Statistics/Applied Math Seminar
Comparison of Generalized Linear Mixed Model Estimation Methods
Abstract: In this talk, I will explore the estimation properties of generalized linear mixed models (GLMMs) with a simulation study. Generalized linear mixed models arose from the necessity to analyze non-normal responses that are correlated or clustered in some way, relying on generalized linear and linear mixed model theory. The likelihood functions of these models lack closed form solutions for parameter estimates and as such, several likelihood-based approximation methods have been developed for inference in GLMMs along with Bayesian approaches, which rely on Markov chain Monte Carlo methods. Through a simulation study, the accuracy and precision of four methods (Laplace approximation, adaptive Gaussian-Hermite Quadrature, Penalized Quasi-likelihood, and a Bayesian hierarchical model) are assessed on simulated responses generated from a biological dataset at multiple sample sizes. While a large dataset (n=599) shows precise and accurate estimation of parameters, smaller datasets (n<250) show dramatic bias in estimation of variance components for likelihood-based methods. The exhibited bias indicates that caution should be exercised when applying these methods to small datasets and that further work needs to be done to explore the properties of these estimation methods.
Tuesday, February 19 at 1:05 pm
Fisher Hall, 326
1400 Townsend Drive, Houghton, MI 49931