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Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function

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  • Zengri Wang

Abstract

Random effects logistic regression models are often used to model clustered binary response data. Regression parameters in these models have a conditional, subject-specific interpretation in that they quantify regression effects for each cluster. Very often, the logistic functional shape conditional on the random effects does not carry over to the marginal scale. Thus, parameters in these models usually do not have an explicit marginal, population-averaged interpretation. We study a bridge distribution function for the random effect in the random intercept logistic regression model. Under this distributional assumption, the marginal functional shape is still of logistic form, and thus regression parameters have an explicit marginal interpretation. The main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework. The generality of the results and some properties of the bridge distribution functions are discussed. An example is used for illustration. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Zengri Wang, 2003. "Matching conditional and marginal shapes in binary random intercept models using a bridge distribution function," Biometrika, Biometrika Trust, vol. 90(4), pages 765-775, December.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:765-775
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    Cited by:

    1. William Dunsmuir & Jieyi He, 2017. "Marginal Estimation of Parameter Driven Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 120-144, January.
    2. Iraj Kazemi & Fatemeh Hassanzadeh, 2021. "Marginalized random-effects models for clustered binomial data through innovative link functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 197-228, June.
    3. Brajendra C. Sutradhar, 2022. "Fixed versus Mixed Effects Based Marginal Models for Clustered Correlated Binary Data: an Overview on Advances and Challenges," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 259-302, May.
    4. Caffo, Brian & An, Ming-Wen & Rohde, Charles, 2007. "Flexible random intercept models for binary outcomes using mixtures of normals," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5220-5235, July.
    5. Bruce J. Swihart & Brian S. Caffo & Ciprian M. Crainiceanu, 2014. "A Unifying Framework for Marginalised Random-Intercept Models of Correlated Binary Outcomes," International Statistical Review, International Statistical Institute, vol. 82(2), pages 275-295, August.
    6. Pan Zhao & Yifan Cui, 2023. "A Semiparametric Instrumented Difference-in-Differences Approach to Policy Learning," Papers 2310.09545, arXiv.org.
    7. Saumard, Adrien & Wellner, Jon A., 2018. "Efron’s monotonicity property for measures on R2," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 212-224.
    8. 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.
    9. Lanjia Lin & Dipankar Bandyopadhyay & Stuart R. Lipsitz & Debajyoti Sinha, 2010. "Association Models for Clustered Data with Binary and Continuous Responses," Biometrics, The International Biometric Society, vol. 66(1), pages 287-293, March.
    10. Jason Roy & Michael J. Daniels, 2008. "A General Class of Pattern Mixture Models for Nonignorable Dropout with Many Possible Dropout Times," Biometrics, The International Biometric Society, vol. 64(2), pages 538-545, June.
    11. 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.
    12. Laura Boehm & Brian J. Reich & Dipankar Bandyopadhyay, 2013. "Bridging Conditional and Marginal Inference for Spatially Referenced Binary Data," Biometrics, The International Biometric Society, vol. 69(2), pages 545-554, June.
    13. Stephens Alisa & Tchetgen Tchetgen Eric & De Gruttola Victor, 2014. "Locally Efficient Estimation of Marginal Treatment Effects When Outcomes Are Correlated: Is the Prize Worth the Chase?," The International Journal of Biostatistics, De Gruyter, vol. 10(1), pages 59-75, May.
    14. Zengri Wang & Thomas A. Louis, 2004. "Marginalized Binary Mixed-Effects Models with Covariate-Dependent Random Effects and Likelihood Inference," Biometrics, The International Biometric Society, vol. 60(4), pages 884-891, December.
    15. Shaun R. Seaman & Menelaos Pavlou & Andrew J. Copas, 2014. "Methods for observed-cluster inference when cluster size is informative: A review and clarifications," Biometrics, The International Biometric Society, vol. 70(2), pages 449-456, June.
    16. Nooraee, Nazanin & Molenberghs, Geert & van den Heuvel, Edwin R., 2014. "GEE for longitudinal ordinal data: Comparing R-geepack, R-multgee, R-repolr, SAS-GENMOD, SPSS-GENLIN," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 70-83.
    17. Victor De Oliveira, 2017. "Geostatistical Binary Data: Models, Properties And Connections," Working Papers 0151mss, College of Business, University of Texas at San Antonio.
    18. Huang, Youjun & Pan, Jianxin, 2021. "Joint generalized estimating equations for longitudinal binary data," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    19. Iddi, Samuel & Molenberghs, Geert, 2012. "A combined overdispersed and marginalized multilevel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1944-1951.
    20. Jonathan S. Schildcrout & Patrick J. Heagerty, 2007. "Marginalized Models for Moderate to Long Series of Longitudinal Binary Response Data," Biometrics, The International Biometric Society, vol. 63(2), pages 322-331, June.

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