On multivariate mixed model analysis

Abstract

A general multivariate mixed effect linear model is introduced. Special cases of the model include the multivariate nested error covariance component regression and the random coefficient repeated measure model. Discussion is given on modeling the random effect structure and its effect on statistical inference. A procedure for testing certain class of hypotheses concerning the random effect structure is developed. The procedure is based on a statistic in a readily computable form, facilitating the use at the model building stage. 1. The Model. This paper is concerned with introducing a general multivariate mixed effect model, and with developing a procedure for testing hypotheses concerning the random effect structure in such a model. For simplicity we concentrate here on mixed models with the one-way random effect structure, i.e., with the random effect (other than the error term) involving one unknown covariance matrix. To introduce our general model, first consider the most widely used univariate mixed effect model with the one-way classification random effect or with the nested error structure. The response yij and the k ? 1 explanatory variable Xij for the j-th individual in the z-th group are assumed to satisfy