A mixture likelihood approach for generalized linear models

A mixture model approach is developed that simultaneously estimates the posterior membership probabilities of observations to a number of unobservable groups or latent classes, and the parameters of a generalized linear model which relates the observations, distributed according to some member of the exponential family, to a set of specified covariates within each Class. We demonstrate how this approach handles many of the existing latent class regression procedures as special cases, as well as a host of other parametric specifications in the exponential family heretofore not mentioned in the latent class literature. As such we generalize the McCullagh and Nelder approach to a latent class framework. The parameters are estimated using maximum likelihood, and an EM algorithm for estimation is provided. A Monte Carlo study of the performance of the algorithm for several distributions is provided, and the model is illustrated in two empirical applications.     

A latent class vector model for preference ratings

A latent class formulation of the well-known vector model for preference data is presented. Assuming preference ratings as input data, the model simultaneously clusters the subjects into a small number of homogeneous groups (or latent classes) and constructs a joint geometric representation of the choice objects and the latent classes according to a vector model. The distributional assumptions on which the latent class approach is based are analogous to the distributional assumptions that are consistent with the common practice of fitting the vector model to preference data by least squares methods. An EM algorithm for fitting the latent class vector model is described as well as a procedure for selecting the appropriate number of classes and the appropriate number of dimensions. Some illustrative applications of the latent class vector model are presented and some possible extensions are discussed. Geert De Soete is supported as “Bevoegdverklaard Navorser” of the Belgian “Nationaal Fonds voor Wetenschappelijk Onderzoek.”     

A latent class procedure for the structural analysis of two-way compositional data

This paper develops a new procedure for simultaneously performing multidimensional scaling and cluster analysis on two-way compositional data of proportions. The objective of the proposed procedure is to delineate patterns of variability in compositions across subjects by simultaneously clustering subjects into latent classes or groups and estimating a joint space of stimulus coordinates and class-specific vectors in a multidimensional space. We use a conditional mixture, maximum likelihood framework with an E-M algorithm for parameter estimation. The proposed procedure is illustrated using a compositional data set reflecting proportions of viewing time across television networks for an area sample of households.