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Goodness‐of‐fit Tests for Mixed Models

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  • Christian Ritz

Abstract

. Mixed linear models have become a very useful tool for modelling experiments with dependent observations within subjects, but to establish their appropriateness several assumptions have to be checked. In this paper, we focus on the normality assumptions, using goodness‐of‐fit tests that make allowance for possible design imbalance. These tests rely on asymptotic results, which are established via empirical process theory. The power of the tests is explored empirically, and examples illustrate some aspects of the usage of the tests.

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  • Christian Ritz, 2004. "Goodness‐of‐fit Tests for Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 443-458, September.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:3:p:443-458
    DOI: 10.1111/j.1467-9469.2004.02_101.x
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    Cited by:

    1. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    2. Reza Drikvandi & Geert Verbeke & Geert Molenberghs, 2017. "Diagnosing misspecification of the random-effects distribution in mixed models," Biometrics, The International Biometric Society, vol. 73(1), pages 63-71, March.
    3. Shun Yu & Xianzheng Huang, 2017. "Random-intercept misspecification in generalized linear mixed models for binary responses," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 333-359, August.
    4. Jakob Peterlin & Nataša Kejžar & Rok Blagus, 2023. "Correct specification of design matrices in linear mixed effects models: tests with graphical representation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 184-210, March.
    5. Shun Yu & Xianzheng Huang, 2019. "Link misspecification in generalized linear mixed models with a random intercept for binary responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 827-843, September.
    6. Tang, Min & Slud, Eric V. & Pfeiffer, Ruth M., 2014. "Goodness of fit tests for linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 176-193.

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