# 7. Four Useful Finite Mixture Models for Regression Analyses of Panel Data with a Categorical Dependent Variable

Abstract

This paper describes and contrasts two useful ways to employ a latent class variable as a mixture variable in regression analyses of panel data with a categorical dependent variable. One way is to model unobserved heterogeneity in the trajectory, or change in the distribution, of the dependent variable. Two models that accomplish this are the latent trajectory model and latent growth curve model for a categorical dependent variable having ordered categories. Each latent class here represents a distinct trajectory of the dependent variable. The latent trajectory model introduces covariate effects on the composition of latent classes, while the latent growth curve model introduces covariate effects on both the “intercept” and the “slope” of growth in logit, which may vary among latent classes.The other useful way is to model unobserved heterogeneity in the state dependence of the dependent variable. Two models that accomplish this are introduced for a simultaneous analysis of response probability and respon...