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 observed, or manifest, variables. A more general model, proposed herein, adds a single parameter and involves drawing, separately and independently for each individual, a latent set of mixing weights from a Dirichlet distribution whose dispersion is governed by the added parameter. The person's set of response probabilities then consists of weighted averages of the probabilities 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 same function. We give examples of formulations of the Dirichlet model, along with numerical illustrations using published data. The first two model formulations involve Guttman scaling and panel analysis and effectively have no latent-class models that compete.

Duke Scholars

Author Kenneth G. Manton Trinity College of Arts & Sciences