Improved Estimation and Inference in the Generalized Linear Mixed Model with Firth Estimates

• Activity Number: 444
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Christopher Gotwalt*+ and Elizabeth Claassen and Walt Stroup
• Companies: SAS Institute and University of Nebraska and University of Nebraska-Lincoln
• Keywords: Generalize Linear Mixed Model ; Firth Estimate

Abstract

In small samples it is well known that the standard methods for estimating variance components in the generalized linear mixed model (GLMM), pseudo-likelihood and maximum likelihood, yield estimates that are biased downward. An important consequence of this is that inferences on fixed effects will have inflated type I error rates because their precision is overstated. We introduce a new method for estimating parameters in GLMMs that applies a Firth bias adjustment to the likelihood based GLMM estimating equation. We apply this technique to one and two treatment logistic regression models with a single random effect. We show simulation results that demonstrate that the Firth adjusted variance component estimates are substantially less biased than pseudo-likelihood and maximum likelihood and that inferences using the Firth estimates maintain their type I error rates more closely than the standard methods.