Robustified Maximum Likelihood Estimation in Generalized Partial Linear Mixed Model for Longitudinal Data

Summary In this article, we study the robust estimation of both mean and variance components in generalized partial linear mixed models based on the construction of robustified likelihood function. Under some regularity conditions, the asymptotic properties of the proposed robust estimators are shown. Some simulations are carried out to investigate the performance of the proposed robust estimators. Just as expected, the proposed robust estimators perform better than those resulting from robust estimating equations involving conditional expectation like Sinha (2004, Journal of the American Statistical Association99, 451–460) and Qin and Zhu (2007, Journal of Multivariate Analysis98, 1658–1683). In the end, the proposed robust method is illustrated by the analysis of a real data set.