Validation Data-Located Modification for the Multilevel Analysis of Miscategorized Nominal Response with Covariates Subject to Measurement Error

In many longitudinal and hierarchical epidemiological frameworks, observations regarding to each individual are recorded repeatedly over time. In these follow-ups, accurate measurements of time-dependent covariates might be invalid or expensive to be obtained. In addition, in the recording process, or as a result of other undetected reasons, miscategorization of the response variable might occur, that does not demonstrate the true condition of the response process. In contrast with binary outcome by which classification error occurs between two categories, disorderliness in categorical outcome has more intricate impacts, as a result of the increased number of categories and asymmetric miscategorization matrix. When no modification is made, insensitivity of errors in either covariate or response variable, results in potentially incorrect conclusion, tends to bias the statistical inference and eventually degrades the efficiency of the decision-making procedure. In this article, we provide an approach to simultaneously adjust for misclassification in the correlated nominal response and measurement error in the covariates, incorporating validation data in the estimation of misclassification probabilities, using the multivariate Gauss–Hermite quadrature technique for the approximation of the likelihood function. Simulation results demonstrate the effects of modifying covariate measurement error and response misclassification on the estimation procedure.