Iteratively Reweighted Poisson Regression for Fitting Generalized Linear Model with Multiple Responses

• Activity Number: 574
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Yiwen Zhang*+ and Hua Zhou
• Companies: North Carolina State University and North Carolina State University
• Keywords: Dirichlet-multinomial ; GLM ; MM algorithm ; multinomial-logit ; multiple responses ; negative-multinomial

Abstract

Generalized linear models with multiple responses (MGLMs) are seeing wider use in modern applications such as pattern recognition, document clustering, and image reconstruction. Examples of MGLMs include multinomial-logit models, Dirichlet-multinomial overdispersion models, and negative-multinomial models. Maximum likelihood estimation of MGLMs is difficult due to the high-dimensionality of the parameter space and possible non-concavity of the log-likelihood function. In this article, we propose iteratively reweighted Poisson regression as a unified framework for maximum likelihood estimation of MGLMs. The derivation hinges on the minorization-maximization (MM) principle which generalizes the celebrated expectation-maximization (EM) algorithm. MM algorithm operates by constructing a surrogate function with parameters separated. Optimizing such a surrogate function drives the objective function in the correct direction. This leads to a stable algorithm which possesses good global convergence property and is extremely simple to code. The proposed algorithm is tested on classical and modern examples.