A Bayesian mixture of experts approach to covariate misclassification

Abstract

AbstractThis article considers misclassification of categorical covariates in the context of regression analysis; if unaccounted for, such errors usually result in mis‐estimation of model parameters. With the presence of additional covariates, we exploit the fact that explicitly modelling non‐differential misclassification with respect to the response leads to a mixture regression representation. Under the framework of mixture of experts, we enable the reclassification probabilities to vary with other covariates, a situation commonly caused by misclassification that is differential on certain covariates and/or by dependence between the misclassified and additional covariates. Using Bayesian inference, the mixture approach combines learning from data with external information on the magnitude of errors when it is available. In addition to proving the theoretical identifiability of the mixture of experts approach, we study the amount of efficiency loss resulting from covariate misclassification and the usefulness of external information in mitigating such loss. The method is applied to adjust for misclassification on self‐reported cocaine use in the Longitudinal Studies of HIV‐Associated Lung Infections and Complications.