Ch. Morrell, Likelihood ratio testing of variance components in the linear mixed-effects model using restricted maximum likelihood, BIOMETRICS, 54(4), 1998, pp. 1560-1568
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.