Goodness-of-Fit Tests in Mixed Models

Abstract

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.

Adaptive estimation of marginal random-effects densities in linear mixed-effects models

“…Some approaches are based on normal mixtures, see Ghidey et al (2004), Komárek and Lesaffre (2008). For nonparametric approach, we can cite Claeskens and Hart (2009) who develop a nonparametric goodness-offit test in mixed models providing a nonparametric estimator if the normality hypothesis is rejected. Mixed models are also studied in Bayesian litterature, see Ibrahim and Kleinman (1998) who allow the prior to be nonparametric by taking a Dirichlet process.…”