A Simple Method for Testing Variance Components in Unbalanced Nested Model

Abstract

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), 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.

Keywords:

• Generalized p value
• Unbalanced nested model
• Unweighted sums of squares
• Variance components

Mathematics Subject Classification:

• 62F03
• 62J10

Acknowledgment

The authors thank referees for their valuable comments. This work was partially supported by Grant 10771126 from National Natural Science Foundation of China and Grant ZR2010AM008 from Shandong Provincial Natural Science Foundation of China.