Robust estimation for longitudinal data based upon minimum Hellinger distance

Generalized linear mixed models have been widely used in the analysis of correlated data in a lot of research areas. The linear mixed model with normal errors has been a popular model for the analysis of repeated measures and longitudinal data. Outliers, however, can severely have an wrong influence on the linear mixed model. The aforementioned model has not fully taken those severe outliers into consideration. One of the popular robust estimation methods, M-estimator attains robustness at the expense of first-order or second-order efficiency whereas minimum Hellinger distance estimator is efficient and robust. In this paper, we propose more robust Bayesian version of parameter estimation via pseudo posterior distribution based on minimum Hellinger distance. It accommodates an appropriate nonparametric kernel density estimation for longitudinal data to require the proposed cross-validation estimator. We conduct simulation study and real data study with the orthodontic study data and the Alzheimers Disease (AD) study data. In simulation study, the proposed method shows smaller biases, mean squared errors, and standard errors than the (residual) maximum likelihood method (REML) in the presence of outliers or missing values. In real data analysis, standard errors and variance-covariance components for the proposed method in two data sets are shown to be lower than those for REML method.