Latent Variable Analysis With Categorical Outcomes: Multiple-Group And Growth Modeling In Mplus

This note describes latent variable modeling with categorical outcomes in several groups and for longitudinal data. Different parameterizations are discussed as well as issues of identification. A comparison is made between formulating the modeling in terms of conditional probabilities versus using a latent response variable formulation. Two parameterizations used in Mplus are described, including a new parameterization introduced in Version 2.1, May 2002. Differences between binary outcomes and polytomous outcomes are discussed. The LISREL approach is also presented and compared to the Mplus approaches. It is shown that the Mplus approach avoids the LISREL restriction of across-group or across-time invariance of all thresholds parameters, making it possible to study (partial) non invariance also in the thresholds. The techniques are illustrated by factor analysis of antisocial behavior items and by Monte Carlo simulation examples of multiple-group factor analysis and growth modeling, showing good chi-square testing and estimation performance at rather low sample sizes.