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A Simulation‐based Goodness‐of‐fit Test for Random Effects in Generalized Linear Mixed Models

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  • RASMUS WAAGEPETERSEN

Abstract

. The goodness‐of‐fit of the distribution of random effects in a generalized linear mixed model is assessed using a conditional simulation of the random effects conditional on the observations. Provided that the specified joint model for random effects and observations is correct, the marginal distribution of the simulated random effects coincides with the assumed random effects distribution. In practice, the specified model depends on some unknown parameter which is replaced by an estimate. We obtain a correction for this by deriving the asymptotic distribution of the empirical distribution function obtained from the conditional sample of the random effects. The approach is illustrated by simulation studies and data examples.

Suggested Citation

  • Rasmus Waagepetersen, 2006. "A Simulation‐based Goodness‐of‐fit Test for Random Effects in Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 721-731, December.
    • Handle: RePEc:bla:scjsta:v:33:y:2006:i:4:p:721-731
    DOI: 10.1111/j.1467-9469.2006.00504.x
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    References listed on IDEAS

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    1. Sophia Rabe-Hesketh & Anders Skrondal & Andrew Pickles, 2004. "GLLAMM Manual," U.C. Berkeley Division of Biostatistics Working Paper Series 1160, Berkeley Electronic Press.
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    Cited by:

    1. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    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. Gilles Guillot & Niklas Lorén & Mats Rudemo, 2009. "Spatial prediction of weed intensities from exact count data and image‐based estimates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 525-542, September.
    4. Lin, Kuo-Chin & Chen, Yi-Ju, 2015. "Detecting misspecification in the random-effects structure of cumulative logit models," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 126-133.
    5. 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.
    6. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    7. 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.
    8. Alonso, A. & Litière, S. & Molenberghs, G., 2008. "A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4474-4486, May.

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