Presentation: Improved Bias Reduction for Generalized Linear Models
Candidate: Andrew Humbert, Graduate Student, UW Biostatistics
Committee Members: Brian Leroux (co-chair), Noah Simon (co-chair), Marco Carone, Susanne May, Joseph (Chris) Delaney (GSR)
Abstract: Generalized linear models (GLMs) are regression models that allow the specification of a working distribution from the exponential family as well as a nonlinear relationship between covariates and outcomes. Maximum likelihood estimators (MLEs) for the coefficients are asymptotically normal and consistent, even under some types of model misspecification. In small sample settings, however, the MLEs for GLMs may be biased. Bias approximations have been developed but little is known about how bias is impacted by the distribution of outcomes, distribution of predictors, parameter values, and sample size. Firth proposed a preventative bias reduction method that directly produces bias-reduced estimates when the distribution assumption of the model is met but is not valid otherwise. We provide a detailed characterization of bias, propose a bias reduction method robust to misspecification of the distribution, and briefly discuss extensions of bias reduction methods to clustered and high dimensional data.