Diagnostic Measures for Generalized Linear Models with Missing Covariates

Abstract.  In this paper, we carry out an in‐depth investigation of diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for generalized linear models. Our diagnostic measures include case‐deletion measures and conditional residuals. We use the conditional residuals to construct goodness‐of‐fit statistics for testing possible misspecifications in model assumptions, including the sampling distribution. We develop specific strategies for incorporating missing data into goodness‐of‐fit statistics in order to increase the power of detecting model misspecification. A resampling method is proposed to approximate the p‐value of the goodness‐of‐fit statistics. Simulation studies are conducted to evaluate our methods and a real data set is analysed to illustrate the use of our various diagnostic measures.

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