Robust model selection in generalized linear models

TL;DR

This paper develops a robust model selection method for generalized linear models, extending previous linear regression techniques with improved bootstrap estimators and applicability to various regression types.

Contribution

It introduces a new robust model selection approach for generalized linear models, enhancing existing methods with bias adjustment and broader model comparison capabilities.

Findings

The method effectively compares robust and nonrobust estimators.

It improves model selection accuracy over previous approaches.

The approach is applicable to logistic, Poisson, and gamma regressions.

Abstract

In this paper, we extend to generalized linear models (including logistic and other binary regression models, Poisson regression and gamma regression models) the robust model selection methodology developed by Mueller and Welsh (2005; JASA) for linear regression models. As in Mueller and Welsh (2005), we combine a robust penalized measure of fit to the sample with a robust measure of out of sample predictive ability which is estimated using a post-stratified m-out-of-n bootstrap. A key idea is that the method can be used to compare different estimators (robust and nonrobust) as well as different models. Even when specialized back to linear regression models, the methodology presented in this paper improves on that of Mueller and Welsh (2005). In particular, we use a new bias-adjusted bootstrap estimator which avoids the need to centre the explanatory variables and to include an intercept in every model. We also use more sophisticated arguments than Mueller and Welsh (2005) to establish an essential monotonicity condition.