Abstract
This paper considers a widely used mixed effects model in repeated measures under heteroscedasticity. Hypotheses of the equality of the fixed effects and the simultaneous confidence intervals for all pair-wise differences are discussed. A generalized F-test has been proposed to test the equality of the fixed effects in the model, but simulation results for evaluating its performance have not been shown in the literature. Moreover, the generalized F-test cannot be used to deduce the simultaneous confidence intervals for all pair-wise differences of the fixed effects. The authors propose two new p-values to test the hypotheses of equality of the fixed effects and simultaneous confidence intervals of the differences of the effects based on the generalized pivotal quantities derived in this paper. The authors also compare the empirical performances of the proposed tests and the generalized F-test. The type I error rates and powers of these tests are evaluated using the Monte Carlo simulation. The simulation studies show that the generalized F-test does not perform well in terms of type I error rate under various sample size and parameter combinations. However, the type I error probabilities of the proposed tests are always close to the nominal value. It can also be seen that the simultaneous confidence intervals perform well.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 11126243 and 11071015, Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHR 201107123), and School Scientific Found under Grant No. 101002207.
This paper was recommended for publication by Editor Guohua ZOU.
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Mu, W., Xu, X. Inference for repeated measures models under heteroscedasticity. J Syst Sci Complex 25, 1158–1170 (2012). https://doi.org/10.1007/s11424-012-0170-x
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DOI: https://doi.org/10.1007/s11424-012-0170-x