Introduction to latent class / profile analysis

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. He 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.


Related Articles

A reviewer recently asked me to comment on the issue of equivalent models in my structural equation model. What is the difference between alternative models and equivalent models within an SEM?

An equivalent model can be thought of as a re-parameterization of the original model. In other words, it is just a different way of “packaging” the same information in the data and no equivalent model can be distinguished from another based on fit alone. If you were to fit a series of equivalent models to the same sample data you obtain exactly the same chi-square test statistic, RMSEA, CFI, TLI, and any other omnibus measure of fit. It is often best to treat this as a limitation of any given study and to potentially present one or a small number of equivalent model options to the reader so that these too might be considered as plausible representations of the data.


Your email address will not be published. Required fields are marked *