Mixture modeling refers to modeling with categorical latent variables that represent subpopulations where population membership is not known but is inferred from the data. This is referred to as finite mixture modeling in statistics (McLachlan & Peel, 2000).
A special case is latent class analysis (LCA) where the latent classes explain the relationships among the observed dependent variables similar to factor analysis. In contrast to factor analysis, however, LCA provides classification of individuals. Confirmatory LCA with multiple categorical latent variables can be estimated. In Mplus, mixture modeling can be applied to any of the analyses discussed in the other example chapters including regression analysis, path analysis, confirmatory factor analysis (CFA), structural equation modeling (SEM), growth modeling, and multilevel modeling. Observed dependent variables can be continuous, censored, binary, ordered categorical (ordinal), unordered categorical (nominal), counts, or combinations of these variable types. LCA and general mixture models can be extended to include continuous latent variables.
In mixture modeling with longitudinal data, unobserved heterogeneity in the development of an outcome over time is captured by categorical and continuous latent variables. The simplest longitudinal mixture model is latent class growth analysis (LCGA). In LCGA, the mixture corresponds to different latent trajectory classes. No variation across individuals is allowed within classes (Nagin, 1999; Roeder, Lynch, & Nagin, 1999). Another longitudinal mixture model is the growth mixture model (GMM). In GMM, within-class variation is allowed for the latent trajectory classes. The within-class variation is represented by random effects, that is, continuous latent variables, as in regular growth modeling (Muthén & Shedden, 1999; Muthén et al., 2002). All of the growth models discussed in Chapter 6 can be generalized to mixture modeling. Yet another mixture model for analyzing longitudinal data is latent transition analysis (LTA; Collins & Wugalter, 1992; Reboussin et al., 1998), also referred to as hidden Markov modeling, where latent class indicators are measured over time and individuals are allowed to transition between latent classes. With discrete-time survival mixture analysis (DTSMA; Muthén & Masyn, 2004), the repeated observed outcomes represent event histories. For mixture modeling with longitudinal data, observed outcome variables can be continuous, censored, binary, ordered categorical (ordinal), counts, or combinations of these variable types.
For both cross-sectional and longitudinal mixture modeling, Mplus has three estimator choices for all dependent variable types: maximum likelihood (ML) and maximum likelihood with robust standard errors and chi-square (MLR, MLF).