We consider the problem of testing for zero variance components in linear mixed models with correlated or heteroscedastic errors. In the case of independent and identically distributed errors, a valid test exists, which is based on the exact finite sample distribution of the restricted likelihood ratio test statistic under the null hypothesis. We propose to make use of a transformation to derive the (approximate) null distribution for the restricted likelihood ratio test statistic in the case of a general error covariance structure. The method can also be applied in the case of testing for a random effect in linear mixed models with several random effects by writing the model as one with a single random effect and a more complex covariance structure. The proposed test proves its value in simulations and is finally applied to an interesting question in the field of well-being economics.
"Restricted likelihood ratio testing in linear mixed models with general error covariance structure." Electron. J. Statist. 5 1718 - 1734, 2011. https://doi.org/10.1214/11-EJS654