Dirichlet generalizations of latent-class models

With a latent-class model, each individual belongs to a single latent class , which determines the person's set of response probabilities for the obser ved, or manifest, variables. A more general model, proposed herein, adds a single parameter and involves drawing, separately and independently for eac h individual, a latent set of mixing weights from a Dirichlet distribution whose dispersion is governed by the added parameter. The person's set of re sponse probabilities then consists of weighted averages of the probabilitie s for the classes, where the weights are the person's Dirichlet values. The posterior probabilities commonly used under latent-class models generalize under Dirichlet models to posterior expectations, which serve much the sam e function. We give examples of formulations of the Dirichlet model, along with numerical illustrations using published data. The first two model form ulations involve Guttman scaling and panel analysis and effectively have no latent-class models that compete.