A Mixture Likelihood Approach for Generalized Linear-Models

Abstract: A mixture model approach is developed that simultaneously estimates the posterior membership robabilities of observations to a number of unobserv-able 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 demon-strate how this approach andles many of the existing latent class regression pro-cedures 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 i provided, and the model is illustrated in two empirical applications