Mixture Model Analysis with Misclassified Covariates: Methods and Applications

Abstract

Mixture models are crucial for analyzing data with underlying sub-populations. Misclassification introduces discrepancies between observations and true values, which can severely bias parameter estimation, especially for mixture models when subgroups are not easily identifiable. We propose a method to enhance parameter estimation within the framework of mixture models, and mitigate the impact of misclassified covariates by utilizing them as surrogates in the Expectation-Maximization algorithm. Simulations consider both non-differential and differential misclassification with varying sample sizes, sensitivities, specificities, subgroup proportions and misclassified covariate proportions. Results demonstrate robust performance compared to naive or ad hoc approaches ignoring the misclassification issue, even under challenging conditions, such as low sensitivity and specificity for the misclassified covariate, or small sample sizes. For illustration, we apply our method to the 2015 Behavioral Risk Factor Surveillance System data. We conclude with a discussion of the implications of our findings and directions for future research.