Testing for random interaction: The symmetry assumption

The F-test for the hypothesis of no interaction effects in any mixed model is valid under the assumption of normality, symmetry, and variance homogeneity of the error terms. We consider the balanced two-way mixed model in which the usual assumptions do not hold. The model allows for dependence of the random main and interaction effects, variance heterogeneity in the random interaction effects and error terms and also do not require normality. We propose the test for testing the hypothesis of no interaction effect in this model. The asymptotic null distribution of the test statistic is the normal distribution and studied under the condition that the number of levels of random effect tends to be large.