This short course discusses recent advances in latent variable modeling. Models and applications are discussed using the general modeling framework of the Mplus program (www.statmodel.com). The generality of the Mplus framework comes from the unique use of both continuous and categorical latent variables. While continuous latent variables have seen frequent use in factor analysis, structural equation modeling, and random effects growth modeling, modeling that includes categorical latent variables, i.e. finite mixture modeling, is less wide spread in practice. The short course focuses on recently developed models that use categorical latent variables, either alone or together with continuous latent variables. An overview of conventional and new techniques is given including complier-average causal effect estimation (regression mixture analysis), latent class analysis, factor and IRT mixture modeling, latent transition analysis, growth mixture modeling, and survival analysis with latent variables. For each topic, issues of model specification, identification, ML estimation, testing, and model modification are discussed. Several health examples are examined. Modeling strategies are presented. Mplus input setups are provided and Mplus output is used for interpretation of analysis results. The presentation is in lecture format with no need for computer analyses.

Course content:

Categorical latent variable modeling with cross-sectional data

- Linear, logit, and count regression mixture analysis

- Randomized response modeling of sensitive questions

- Complier-average causal effect (CACE) estimation in randomized trials

- Latent class analysis

- Latent class analysis with covariates

- Confirmatory latent class analysis. Twin modeling

- Violations of conditional independence

- Factor mixture modeling, IRT mixture modeling

Categorical latent variable modeling with longitudinal data

- Hidden Markov modeling, latent transition analysis

- Latent class growth analysis

- Growth mixture modeling with latent trajectory classes

- Randomized trials and treatment effects varying across latent trajectory classes

- Latent class growth analysis vs. growth mixture modeling

- Numerical integration, mixtures, and non-parametric representation of factor (random effect) distributions

- Discrete- and continuous-time survival modeling with latent variables