Mixed models, with both random and fixed effects, are most often estimated on the assumption that the random effects are normally distributed. In this paper we propose several formal tests of the hypothesis that the random effects and/or errors are normally distributed. Most of the proposed methods can be extended to generalized linear models where tests for non-normal distributions are of interest. Our tests are nonparametric in the sense that they are designed to detect virtually any alternative to normality. In case of rejection of the null hypothesis, the nonparametric estimation method that is used to construct a test provides an estimator of the alternative distribution. © 2009 Sociedad de Estadística e Investigación Operativa.
|Original language||English (US)|
|Number of pages||27|
|State||Published - May 12 2009|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Part of this research has been performed while G. Claeskens was visiting the IsaacNewton Institute at Cambridge University, U.K. The work of Professor Hart was partially supported byNSF Grant DMS-0604801 and by Award No. KUS-C1-016-04, made by King Abdullah University ofScience and Technology (KAUST). The authors wish to thank W. Ghidey and M. Davidian for providingsome software. They also thank the reviewers for their constructive remarks.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.