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) 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.
Highlights
We are interested in testing for zero variance components in the context of Linear Mixed Models (LMMs)
We set up a simulation study to investigate the performance of the proposed approximation of the Restricted Likelihood Ratio Test (RLRT) distribution in the case of correlated errors
This shows that the transformation approach is a very promising approximation when testing for a random effect in linear mixed models with several random effects
Summary
We are interested in testing for zero variance components in the context of Linear Mixed Models (LMMs). Within the LMM framework it is possible to test whether individuals or clusters differ from other observation units in a way that cannot be predicted by the considered covariates, or whether an estimated smooth function is different from a polynomial of a given degree. Such test problems are equivalent to testing whether the variance of the corresponding random effect is different from zero. We introduce the considered class of models and discuss the problem of testing for zero variance components in the case of i.i.d. errors.
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