A Hybrid Bayesian Laplacian Approach for Generalized Linear Mixed Models

• Activity Number: 27
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Marinela Capanu*+ and Mithat Gonen and Colin B. Begg
• Companies: Memorial Sloan-Kettering Cancer Center and Memorial Sloan-Kettering Cancer Center and Memorial Sloan-Kettering Cancer Center
• Keywords: PQL ; generalized linear mixed model ; pseudo-likelihood ; Bayesian ; Laplace ; binary cluster data

Abstract

The analytical intractability of generalized linear mixed models has generated a lot of research in the past two decades. Two main classes of approximations have been developed: likelihood-based methods and Bayesian methods. Many of the proposed methods have been shown to produce biased estimates especially for certain settings such as binary clustered data with small cluster sizes, or are known to be computationally intensive, limiting their use in practice. In this article we build on our previous method (Capanu and Begg, Biometrics, 2010) and propose a hybrid approach that provides a bridge between the likelihood-based and Bayesian approaches by employing Bayesian estimation for the variance components followed by Laplacian estimation for the regression coefficients with the goal of obtaining good statistical properties, with relatively good computing speed, and using widely available software. The hybrid approach is shown to perform well against the other competitors considered. We illustrate the methods using simulations based on the widely-analyzed salamander mating dataset and on another important dataset involving the Guatemalan Child Health survey.