A mixed model for complete three or higher-way layout with two random effects factors

The classical FF-test for testing the hypothesis of no fixed main effects in a mixed model is valid under normality, variance homogeneity and symmetry assumption. We consider a mixed model in which one fixed and two random main effects are crossed. A new test procedure for testing the hypothesis of no fixed main effects is developed under violations of normality, variance homogeneity and symmetry assumptions. The asymptotic distribution of the proposed test statistic is studied under the condition that the numbers of levels of two main random effects are large. The asymptotic distribution of the test statistic is the chi-square distribution. The theory presented in this article is applicable for complete four or higher-way layout with two random factors.