010", A.method = "delta")
## Scaled Chi Square Difference Test (method = "satorra.bentler.2010")
## 
##                  Df AIC BIC  Chisq Chisq diff Df diff Pr(>Chisq)
## fit.scalar.WLSMV 40         201.38                              
## fit.config.WLSMV 41         210.49     1.2625       1     0.2612