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Checking for normality in linear mixed models

Science China Mathematics 2012年第4期55卷 787-804页

作者： wu ping 1.,zhu lixing 2,3 & fang yun 4 1.school of finance and statistics,east China normal university,shanghai 200241.China 2 school of statistics and Mathematics,yunnan university of finance and Economics,yunnan 650221,China 3 The Department of Mathematics,Hong Kong Baptist university,Hong Kong 999077,China 4 Mathematics and Science College,shanghai normal university,shanghai 200234,China 1. school of {1. and statistics East China Normal University Shanghai 200241 China2. School of Statistics and Mathematics Yunnan University of Finance and Economics Yunnan 650221 China3. The Department of Mathematics Hong Kong Baptist University Hong Kong 999077 China4. Mathematics and Science College Shanghai Normal University Shanghai 200234 China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1.V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

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