Ben Kite, Center for Research Methods and Data Analysis, University of Kansas <bakite@ku.edu>
Please visit http://crmda.ku.edu/guides
Keywords: Structural Equation Modeling, Latent Growth Curve Model, R, lavaan
2019 February 01
Abstract
This guide outlines how to specify and fit a basic latent growth curve model in R using the lavaan package. The estimation results can be compared to the same model fitted with Mplus.Load the lavaan package.
library(lavaan)This is lavaan 0.6-3lavaan is BETA software! Please report any bugs.Load the data, give the columns names.
dat <- read.table("../../data/anxiety.dat", header = F)
names(dat) <- c("a1", "a2", "a3", "a4")Build the LGC model with lavaan syntax. Here we are specifying a linear slope. Notice how the manifest variable intercepts are fixed to 0, and the last two lines request the means for the intercept and slope latent variables.
model <-
' intercept =~ 1*a1 + 1*a2 + 1*a3 + 1*a4
slope =~ 0*a1 + 1*a2 + 2*a3 + 3*a4
a1 ~ 0*1
a2 ~ 0*1
a3 ~ 0*1
a4 ~ 0*1
intercept ~ 1
slope ~ 1
'Run the model using the sem function, request a summary of the output.
output <- sem(model, data = dat)
summary(output, standardized = TRUE, fit.measures = TRUE)lavaan 0.6-3 ended normally after 45 iterations
Optimization method NLMINB
Number of free parameters 9
Number of observations 485
Estimator ML
Model Fit Test Statistic 27.288
Degrees of freedom 5
P-value (Chi-square) 0.000
Model test baseline model:
Minimum Function Test Statistic 1182.102
Degrees of freedom 6
P-value 0.000
User model versus baseline model:
Comparative Fit Index (CFI) 0.981
Tucker-Lewis Index (TLI) 0.977
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -567.499
Loglikelihood unrestricted model (H1) -553.855
Number of free parameters 9
Akaike (AIC) 1152.997
Bayesian (BIC) 1190.654
Sample-size adjusted Bayesian (BIC) 1162.089
Root Mean Square Error of Approximation:
RMSEA 0.096
90 Percent Confidence Interval 0.063 0.133
P-value RMSEA <= 0.05 0.013
Standardized Root Mean Square Residual:
SRMR 0.053
Parameter Estimates:
Information Expected
Information saturated (h1) model Structured
Standard Errors Standard
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
intercept =~
a1 1.000 0.388 0.833
a2 1.000 0.388 0.906
a3 1.000 0.388 0.911
a4 1.000 0.388 0.903
slope =~
a1 0.000 0.000 0.000
a2 1.000 0.083 0.193
a3 2.000 0.166 0.389
a4 3.000 0.249 0.578
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
intercept ~~
slope -0.011 0.003 -3.472 0.001 -0.349 -0.349
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.a1 0.000 0.000 0.000
.a2 0.000 0.000 0.000
.a3 0.000 0.000 0.000
.a4 0.000 0.000 0.000
intercept 0.698 0.020 35.050 0.000 1.796 1.796
slope -0.062 0.006 -10.513 0.000 -0.753 -0.753
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.a1 0.067 0.007 8.910 0.000 0.067 0.306
.a2 0.048 0.004 11.119 0.000 0.048 0.264
.a3 0.048 0.004 11.383 0.000 0.048 0.265
.a4 0.040 0.006 6.658 0.000 0.040 0.215
intercept 0.151 0.013 11.871 0.000 1.000 1.000
slope 0.007 0.001 4.790 0.000 1.000 1.000R version 3.5.1 (2018-07-02)
Platform: x86_64-redhat-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)
Matrix products: default
BLAS/LAPACK: /usr/lib64/R/lib/libRblas.so
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lavaan_0.6-3 stationery_0.98.5.7
loaded via a namespace (and not attached):
[1] Rcpp_1.0.0 digest_0.6.18 MASS_7.3-51.1 plyr_1.8.4
[5] xtable_1.8-3 magrittr_1.5 stats4_3.5.1 evaluate_0.12
[9] zip_1.0.0 stringi_1.2.4 pbivnorm_0.6.0 openxlsx_4.1.0
[13] rmarkdown_1.11 tools_3.5.1 stringr_1.3.1 foreign_0.8-71
[17] kutils_1.59 yaml_2.2.0 xfun_0.4 compiler_3.5.1
[21] mnormt_1.5-5 htmltools_0.3.6 knitr_1.21 Available under Created Commons license 3.0 