Hypothesis testing in unbalanced two-fold nested random models
In many applications of linear random models to multilevel data, it is of interest to test whether the random effects variance components are zero. In this paper we propose approximate tests for testing significance of variance components in the unbalanced two-fold nested random model in the presence of non-normality. In the derivations of the asymptotic distributions of the test statistics, as an intermediate result, the explicit form of the asymptotic covariance matrix of the vector of mean squares in this model is obtained. We also study the influence of some special type of designs on the asymptotic covariance matrix and on the distribution of the proposed test statistics.