An encyclopedia review of latent class (LC) analysis (International Encyclopedia of Education, 4th ed.). Vermunt frames a model as "latent class / mixture" whenever some of its parameters differ across unobserved subgroups, and shows that this single idea unifies four seemingly unrelated applications: clustering, scaling, density estimation, and random-effects modeling. The article describes simple LC models for clustering, restricted LC models for scaling, and mixture-regression models for nonparametric random-effects modeling, and reviews maximum-likelihood estimation, identification, model selection, recent developments, and software.
"A statistical model can be called a latent class (LC) or mixture model if it assumes that some of its parameters differ across unobserved subgroups, latent classes, or mixture components. This rather general idea has several seemingly unrelated applications, the most important of which are clustering, scaling, density estimation, and random-effects modeling."
A clean, authoritative map of a field that is easy to get lost in because the same machinery wears many names. The most useful organizing move is Vermunt's insistence that clustering, scaling, density estimation, and random-effects modeling are all one mixture engine under constraints — which is exactly the "one finite-mixture engine, several applied models" theme the wiki's latent-class and Magidson-Vermunt material already develops. Its distinctive practical contribution here is foregrounding three-step analysis and its bias correction, the workflow most applied users actually run and most get subtly wrong. As a review it adds breadth (latent Markov, growth mixtures) rather than new theory, and it complements — rather than supersedes — the identifiability and misspecification cautions (Albert-Dodd) that the concept page keeps front and center.