Likelihood inference in generalized linear mixed measurement error models

The generalized linear mixed models (GLMMs) for clustered data are studied when covariates aremeasured with error. Themost conventional measurement error models are based on either linear mixed models (LMMs) or GLMMs. Even without the measurement error, the frequentist analysis of LMM, and particularly of GLMM, is computationally difficult. On the other hand, Bayesian analysis of LMM and GLMM is computationally convenient in both cases without and with the measurement error. Recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. As an application of data cloning, we conduct a frequentist analysis of GLMMwith covariates subject to themeasurement errormodel. The performance of the proposed approachwhich yields themaximum likelihood estimation is evaluated by two important real data types, Normal and logistic linearmixedmeasurement error models, and also through simulation studies. © 2012 Elsevier B.V. All rights reserved.