On the equivalence between the LRT and F-test for testing variance components in a class of linear mixed models

Fares Qeadan () and Ronald Christensen ()
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Fares Qeadan: University of Utah
Ronald Christensen: University of New Mexico

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 3, No 2, 313-338

Abstract: Abstract For the special case of balanced one-way random effects ANOVA, it has been established that the generalized likelihood ratio test (LRT) and Wald’s test are largely equivalent in testing the variance component. We extend these results to explore the relationships between Wald’s F test, and the LRT for a much broader class of linear mixed models; the generalized split-plot models. In particular, we explore when the two tests are equivalent and prove that when they are not equivalent, Wald’s F test is more powerful, thus making the LRT test inadmissible. We show that inadmissibility arises in realistic situations with common number of degrees of freedom. Further, we derive the statistical distribution of the LRT under both the null and alternative hypotheses $$H_0$$ H 0 and $$H_1$$ H 1 where $$H_0$$ H 0 is the hypothesis that the between variance component is zero. Providing an exact distribution of the test statistic for the LRT in these models will help in calculating a more accurate p-value than the traditionally used p-value derived from the large sample chi-square mixture approximations.

Keywords: F-test; LRT; Generalized split-plot; Variance component; Random effect; Mixed model; 62C15; 62E15; 62F03; 62F10; 62K99 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-020-00777-z

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