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Detecting misspecification in the random-effects structure of cumulative logit models

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  • Lin, Kuo-Chin
  • Chen, Yi-Ju

Abstract

A common approach to analyzing longitudinal ordinal data is to apply generalized linear mixed models (GLMMs). The efficiency and validity of inference for parameters are affected by the random-effects distribution in GLMMs. A proposed test is developed based on the observed data and a reconstructed data set induced from the observed data for diagnosing the random-effects misspecification in cumulative logit models for longitudinal ordinal data, extending the idea presented by Huang (2009) for longitudinal binary data. The proposed test statistic has the quadratic form of the difference of maximum likelihood estimators between the observed data and the reconstructed data, and it follows a limiting chi-squared distribution when the model is correctly specified. The simulation studies are conducted to assess the performance of the proposed test, and a clinical trial example demonstrates the application of the proposed test.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:92:y:2015:i:c:p:126-133
    DOI: 10.1016/j.csda.2015.07.002
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    References listed on IDEAS

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    1. Saskia Litière & Ariel Alonso & Geert Molenberghs, 2007. "Type I and Type II Error Under Random-Effects Misspecification in Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1038-1044, December.
    2. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
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    5. Xianzheng Huang, 2009. "Diagnosis of Random-Effect Model Misspecification in Generalized Linear Mixed Models for Binary Response," Biometrics, The International Biometric Society, vol. 65(2), pages 361-368, June.
    6. 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.
    7. 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.
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    1. 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.

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