An F-type Multiple Testing Approach for Assessing Randomness of Linear Mixed Models: Scientific Explanation
The significance of all or a subset of the random effects is often of primary importance in linear mixed models. For this reason, several strategies have been suggested, but none of them are fully satisfactory. The F-test is one of the oldest methods for measuring randomness, but it is often ignored in modern applications due to its low statistical strength and inapplicability in certain critical circumstances. In this paper, a two-step procedure for generalising an F-test and increasing its statistical power is created. We obtain a “repeatable” F-type test in the first step by comparing two covariance matrices of a least squares statistic. In the second stage, we repeat the test on the same data by adjusting the predicted matrix that defines the least squares statistic, resulting in a collection of associated statistics that can be analysed using a multiple testing method. The resulting test is sufficiently general, simple to compute, and has an exact distribution under both the null and alternative hypothesis, as well as a significant improvement in statistical power over the F-test. Based on these findings, we assume that our two-stage approach, which combines a “repeatable” F-type test with multiple testing, can suggest a procedure for improving statistical power in linear mixed models.
Author (s) Details
Department of Statistics, Informatics, Applications V.le Morgagni, 59 50134 Florence, Italy.
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