Multiple Group Confirmatory Factor Analysis (Scalar Invariance) Example
Multiple Group Confirmatory Factor Analysis (Scalar Invariance) Example
Tags: SEM, Measurement Invariance, Scalar Invariance, Equal , Mplus
2019-02-04
Abstract: This guide outlines how to perform the third step/test in measurement invariance testing - scalar invariance (or equal intercepts). The model estimation results can be compared to the Measurement Invariance Example in R. NOTE: The model estimation terminated normally with Mplus 8.0, but encountered estimation issues with Mplus 8.2 - the output files from both are provided here.
Table of Contents
1 The lavaan Example
2 TITLE Command
This is the third and final input file for this example.
TITLE: Example 3 - Multiple Group Confirmatory Factor Analysis (Scalar Invariance)
3 DATA Command
DATA: FILE IS "../../data/job_placement.csv";
4 VARIABLE Command
VARIABLE: NAMES ARE id wjcalc wjspl wratspl wratcalc waiscalc waisspl edlevel newschl suspend expelled haveld female age; USEVARIABLES ARE wratcalc wjcalc waiscalc wratspl wjspl waisspl; MISSING ARE all(99999); GROUPING IS female(0=male 1=female);
5 MODEL Command
Again, the only changes come in the MODEL command. Here the item intercepts need to be constrained across groups, this is accomplished by removing the "[wratcalc wjcalc waiscalc wratspl wjspl waisspl];" line from the "MODEL female:" section. Further, the constraints that set the latent variable means for females "[MATH@0 SPELL@0];" should be removed (resulting in "[MATH SPELL];"). Now the latent variable means and variances are freely estimated for females.
MODEL: MATH BY wratcalc* wjcalc waiscalc; SPELL BY wratspl* wjspl waisspl; [wratcalc wjcalc waiscalc wratspl wjspl waisspl]; MATH@1 SPELL@1; [MATH@0 SPELL@0]; MODEL female: MATH SPELL; [MATH SPELL];
6 OUTPUT Command
Additional output can be requested.
OUTPUT: SAMPSTAT; TECH1; STANDARDIZED;
7 Run the Model with Mplus 8.0
mplus8 cfa-01-3-scalar.inp
Mplus VERSION 8 (Linux) MUTHEN & MUTHEN Running input file 'cfa-01-3-scalar.inp'... Beginning Time: 10:12:37 Ending Time: 10:12:37 Elapsed Time: 00:00:00 Output saved in 'cfa-01-3-scalar.out'.
8 Review the Results from Mplus 8.0
Click cfa-01-3-scalar.out to see the output.
9 Review the Results from Mplus 8.2
Click cfa-01-3-scalar-mplus-82.out to see the output.