Improvement of Rates of Convergence of Iterative Methods of Variance Component Estimation

Exact relationships of quadratic forms for restricted maximum likelihood and the pseudo expectation methods were presented for balanced data and a model containing only one random factor. These relationships were extended to unbalanced data as approximations and schemes for improving the convergence rates of the two methods of variance component estimation were compared empirically using simulated data. The proposed scheme for restricted maximum likelihood was found inappropriate since it converged rapidly but to a different final estimate than usual restricted maximum likelihood. The scheme for the pseudo expectation method also converged rapidly and to the same final estimates as the usual pseudo expectation method, and hence is recommended as a means of obtaining a good prior for restricted maximum likelihood.