ABSTRACT
This chapter provides more confirmatory flavors of Latent class analysis (LCA), in which a particular number of latent classes are specified, possibly with constraints on the conditional probabilities that capture the dependence structure of the observables. It focuses on conventional approaches to LCA. Treatments and overviews of LCA from conventional perspectives can be found in Collins and Lanza, Dayton, Dayton and Macready, Lazarsfeld and Henry, and McCutcheon. The chapter presents a Bayesian analysis for the general case of polytomous observable and latent variables and also presents Bayesian analysis for the special case of dichotomous observable and latent variables. It discusses strategies for resolving indeterminacies associated with the use of discrete latent variables. Analysts employ discrete latent variables when they want to organize their thinking about examinees in terms of categories or groupings, as opposed to organizing their thinking about examinees along a continuum by using continuous latent variables.
