Including Mean-variance Relationships in Heteroskedastic Mixed Linear Models: Theory and Application

In mixed linear models, it is usually assumed that both residual and random effects have homogeneous components of variance. This paper presents models and corresponding techniques of estimation to relax this restrictive assumption. Models proposed include log link functions linearly relating variance components to explanatory variables that can be either discrete or continuous. Special emphasis is given to two aspects of modelling. First, a structural model for residual variances is considered which incorporates, in addition to classical covariates, a function of the data expectation to take into account mean-variance relationships. Secondly, residual and random effect component of variances are linked via a linear functional relationship. Estimation and testing procedures are based on restricted maximum likelihood procedures (REML) via the expectation-maximization (EM) algorithm. The procedure is illustrated by the analysis of birth weight of rats that were used in a toxicology experiment.