A simple and fast alternative to the EM algorithm for incomplete categorical data and latent class models

Abstract

Incomplete categorical data and latent class models play an important role in biostatistical and medical literature. The most common maximum likelihood procedure for accommodating these types of models is the EM algorithm. We present a faster alternative to these EM approaches that improves upon a recently introduced maximum likelihood-based alternative by Molenberghs and Goetghebeur (1997. J. Roy. Statist. Soc. Ser. B 59, 401–414) in two ways: by accommodating higher-dimensional problems via more time points in longitudinal problems and by employing a less tedious iteratively reweighted least-squares (IRLS) approach than the Newton–Raphson procedure used by MG. This IRLS approach also will facilitate the potential extension to models with random effects in the context of complete and incomplete categorical data and latent classes. We illustrate our method with a latent class application. As with the MG approach, we maximize the observed likelihood instead of the complete data likelihood under a multivariate generalized logistic model with composite link function. This results in a faster convergence rate than the EM algorithm, and allowing easily obtainable variance estimates. We illustrate the proposed estimation procedure using data from an HIV study involving four dichotomous tests measured on each individual, assuming a latent class disease variable with two levels.