Exact Tests for the Random and Fixed Effects in an Unbalanced Mixed Two-Way Cross-Classification Model

Abstract

The testing of both variance components and fixed effects in an unbalanced mixed model has relied on approximate techniques, particularly, Satterthwaite's approximation of the test statistics. The derived tests have unknown distributions, both under the null and alternative hypotheses, due to the lack of independence and chi-squaredness of the mean squares involved. Hence, the appeal for exact testing techniques is understandable. This article presents exact tests concerning the variance components of the random effects and estimable linear functions of the fixed effects in an unbalanced mixed two-way cross-classification with interaction model. The derivations are based on techniques similar to those applied by Khuri and Littell (1987, Biometrics 43, 545-560) to the same model, but with all random effects. The proposed methodology requires that the data under consideration contain no empty cells.