Longitudinal Research Using Mixture Models

This chapter provides a state-of-the-art overview of the use of mixture and latent class models for the analysis of longitudinal data. It first describes the three basic types mixture models for longitudinal data: the mixture growth, mixture Markov, and latent Markov model. Subsequently, it presents an integrating framework merging various recent developments in software and algorithms, yielding mixture models for longitudinal data that can (1) not only be used with categorical, but also with continuous response variables (as well as combinations of these), (2) be used with very long time series, (3) include covariates (which can be numeric or categorical, as well as time-constant or time-varying), (4) include parameter restrictions yielding interesting measurement models, and (5) deal with missing values (which is very important in longitudinal research). Moreover, it discusses other advanced models, such as latent Markov models with dependent classification errors across time points, mixture growth and latent Markov models with random effects, and latent Markov models for multilevel data and multiple processes. The appendix shows how the presented models can be defined using the Latent GOLD syntax system (Vermunt and Magidson, 2005, 2008).