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Logistic Regression for Correlated Binary Data

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  • S. le Cessie
  • J. C. van Houwelingen

Abstract

The modelling of correlated binary outcomes, in such a way that the marginal response probabilities are still logistic, is considered. Different association measures for the dependence between correlated observations are discussed. For paired correlated data the full likelihood can be evaluated; for an arbitrary number of correlated observations a pseudolikelihood approach to obtain parameter estimates is proposed. The results are illustrated on data from a Dutch follow‐up study on preterm infants.

Suggested Citation

  • S. le Cessie & J. C. van Houwelingen, 1994. "Logistic Regression for Correlated Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 95-108, March.
    • Handle: RePEc:bla:jorssc:v:43:y:1994:i:1:p:95-108
    DOI: 10.2307/2986114
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    Cited by:

    1. Kuk, Anthony Y. C. & Nott, David J., 2000. "A pairwise likelihood approach to analyzing correlated binary data," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 329-335, May.
    2. Bhat, Chandra R., 2011. "The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models," Transportation Research Part B: Methodological, Elsevier, vol. 45(7), pages 923-939, August.
    3. Euán, Carolina & Sun, Ying, 2020. "Bernoulli vector autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
    4. Paik, Jane & Ying, Zhiliang, 2012. "A composite likelihood approach for spatially correlated survival data," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 209-216, January.
    5. Taha Hossein Rashidi & Matthew J. Roorda, 2018. "A business establishment fleet ownership and composition model," Transportation, Springer, vol. 45(3), pages 971-987, May.
    6. Sanjoy K. Sinha & Andrea B. Troxel & Stuart R. Lipsitz & Debajyoti Sinha & Garrett M. Fitzmaurice & Geert Molenberghs & Joseph G. Ibrahim, 2011. "A Bivariate Pseudolikelihood for Incomplete Longitudinal Binary Data with Nonignorable Nonmonotone Missingness," Biometrics, The International Biometric Society, vol. 67(3), pages 1119-1126, September.
    7. M.-L. Feddag, 2016. "Pairwise likelihood estimation for the normal ogive model with binary data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(2), pages 223-237, April.
    8. Feddag, M.-L. & Bacci, S., 2009. "Pairwise likelihood for the longitudinal mixed Rasch model," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1027-1037, February.
    9. Reem Aljarallah & Samer A Kharroubi, 2021. "Use of Bayesian Markov Chain Monte Carlo Methods to Model Kuwait Medical Genetic Center Data: An Application to Down Syndrome and Mental Retardation," Mathematics, MDPI, vol. 9(3), pages 1-11, January.
    10. Hatzikyriakou, Adam & Lin, Ning, 2017. "Impact of performance interdependencies on structural vulnerability: A systems perspective of storm surge risk to coastal residential communities," Reliability Engineering and System Safety, Elsevier, vol. 158(C), pages 106-116.
    11. Paleti, Rajesh & Bhat, Chandra R., 2013. "The composite marginal likelihood (CML) estimation of panel ordered-response models," Journal of choice modelling, Elsevier, vol. 7(C), pages 24-43.
    12. Bryan Ting & Fred Wright & Yi-Hui Zhou, 2022. "Fast Multivariate Probit Estimation via a Two-Stage Composite Likelihood," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 533-549, December.
    13. Renard, Didier & Molenberghs, Geert & Geys, Helena, 2004. "A pairwise likelihood approach to estimation in multilevel probit models," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 649-667, January.
    14. Zhao Zhang & Chun-Yan Xiao & Zhi-Guo Zhang, 2023. "Analysis and Empirical Study of Factors Influencing Urban Residents’ Acceptance of Routine Drone Deliveries," Sustainability, MDPI, vol. 15(18), pages 1-27, September.
    15. Joe, Harry & Lee, Youngjo, 2009. "On weighting of bivariate margins in pairwise likelihood," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 670-685, April.
    16. Spiess, Martin & Hamerle, Alfred, 2000. "A comparison of different methods for the estimation of regression models with correlated binary responses," Computational Statistics & Data Analysis, Elsevier, vol. 33(4), pages 439-455, June.
    17. Lajmi Lakhal-Chaieb & Thierry Duchesne, 2017. "Association measures for bivariate failure times in the presence of a cure fraction," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 517-532, October.
    18. Shujie Ma & Yanyuan Ma & Yanqing Wang & Eli S. Kravitz & Raymond J. Carroll, 2017. "A Semiparametric Single-Index Risk Score Across Populations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1648-1662, October.
    19. Peng, Cheng & Yang, Yihe & Zhou, Jie & Pan, Jianxin, 2022. "Latent Gaussian copula models for longitudinal binary data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    20. Olfa KAMMOUN & Mohieddine RAHMOUNI, 2013. "Intellectual Property Rights, Appropriation Instruments and Innovation Activities: Evidence from Tunisian Firms," Cahiers du GREThA (2007-2019) 2013-01, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
    21. Vaclav Fidler & Nico Nagelkerke, 2013. "The Mantel-Haenszel Procedure Revisited: Models and Generalizations," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-4, March.
    22. Johan Verbeeck & Martin Geroldinger & Konstantin Thiel & Andrew Craig Hooker & Sebastian Ueckert & Mats Karlsson & Arne Cornelius Bathke & Johann Wolfgang Bauer & Geert Molenberghs & Georg Zimmermann, 2023. "How to analyze continuous and discrete repeated measures in small‐sample cross‐over trials?," Biometrics, The International Biometric Society, vol. 79(4), pages 3998-4011, December.
    23. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    24. Wimhurst, Joshua J. & Greene, J. Scott & Koch, Jennifer, 2023. "Predicting commercial wind farm site suitability in the conterminous United States using a logistic regression model," Applied Energy, Elsevier, vol. 352(C).
    25. Yang Wu & Malay Ghosh, 2017. "Asymptotic Expansion of the Posterior Based on Pairwise Likelihood," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 39-75, February.

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