Although latent class analysis (LCA) and latent profile analysis (LPA) were developed decades ago, these models have gained increasing recent prominence as tools for understanding heterogeneity within multivariate data. Dan introduces these models through a hypothetical example where the goal is to identify voter blocks within the Republican Party by surveying which issues voters regard as most important...

Dan begins by contrasting LCA/LPA models to the more familiar factor analysis model: Whereas factor analysis assumes that individuals differ by degrees on continuous latent dimensions (e.g., fiscal conservatism, social conservatism), LCA/LPA models instead posit that individuals fall into latent categories (e.g., fiscal conservatives, social conservatives). Dan then describes the implementation and interpretation of LCA/LPA models and the potential inclusion of predictors and outcomes of class membership. He also briefly notes several advanced extensions of LCA/LPA, including latent transition analysis, growth mixture modeling, and factor mixture models.

Early references on LCA and LPA include:

Gibson, W. A. (1959). Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 24, 229–252.

Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mifflin.