Finite Mixture Multivariate Generalized Linear Models Using Gibbs Sampling and E-M Algorithms

Finite mixture multivariate generalized linear modeling has been shown to be an important analytic tool for many research fields, for example, image recognition, astronomical data classification, biomedicine diagnosis, and biological classification. Recent statistical and computational advances have further encouraged researchers to explore the modeling possibility using the Bayesian framework. We compare Expectation (E)-Maximization (M) algorithms for maximum likelihood estimation of classical statistics with Gibbs sampling methods of Bayesian statistics in estimating finite mixture multivariate generalized linear models. A Monte Carlo study to compare the two methods is provided for practical reference. We also propose two finite mixture multivariate generalized linear models that can allow more flexibility in modeling substantive applications. The Longitudinal Study of American Youth (LSAY) data set is also analyzed as a practical application.