Statistica Sinica 21 (2011), 1857-1880
doi:10.5705/ss.2009.306

ESTIMATION IN MULTIVARIATE $\bm t$ LINEAR MIXED

MODELS FOR MULTIPLE LONGITUDINAL DATA

Wan-Lun Wang and Tsai-Hung Fan

Feng Chia University and National Central University

Abstract: The multivariate linear mixed model (MLMM) is a frequently used tool for a joint analysis of more than one series of longitudinal data. Motivated by a concern of sensitivity to potential outliers or data with longer-than-normal tails and possible serial correlation, we develop a robust generalization of the MLMM that is constructed by using the multivariate $t$ distribution and a parsimonious AR($p$) dependence structure for the within-subject errors. A score test for the inspection of autocorrelation among within-subject errors is derived. A hybrid ECME-scoring procedure is developed for computing the maximum likelihood estimates with standard errors as a by-product. The methodology is illustrated through an application to a set of AIDS data and several simulation studies.

Key words and phrases: AR(p), ECME algorithm, outliers, random effects, score test.