Statistics, Department of


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A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfilment of Requirements For the Degree of Doctor of Philosophy, Major: Statistics, Under the Supervision of Professor Walter W. Stroup. Lincoln, Nebraska: May, 2014

Copyright (c) 2014 Elizabeth A. Claassen


In small samples it is well known that the standard methods for estimating variance components in a 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 maximum likelihood-based GLMM estimating algorithm. 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 maximum likelihood estimates and that inferences using the Firth estimates maintain their Type I error rates more closely than the standard methods.

Adviser: Walter W. Stroup