Chapter 6: General Random Effect Latent Variable Modeling: Random Subjects, Items, Contexts, and Parameters

Bayesian methodology can be used to estimate cluster specific structural equation models with two-level data where all measurement and structural coefficients, including intercepts, factor loadings, and regression coefficients can be estimated as cluster-level random effects rather than fixed parameters. Bayesian methodology is also well suited for estimating latent variable models where subjects are not the only random mode, but also items and contexts. A general cross-classified structural equation model is presented where observations are nested within two independent clustering variables. The models include continuous and categorical dependent variables. Various applications are discussed. The random loading model is used for estimating multiple group factor analysis models with a large number of groups and measurement non-invariance. Individual differences factor analysis model is described in which factor loadings, as well as factor means and variances, are individual-specific. This model is demonstrated using ecological momentary assessment data for mood disorders. Finally, the cross-classified structural framework is demonstrated using time intensive longitudinal structural models.