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Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses

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  • Kuo-Chin Lin
  • Yi-Ju Chen

Abstract

Categorical longitudinal data are frequently applied in a variety of fields, and are commonly fitted by generalized linear mixed models (GLMMs) and generalized estimating equations models. The cumulative logit is one of the useful link functions to deal with the problem involving repeated ordinal responses. To check the adequacy of the GLMMs with cumulative logit link function, two goodness-of-fit tests constructed by the unweighted sum of squared model residuals using numerical integration and bootstrap resampling technique are proposed. The empirical type I error rates and powers of the proposed tests are examined by simulation studies. The ordinal longitudinal studies are utilized to illustrate the application of the two proposed tests.

Suggested Citation

  • Kuo-Chin Lin & Yi-Ju Chen, 2016. "Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2053-2064, August.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:11:p:2053-2064
    DOI: 10.1080/02664763.2015.1126568
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    References listed on IDEAS

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    1. Zhiying Pan & D. Y. Lin, 2005. "Goodness-of-Fit Methods for Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 61(4), pages 1000-1009, December.
    2. Lin, Kuo-Chin, 2010. "Goodness-of-fit tests for modeling longitudinal ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1872-1880, July.
    3. 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.
    4. D. Y. Lin & L. J. Wei & Z. Ying, 2002. "Model-Checking Techniques Based on Cumulative Residuals," Biometrics, The International Biometric Society, vol. 58(1), pages 1-12, March.
    5. Wei Pan, 2002. "Goodness‐of‐fit Tests for GEE with Correlated Binary Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 101-110, March.
    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. Jianxin Pan & Robin Thompson, 2003. "Gauss-Hermite Quadrature Approximation for Estimation in Generalised Linear Mixed Models," Computational Statistics, Springer, vol. 18(1), pages 57-78, March.
    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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