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Wiencierz, Andrea and Greven, Sonja and Küchenhoff, Helmut (2011): Restricted Likelihood Ratio Testing in Linear Mixed Models with General Error Covariance Structure. Department of Statistics: Technical Reports, No.109
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Abstract

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) test distribution for the restricted likelihood ratio test statistic in the case of a general error 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.