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APPROXIMATE F-TESTS BASED ON THE SATTERTHWAITE APPROACH FOR FIXED EFFECTS HYPOTHESES OF BLOCK DESIGN MODELS
Keywords:
F-test, Satterthwaite test, restricted maximum likelihood estimator, linear hypothesis, variance componentsDOI:
https://doi.org/10.17654/0972361724054Abstract
Two approximate F-tests have been previously proposed by Fai and Cornelius, and by Alnosaier to test fixed effects in mixed linear models. Both tests were derived by introducing a scaled Wald-type statistic with two different adjusted estimators of the variance-covariance matrix of the fixed effects estimator, where the test statistics distributed approximately as F distributions. The denominator degrees of freedom and the scale factor are computed by matching the approximate two moments of the scaled test statistic with those of the F distributions. Although both tests use adjusted estimators of variance-covariance matrix of the fixed effects estimator, and scaled statistics, they were found to perform inadequately in some models. In this paper, it is proposed to modify these tests in such a way that the modified tests produce the known values for the estimates of the denominator degrees of freedom and the scale factor when exact tests exist for some testing problems. A simulation study was conducted for some block design models to evaluate the performance of the modified tests, and it shows that the proposed modifications improve the performance of both tests based on their observed levels.
Received: April 22, 2024
Revised: June 5, 2024
Accepted: June 12, 2024
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