A Simple Method for Testing Variance Components in Unbalanced Nested Model

In this article, we consider the unbalanced case of the three fold nested random effects model under partial balance. The distributions of unweighted sums of squares are obtained first. Using the method of generalized p value introduced in Tsui and Weerahandi (1989 Tsui , K. , Weerahandi , S. ( 1989 ). Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters . Journal of the American Statistical Association 84 : 602 – 607 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), a new method is proposed for hypothesis tests involving functions of variance components. To evaluate the sizes of the generalized p value, a simulation study is conducted. The results indicate that the proposed method performs well under all examined conditions.