Likelihood Inference in the Random Effects Logistic Regression Model with ‎Response Misclassification and Covariate Subject to Measurement Error‎

‎Generalized linear mixed models (GLMMs) are common methods for the analysis of clustered data‎. ‎In many longitudinal and hierarchical epidemiological frameworks‎, ‎accurate measurements of variables are invalid or expensive to be obtained and there might be situations that both the response and covariate variables are likely to be mismeasured‎. ‎Insensitivity of errors in either covariate or response variable is‎, ‎not always plausible‎. ‎With nonlinear regression models for the outcome process‎, ‎classification errors for binary responses and measurement error in covariates basically needs to be accounted for in order to make conclusive inferences‎. ‎In this article‎, ‎we provide an approach to simultaneously adjust for non-differential misclassification in the correlated binary response and classical measurement error in the covariates‎, ‎using the multivariate Gauss-Hermite quadrature technique for the approximation of the likelihood function‎. ‎Simulation studies are then conducted to inform the effects of correcting for measurement error and misclassification on the estimation of regression parameters‎. ‎The application of the multivariate Gauss-Hermite quadrature method in the conjunction of measurement error and misclassification problems is further highlighted with real-world data based on a multilevel study of contraceptive methods used by women in Bangladesh‎.