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 dis tribution of the likelihood ratio test statistic using the value of the res tricted likelihood for testing random components in the linear mixed-effect s model when the number of fixed components remains constant. The distribut ion of this test statistic is considered when one additional random compone nt is added. The distribution of the likelihood ratio test statistic comput ed using restricted maximum likelihood is compared to the likelihood ratio test statistic computed from the usual maximum likelihood. The rejection pr oportion is computed under the null hypothesis using a mixture of chi-squar e distributions. The restricted likelihood ratio statistic has a reasonable agreement with the maximum likelihood test statistic. For the parameter co mbinations considered, the rejection proportions are, in most cases, less t han 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.