Exact investigation of all effects for extensions of one-way ANOVA model with random effects

Abstract

Consider the standard one-way analysis of variance model with random effects (variance components model). The customary assumptions of zero means, zero correlations, and equal variances are made for the random terms of this balanced model. The customary normality assumptions are also made when other than point estimates are desired. This standard model is generalized, in several ways, by addition of one or two types of “error” terms. The extended models are applicable to much more general situations than the standard model. However, exact results are developed for investigating the mean and both variance components (of the standard model) and for investigating subsets of these parameters. The generality level for an extended model depends on which parameters are investigated. Customary procedures for the standard model remain usable for some investigations and extensions, but more general models are applicable when use of customary results is not required. A method for rejection of outliers by use of the standard model is described and shown to be applicable for some of the extensions.