A Comparison of Statistics for Assessing Model Invariance in Latent Class Analysis

Latent class analysis (LCA) is a widely used statistical technique for identifying subgroups in the population based upon multiple indicator variables. It has a number of advantages over other un-supervised grouping procedures such as cluster analysis, including stronger theoretical under-pinnings, more clearly defined measures of model fit, and the ability to conduct confirmatory ana-lyses. In addition, it is possible to ascertain whether an LCA solution is equally applicable to mul-tiple known groups, using invariance assessment techniques. This study compared the effective-ness of multiple statistics for detecting group LCA invariance, including a chi-square difference test, a bootstrap likelihood ratio test, and several information indices. Results of the simulation study found that the bootstrap likelihood ratio test was the optimal invariance assessment statis-tic. In addition to the simulation, LCA group invariance assessment was demonstrated in an appli-cation with the Youth Risk Behavior Survey (YRBS). Implications of the simulation results for practice are discussed