Weighted-Average Least Squares Estimation of Generalized Linear Models

Abstract

The weighted-average least squares (WALS) approach, introduced by Magnus et al. (2010) in the context of Gaussian linear models, has been shown to enjoy important advantages over other strictly Bayesian and strictly frequentist model averaging estimators when accounting for problems of uncertainty in the choice of the regressors. In this paper we extend the WALS approach to deal with uncertainty about the specification of the linear predictor in the wider class of generalized linear models (GLMs). We study the large-sample properties of the WALS estimator for GLMs under a local misspecification framework that allows the development of asymptotic model averaging theory. We also investigate the finite sample properties of this estimator by a Monte Carlo experiment whose design is based on the real empirical analysis of attrition in the first two waves of the Survey of Health, Ageing and Retirement in Europe (SHARE).