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A diagnostic test for the mixing distribution in a generalised linear mixed model

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  • Eric J. Tchetgen
  • Brent A. Coull

Abstract

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-squared distribution under the null hypothesis that the mixing distribution is correctly specified. This strategy uses an idea presented by Hausman (1978), who considered analogous tests for the linear mixed model. An important advantage of the methods outlined here is that the resulting diagnostic test is easily implemented in commercial software. We illustrate the method by applying it to data from a clinical trial investigating the effect of hormonal contraceptives in women. Copyright 2006, Oxford University Press.

Suggested Citation

  • Eric J. Tchetgen & Brent A. Coull, 2006. "A diagnostic test for the mixing distribution in a generalised linear mixed model," Biometrika, Biometrika Trust, vol. 93(4), pages 1003-1010, December.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:4:p:1003-1010
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    File URL: http://hdl.handle.net/10.1093/biomet/93.4.1003
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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," MPRA Paper 64220, University Library of Munich, Germany.
    2. 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.
    3. Carolina Perez-Heydrich & Michael G. Hudgens & M. Elizabeth Halloran & John D. Clemens & Mohammad Ali & Michael E. Emch, 2014. "Assessing effects of cholera vaccination in the presence of interference," Biometrics, The International Biometric Society, vol. 70(3), pages 731-741, September.
    4. Bartolucci, Francesco & Bacci, Silvia & Pigini, Claudia, 2017. "Misspecification test for random effects in generalized linear finite-mixture models for clustered binary and ordered data," Econometrics and Statistics, Elsevier, vol. 3(C), pages 112-131.
    5. 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.
    6. 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.
    7. Joseph Puleo & Ashley Buchanan & Natallia Katenka & M. Elizabeth Halloran & Samuel R. Friedman & Georgios Nikolopoulos, 2024. "Assessing Spillover Effects of Medications for Opioid Use Disorder on HIV Risk Behaviors among a Network of People Who Inject Drugs," Stats, MDPI, vol. 7(2), pages 1-27, June.
    8. 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.
    9. Pinho, Luis Gustavo B. & Nobre, Juvêncio S. & Singer, Julio M., 2015. "Cook’s distance for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 126-136.

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