Likelihood ratio testing of variance components in the linear mixed-effects model using restricted maximum likelihood

This paper reports the results of an extensive Monte Carlo study of the distribution of the likelihood ratio test statistic using the value of the restricted likelihood for testing random components in the linear mixed-effects model when the number of fixed components remains constant. The distribution of this test statistic is considered when one additional random component is added. The distribution of the likelihood ratio test statistic computed using restricted maximum likelihood is compared to the likelihood ratio test statistic computed from the usual maximum likelihood. The rejection proportion is computed under the null hypothesis using a mixture of chi-square distributions. The restricted likelihood ratio statistic has a reasonable agreement with the maximum likelihood test statistic. For the parameter combinations considered, the rejection proportions are, in most cases, less than the nominal 5% level for both test statistics, though, on average, the rejection proportions for REML are closer to the nominal level than for ML.