Measurement Invariance and Differential Item Functioning in Latent Class Analysis With Stepwise Multiple Indicator Multiple Cause Modeling

The use of latent class analysis, and finite mixture modeling more generally, has become almost commonplace in social and health science domains. Typically, research aims in mixture model applications include investigating predictors and distal outcomes of latent class membership. The most recent developments for incorporating latent class antecedents and consequences are stepwise procedures that decouple the classification and prediction models. It was initially believed these procedures might avoid the potential misspecification bias in the simultaneous models that include both latent class indicators and predictors. However, if direct effects from the predictors to the indicators are omitted in the stepwise procedure, the prediction model can yield biased estimates. This article presents a logical and principled approach, readily implemented in current software, to testing for direct effects from latent class predictors to indicators using multiple indicator multiple cause modeling. This approach is illustrated with real data and opportunities for future developments are discussed.