Application of Singular Value Decomposition to Restricted Maximum Likelihood Estimation of Variance Components

Smith and Graser have recently proposed an efficient algorithm for computing restricted maximum likelihood estimates of variance components in a class of mixed models. The procedure involves the application of Householder transformation to tridiagonalize the coefficient matrix of the mixed model equations, thus eliminating the need for direct matrix inversion. This technical note extends their computing algorithm and applies the singular value decomposition of the coefficient matrix such that restricted maximum likelihood estimation of variance components in a class of mixed models would become a computational triviality and require little computer time during iteration. A numerical example is given to illustrate the identity of singular value decomposition approach and direct matrix inversion approach of solving the mixed model equations.