Estimation in Mixed-effects Models with Measurement Error

Abstract

Measurement error is common in the regression analysis of longitudinal data. In this chapter we survey some recent methods for estimation in generalized linear mixed models with covariate measurement error. The focus is on a semiparametric method that does not require parametric assumptions for the distributions of the unobserved covariates or of the measurement error, and it allows random effects to have any parametric distribution (not necessarily normal). The proposed approach is based on the marginal moments of the observed response variable and covariates given the instrumental variables. We also introduce a simulation-based estimation procedure for the case where the marginal moments do not have closed forms. The proposed estimators are consistent and asymptotically normally distributed under fairly general conditions. Some numerical examples are presented for illustration.