Abstract: We study impact of class misspecification on the analysis of linear mixed models. Here, the misclassification means that some of the classes or groups associated with the random effects are mismatched. Such misclassification problems are becoming increasingly common in modern data science, including intentional and unintentional misclassifications. One important case of intentional misspecification is related to differential privacy; while a case of unintentional misspecification arises in classified mixed model prediction. Our study shows that tandard asymptotic properties of the maximum likelihood and restricted maximum likelihood estimators, including consistency and asymptotic normality, remain valid under the misclassification provided that the proportion of the misclassified group numbers is asymptotically negligible in a suitable sense. Empirical results of simulation studies fully support our theoretical findings. A real-data example is considered.

Key words and phrases: Asymptotic behavior, differential privacy, linear mixed models, misclassification, random effects, robustness.