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