Comparison of the methods for constructing point estimates for variance components

The purpose of this investigation is to estimate the variance components parameters according to the analysis of variance (ANOVA), maximum likelihood (ML) and restricted maximum likelihood (REML) procedures in the one-way random effects model for balanced data, and to compare these estimation methods. In this study, the simulation studies were made by using the programs written in statistical software Minitab. The variance components estimators for ANOVA, ML and REML were calculated 1000 times by simulation made for the different number of observations and of levels; and the results were comparied and the most appropriate method for this study were investigated. The means and the standard deviations of the estimates were considered as the criteria of this comparison. After the evaluation of the results, it was observed that the values of ANOVA and REML were more and more close to each other. Furthermore, it was seen that ANOVA sometimes can give the negative estimates and REML always gives the nonnegative estimates. Though, the means of estimates of these two methods are close the real value. If we keep in mind the negative estimate situation for the ANOVA method, REML can be found appropriate. But although ANOVA gives the negative estimate, it has good results. Although ML estimation method gives the nonnegative estimates, the results of the treatment variance estimate are away from the real value for the balanced data. Likewise, ANOVA and REML estimates of the treatment variances are more influenced than ML about a increases.