Dual Model Misspecification in Generalized Linear Models with Error in Variables

We study maximum likelihood estimation of regression parameters in generalized linear models for a binary response with error-prone covariates when the distribution of the error-prone covariate or the link function is misspecified. We revisit the remeasurement method proposed by Huang, Stefanski, and Davidian (2006) for detecting latent-variable model misspecification and examine its operating characteristics in the presence of link misspecification. Furthermore, we propose a new diagnostic method for assessing assumptions on the link function. Combining these two methods yields informative diagnostic procedures that can identify which model assumption is violated and also reveal the direction in which the true latent-variable distribution or the true link function deviates from the assumed one.