A Comparison of Three Different Procedures for Estimating Variance Components

As a consequence of various theoretical developments, and of improvements in computing strategies, restricted maximum likelihood (REML) estimation has become a viable procedure for estimating the variance components in mixed linear models. In this article, the procedure of Xu and Atchley (1996) has been extended in such a way that can be applied to any general linear model. Further, alternative estimator based on empirical Bayes approach has been derived for estimating the random- effects variance components in the light of REML function. Comparison between the proposed estimator and the estimators provided by Xu and Atchley (1996) and Moghtased-Azar et al. (2014) has been computed under unbalanced nested-factorial model with two fixed crossed factorial and one nested random factor. Finally, all the estimators in the vignette are activated by an illustrative example.