A mixture likelihood approach for generalized linear models

Abstract

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.

Latent class models for financial data analysis: some statistical developments

“…In order to avoid the problem of likelihood convergence into a local maximum which occurs frequently in LC models, especially when the number of variables is large and the sample size is small (Wedel and DeSarbo, 1995), many different starting values are used. For more background and details on the EM algorithm, see McLachlan and Krishnan (1997).…”

Erratum to: The Generalized Linear Mixed Cluster-Weighted Model

“…Maximization of (17), over β g (and possibly λ g ), can be carried out numerically; details can be found in Wedel and De Sarbo (1995) and Wedel and Kamakura (2001, pp. 120-124), where mixtures of generalized linear models are discussed.…”

“…For example, in healthcare studies, a typical response is the length of stay, while in the educational framework, the response is often the item-category chosen in some test. In the literature about mixture mod-els, such problems are usually approached considering mixtures of generalized linear models (see, e.g., McLachlan 1997, McLachlan and Peel 2000, Wedel and De Sarbo 1995. We remark that Gershenfeld (1999) also coped with the problem of discrete sets of values, such as events, patterns, or conditions, but without really modeling the joint probability of the dependent variable and the covariates.…”

Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects

“…Finite mixtures of multinomial and conditional logit models are part of the GLIMMIX framework (Wedel and DeSarbo, 1995) which covers finite mixtures of generalized linear models. Finite mixtures of multinomial logit models are applied in many different areas including for example medicine (Aitkin, 1999) or economics.…”