Restricted likelihood ratio testing in linear mixed models with general error covariance structure

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.