Random Sequential Packing of Cubes

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 hybrid ECME-scoring procedure is developed for computing the maximum likelihood estimates with standard errors as a by-product. A score test for the inspection of autocorrelation among within-subject errors is derived. Besides, the techniques for the estimation of random effects and prediction of further responses are investigated. The methodology is illustrated through an application to a set of AIDS data and several simulation studies. (This is a joint work with Prof. Tsai-Hung Fan.)?