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Separating between‐ and within‐cluster covariate effects by using conditional and partitioning methods

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  • John M. Neuhaus
  • Charles E. McCulloch

Abstract

Summary. We consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors, which leads to inconsistent estimators. We show that conditional maximum likelihood can eliminate this bias. Conditional likelihood leads naturally to the partitioning of the covariate into between‐ and within‐cluster components and models that include separate terms for these components also eliminate the source of the bias. Another viewpoint that we develop is the idea that many violations of the assumptions (including correlation between the random effects and a covariate) in a generalized linear mixed model may be cast as misspecified mixing distributions. We illustrate the results with two examples and simulations.

Suggested Citation

  • John M. Neuhaus & Charles E. McCulloch, 2006. "Separating between‐ and within‐cluster covariate effects by using conditional and partitioning methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 859-872, November.
    • Handle: RePEc:bla:jorssb:v:68:y:2006:i:5:p:859-872
    DOI: 10.1111/j.1467-9868.2006.00570.x
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    Cited by:

    1. John M. Neuhaus & Alastair J. Scott & Christopher J. Wild & Yannan Jiang & Charles E. McCulloch & Ross Boylan, 2014. "Likelihood-based analysis of longitudinal data from outcome-related sampling designs," Biometrics, The International Biometric Society, vol. 70(1), pages 44-52, March.
    2. Quinn N. Lathrop & Ying Cheng, 2017. "Item Cloning Variation and the Impact on the Parameters of Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 245-263, March.
    3. Alfò, Marco & Carbonari, Lorenzo & Trovato, Giovanni, 2023. "On the effects of taxation on growth: an empirical assessment," Macroeconomic Dynamics, Cambridge University Press, vol. 27(5), pages 1289-1318, July.
    4. Tanya P. Garcia & Yanyuan Ma, 2016. "Optimal Estimator for Logistic Model with Distribution-free Random Intercept," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 156-171, March.
    5. Ying Huang & Brian Leroux, 2011. "Informative Cluster Sizes for Subcluster-Level Covariates and Weighted Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 67(3), pages 843-851, September.
    6. Li Liu & Liming Xiang, 2014. "Semiparametric estimation in generalized linear mixed models with auxiliary covariates: A pairwise likelihood approach," Biometrics, The International Biometric Society, vol. 70(4), pages 910-919, December.
    7. Brumback, Babette A. & He, Zhulin, 2011. "The Mantel-Haenszel estimator adapted for complex survey designs is not dually consistent," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1465-1470, September.
    8. Gerhard Tutz & Margret-Ruth Oelker, 2017. "Modelling Clustered Heterogeneity: Fixed Effects, Random Effects and Mixtures," International Statistical Review, International Statistical Institute, vol. 85(2), pages 204-227, August.
    9. Andrew Bell & Malcolm Fairbrother & Kelvyn Jones, 2019. "Fixed and random effects models: making an informed choice," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 1051-1074, March.
    10. Krieg Sabine & Boonstra Harm Jan & Smeets Marc, 2016. "Small-Area Estimation with Zero-Inflated Data – a Simulation Study," Journal of Official Statistics, Sciendo, vol. 32(4), pages 963-986, December.
    11. Li Zhigang & McKeague Ian W. & Lumey Lambert H., 2014. "Optimal Design Strategies for Sibling Studies with Binary Exposures," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 185-196, November.
    12. Ullah, Inayat & Hussain, Saqib, 2023. "Impact of early access to land record information through digitization: Evidence from Alternate Dispute Resolution Data in Punjab, Pakistan," Land Use Policy, Elsevier, vol. 134(C).
    13. Chenlu Li & Simon C Moore & Jesse Smith & Sarah Bauermeister & John Gallacher, 2019. "The costs of negative affect attributable to alcohol consumption in later life: A within-between random longitudinal econometric model using UK Biobank," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-15, February.
    14. Seonho Shin, 2021. "Were they a shock or an opportunity?: The heterogeneous impacts of the 9/11 attacks on refugees as job seekers—a nonlinear multi-level approach," Empirical Economics, Springer, vol. 61(5), pages 2827-2864, November.
    15. Sylvie Goetgeluk & Stijn Vansteelandt, 2008. "Conditional Generalized Estimating Equations for the Analysis of Clustered and Longitudinal Data," Biometrics, The International Biometric Society, vol. 64(3), pages 772-780, September.
    16. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    17. Sartori, N. & Severini, T.A. & Marras, E., 2010. "An alternative specification of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 575-584, February.
    18. Brumback, Babette A. & Dailey, Amy B. & Brumback, Lyndia C. & Livingston, Melvin D. & He, Zhulin, 2010. "Adjusting for confounding by cluster using generalized linear mixed models," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1650-1654, November.
    19. Brent A Coull, 2011. "A Random Intercepts–Functional Slopes Model for Flexible Assessment of Susceptibility in Longitudinal Designs," Biometrics, The International Biometric Society, vol. 67(2), pages 486-494, June.

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