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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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    2. 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.
    3. 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.
    4. 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.
    5. 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.
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    11. 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).
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    15. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    16. 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.
    17. 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.
    18. 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.
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    20. 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).
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    22. 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.
    23. 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.
    24. 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.
    25. 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.

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