Covariance Estimates of GLMs under Model Misspecification

In analyzing data set we usually assume a tentative model that seems to be valid. But the assumed model may be incorrect in respect of distributional assumption, regression relationship, and so on. The incorrect model usually causes larger variance estimates than the naive variance estimates that are given as the inverse of Hessian matrix. In this paper, we discuss robust variance estimates that are more valid in the presence of model misspecification. Through a Monte Carlo study we investigate the improvement of robust variance estimates against the naive estimates in respect of attaining nominal coverage probabilities for the regression coefficients of generalized linear models. We consider logistic GLMs for binomial responses versus beta-binomial or zero-inflated binomial responses, and also loglinear GLMs for Poisson counts versus negative binomial or zero-inflated counts responses. In the presence of model misspecification, the robust covariance estimator appears to be desirable in attaining nominal significance level.