Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t-Distribution

(Title originally was Robust Estimation in Linear Mixed-Effects Models Using the Multivariate t-Distribution) Linear mixed-effects models are frequently used to analyze repeated measures data which arise in many areas of application, because of the flexibility they offer in modeling the within-subject correlation often present in this type of data. The most popular linear mixed-effects model for a continuous response assumes normal distributions for the random effects and the within-subject errors, making it very sensitive to outlying observations. We consider a robust version of this model in which the multivariate normal distributions are replaced by multivariate t-distributions, with known or unknown degrees-of-freedom, which are allowed to vary with subject. Different EM algorithms for efficient computation of maximum likelihood estimates for this multivariate t model are described. Real and simulated data are used to compare the performance of the Gaussian and the multivariate t models. Simulation results indicate that the latter substantially out- performs the former when outliers are present in the data, even in moderate amounts.