Vermunt extends latent class (LC) and finite mixture models to hierarchical (multilevel) data. As in ordinary multilevel analysis, dependence among lower-level units nested within higher-level units is handled by letting certain model parameters vary randomly across the higher-level observations. Several variants arise depending on where the random effects enter; the paper focuses on an LC model with discrete random effects, which clusters higher-level units by the likelihood of their members' class memberships and yields mixture distributions at two levels (group and subject). Three empirical examples illustrate the models, and an appendix gives an adapted EM algorithm for maximum-likelihood estimation.
"The variant that receives most attention in this article is an LC model with discrete random effects: higher-level units are clustered based on the likelihood of their members belonging to the various LCs. This yields a model with mixture distributions at two levels, namely at the group and the subject level."
This is the paper that makes "latent class model" and "multilevel model" compose cleanly: instead of choosing between soft clustering of subjects and random-effects pooling across groups, you get both, and — in the discrete-random-effects version — the appealing symmetry of classes of subjects nested in classes of groups. That two-level-mixture idea is the practical heart of multilevel LCA in Latent GOLD and is the LC analogue of the multilevel ordinal/nominal models on the wiki. It also sits on a different dependence axis from the within-subject fixes on the LC page (beta-binomial, Gaussian random effects): those absorb residual association within a class; this one models association across the hierarchy. The cost is the usual multilevel-mixture burden — more latent structure, label-switching at two levels, and heavier identification demands.