A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

Abstract This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA‐estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the correspondingF‐quotients and the approximate confidence intervals of variance components are received in a simple way.