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

• Published in: Communications in statistics. Theory and methods Vol. 28; no. 1; pp. 217 - 232
• Main Authors: Wang, Naisyin, Lin, Xihong, Guttierrez, Roberto G.
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Marcel Dekker, Inc 01.01.1999; Taylor & Francis
• Subjects: asymptotic bias; corrected penalized quasi-likelihood; Exact sciences and technology; Linear inference, regression; M-estimator; Mathematics; Probability and statistics; random effects; Sciences and techniques of general use; Statistics; variance components; Statistical regression; Generalized linear model; Mixed model; Loglinear model; Random effect; Statistical estimation; Linear estimation; Covariate; Variance component; Measurement error; Biased estimation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610929908832292

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.