Categorical Causal Modeling: Latent Class Analysis and Directed Log-Linear Models with Latent Variables

Latent class analysis (LCA) is an extremely useful and flexible technique for the analysis of categorical data, measured at the nominal, ordinal, or interval level (the latter with fixed or estimated scores). It is, first, a general measurement model, a particular kind of latent structure model that can be used for the investigation of the reliability and validity of categorical measurements, taking both random and systematic response errors into account. When dealing with test-retest effects, response consistency effects, unobserved heterogeneity, response effects from varying survey (interviewing) conditions, and so on, it is useful to take a consistent causal modeling point of view and to integrate LCA into a general causal log-linear model with latent variables. The resulting directed log-linear modeling approach integrates insights from Goodman's modified path approach, the modified LISREL approach, and directed graphical modeling.