Consistent Estimation in Generalized Linear Mixed Models with Measurement Error

Abstract

We propose the instrumental variable method for consistent estimation of generalized linear mixed models with measurement error.This method does not require parametric assumptions for the distributions of the unobserved covariates or of the measurement errors, and it allows random effects to have any parametric distributions (not necessarily normal).We also propose simulation-based estimators for the situation where the marginal moments do not have closed forms.The proposed estimators are not only computationally attractive but also strongly root-n consistent.Moreover, the proposed estimators have a bounded influence function so they are robust against data outliers.The methodology is illustrated through simulation studies.