TESTS FOR SPATIAL AND TEMPORAL CORRELATION IN MIXED MODELS FOR CLIMATE DATA

This paper reports the results of a simulation study of the likelihood ratio test of independence in models with spatial and temporal covariance structure for a given (fixed) regression part of a random coefficient model. Results show that the null distribution of the likelihood ratio test statistic is not distributed as a 50:50 mixture of the constant zero and 2 distribution with one degree of freedom. A pair of mixed models with the same regression part but different covariance structures, one a special case of the other, are commonly compared by the likelihood ratio test (LRT) Verbeke & Molenberghs (2000). The two models, the null and the alternative, are fitted by maximum likelihood and the LRT statistic is derived from the values of the likelihood at the two maxima. The restricted maximum likelihood (REML) can be applied instead of the (full) maximum likelihood Patterson & Thompson (1971). Cox & Hinkley (1974) showed that under certain of regularity conditions the LRT statistic has a 2 distribution with degrees of freedom given by the difference in the number of parameters in the null and the alternative models.