Goodness of fit tests for linear mixed models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:130

Article

Tang, Min¹  Slud, Eric V.^2,3  Pfeiffer, Ruth M.⁴ 

[1] Novartis Pharmaceut, E Hanover, NJ 07936 USA

[2] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[3] US Bur Census, Ctr Stat Res & Methodol, Suitland, MD USA

[4] Natl Canc Inst, Div Canc Epidemiol & Genet, Bethesda, MD USA

关键词: Asymptotic efficiency;    Information matrix;    Maximum likelihood estimators;    Method of moments;    Model fit;    Random effects;   

DOI  :  10.1016/j.jmva.2014.03.012

来源: Elsevier

【 摘 要 】

Linear mixed models (LMMs) are widely used for regression analysis of data that are assumed to be clustered or correlated. Assessing model fit is important for valid inference but to date no confirmatory tests are available to assess the adequacy of the fixed effects part of LMMs against general alternatives. We therefore propose a class of goodness-of-fit tests for the mean structure of LMMs. Our test statistic is a quadratic form of the difference between observed values and the values expected under the estimated model in cells defined by a partition of the covariate space. We show that this test statistic has an asymptotic chi-squared distribution when model parameters are estimated by maximum likelihood or by least squares and method of moments, and study its power under local alternatives both analytically and in simulations. Data on repeated measurements of thyroglobulin from individuals exposed to the accident at the Chernobyl power plant in 1986 are used to illustrate the proposed test. Published by Elsevier Inc.

【 授权许可】

Free