Maximum Likelihood Estimation with Binary Data Regression Models: Small-Sample and Large-Sample Features

• Activity Number: 534
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Roland C. Deutsch*+ and John M. Grego and Brian Habing and Walter W. Piegorsch
• Companies: The University of North Carolina at Greensboro and University of South Carolina and University of South Carolina and The University of Arizona
• Keywords: Binomial Response Models ; Maximum Likelihood Estimator ; Asymptotic Normality ; Complementary Log-Log Link ; Complementary Log Link

Abstract

Many inferential procedures for generalized linear models rely on the asymptotic normality of the MLE. Fahrmeir & Kaufmann (1985) present mild conditions under which the MLEs in GLiMs are asymptotically normal. Limited study has appeared for binomial response models beyond the familiar logit and probit links, and for more general links such as the complementary log-log link, and the less well-known complementary log link. We verify the asymptotic normality conditions of the MLEs for these models under the assumption of a fixed number of experimental groups and present a simple set of conditions for any twice differentiable monotone link function. We also study the quality of the approximation for constructing asymptotic Wald confidence regions. Our results show that for small sample sizes with certain link functions, the approximation can be problematic (i.e. boundary cases)