Chapter 4 - Advances in Latent Variable Measurement Modeling

Abstract

Latent variable mixture modeling is part of a latent variable modeling framework and is flexible with regard to the type of data that can be analyzed. Observed variables used to determine latent classes (LCs) can be continuous, censored, binary, ordered/unordered categorical counts, or combinations of these variable types, and the data can be collected in a cross-sectional and/or longitudinal manner. Consequently, a diverse array of research questions involving LCs can be investigated. For example, hypotheses can focus on predicting class membership, identifying mean differences in outcomes across LCs, or describing the extent to which LC membership moderates the relationship between two or more variables. The literature has used many names to describe mixture modeling, or finite mixture modeling as it is known in the statistics literature. Names vary according to the type of data used for indicators (continuous vs. categorical, akin to cross-sectional latent profile analysis vs. latent class analysis, etc.), whether continuous latent variables are included with categorical latent class variables (cross-sectional factor mixture models, longitudinal growth mixture models), whether the data were collected cross-sectionally or longitudinally (latent class vs. latent transition), and whether variability is allowed within the LCs (latent class growth modeling vs. growth mixture modeling).