An algorithm for restricted maximum likelihood estimation in balanced multivariate variance components models

Restricted maximum likelihood (REML) estimation of variance components in multivariate linear models is a computationally intensive task. Calvin and Dykstra (1991a) have developed a general maximum likelihood estimation algorithm for a product of Wishart densities when the parameter matrices of the Wishart distributions follow a partial order of the Lowner type (Lowner, 1934). The algorithm is iterative in nature and does not require the computation of derivatives. It is guaranteed to converge to the correct solution and, for an important class of models, can be applied to the problem of REML estimation of variance components. In this paper, we define the class of models for which the algorithm is applicable. This class includes all two-factor models and all nested models as special cases. We also relate the general algorithm to the problem of REML estimation for balanced multivariate variance components models. An implementation is supplied in the Appendix and computational aspects of the algorithm are also discussed.