Asymptotic Expansions of the Null Distribution of the LR Test Statistic for Random-Effects Covariance Structure in a Parallel Profile Model

This paper is concerned with the null distribution of the likelihood ratio test statistic −2log Λ for testing the adequacy of a random-effects covariance structure in a parallel profile model. It is known that the null distribution of −2log Λ converges to χ2f or 0.5χ2f + 0.5χ2f+1 when the sample size tends to infinity. In order to extend this result, we derive asymptotic expansions of the null distribution of −2log Λ. The accuracy of the approximations based on the limiting distribution and an asymptotic expansion are compared through numerical experiments.