A bias correction regression calibration approach in generalized linear mixed measurement error models

Abstract

Two major topics are discussed when a fixed effect covariate is measured with error in a generalized linear mixed effects model: (i) the applicability of a direct regression calibration approach in various situations and (ii) a bias correction regression calibration approach. When the fixed and random effect structures are both misspecified, we find that a direct bias correction to the naive estimators is often not feasible due to lack of analytical bias expressions. While the direct regression calibration approach still often leads to inconsistent estimators, a combination of using the regression calibration to correct for the misspecified fixed effects and applying direct bias correction to correct for the misspecified random effects provides a simple, fast, and easy to implement method. Applications of this approach to linear, loglinear, probit and logistic mixed models arc discussed in detail A small simulation study is presented for the logistic normal mixed model.