Testing the absence of random effects in the nested-error regression model using orthogonal transformations

Testing the absence of random effects in the nested error regression model is nonstandard because it requires the null value of the random effects variance to be on the boundary of its space. In this paper, we propose a test statistic that can be obtained by applying two successive orthogonal transformations to the response vector such that the components of the resulting new vector are uncorrelated variates having zero mean and a common variance. Consequently, two new tests are proposed. The first assumes the normality of the responses and is based on approximating the distribution of the test statistic as a weighted sum of chi-square variates. The second test is a distribution-free permutation test based on the same test statistic. Our simulation experiments indicate that both tests have empirical significance levels that are close to the chosen nominal level. The statistical power of the first test is studied analytically. Empirical power comparisons indicate that the first test outperforms recently developed tests. The second test also has a competitive performance among them. Using a real dataset, the use of the proposed tests is illustrated.