Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Dependence Modeling

Ed. by Puccetti, Giovanni

Covered by:

Open Access
See all formats and pricing
More options …

Some New Random Effect Models for Correlated Binary Responses

Fodé Tounkara
  • Department of Mathematics and Statistics, Université Laval„ 1045 av. de la Médecine, Québec (Québec) G1V 0A6 Canada
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Louis-Paul Rivest
  • Department of Mathematics and Statistics, Université Laval„ 1045 av. de la Médecine, Québec (Québec) G1V 0A6 Canada
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2014-12-01 | DOI: https://doi.org/10.2478/demo-2014-0006


Exchangeable copulas are used to model an extra-binomial variation in Bernoulli experiments with a variable number of trials. Maximum likelihood inference procedures for the intra-cluster correlation are constructed for several copula families. The selection of a particular model is carried out using the Akaike information criterion (AIC). Profile likelihood confidence intervals for the intra-cluster correlation are constructed and their performance are assessed in a simulation experiment. The sensitivity of the inference to the specification of the copula family is also investigated through simulations. Numerical examples are presented.

Keywords: Multivariate exchangeable copulas; Exchangeable binary data; Profile interval; Maximum likelihood

MSC: 62H05


  • [1] Ahmed, M. and Shoukri, M. (2010). A bayesian estimator of the intracluster correlation coefficient from correlated binary responses. J. Data Sci., 8:127–137. Google Scholar

  • [2] Alanko, T. and Duffy, J. C. (1996). Compound binomial distribution for modeling consumption data. The Statistician, 45:269– 286. CrossrefGoogle Scholar

  • [3] Ananth, C. V. and Preisser, J. S. (1999). Bivariate logistic regression: Modeling the association of small for gestational age births in twin gestations. Stat. Med., 18:2011–2023. CrossrefGoogle Scholar

  • [4] Chakraborty, H., Moore, J., Carlo, W. A., Hartwell, T. D., and Wright, L. L. (2009). A simulation based technique to estimate intracluster correlation for a binary variable. Contemporary Clinical Trials, 30:71–80. CrossrefPubMedWeb of ScienceGoogle Scholar

  • [5] Eldridge, S. and Kerry, S. (2012). A Practical Guide to Cluster Randomised Trials in Health Services Research. Wiley, New York. Google Scholar

  • [6] Feng, Z. and Crizzle, J. E. (1992). Correlated binomial variates: Properties of estimators of intraclass correlation and its effect on sample size calculation. Stat. Med., 11:1600–1614. Google Scholar

  • [7] Fleiss, J. L. and Cuzick, J. (1979). The reliability of dichotomous judgments: Unequal numbers of judges per subject. Appl. Psychol. Meas., 3:537–542. CrossrefGoogle Scholar

  • [8] Kuk, A. Y. C. (2004). A generalized estimating equation approach to modelling foetal response in developmental toxicity studies when the number of implants is dose dependent. J. Roy. Statist. Soc. Ser. C, 52:52–61. Google Scholar

  • [9] Légaré, F., Labrecque, M., LeBlanc, A., Njoya, M., Laurier, C., Côté, L., Godin, G., Thivierge, R. L., O’Connor, A., and S., S.-J. (2011). Training family physicians in shared decision making for the use of antibiotics for acute respiratory infections: a pilot clustered randomized controlled trial. Health Expect., 1:96–110. Web of ScienceCrossrefGoogle Scholar

  • [10] Liang, K. Y., Qaqish, B., and Zeger, S. (1992). Multivariate regression analyses for categorical data. J. Roy. Statist. Soc. Ser. B., 54:3–40. Google Scholar

  • [11] Lipsitz, S. R., Laird, N. M., and Harrington, D. P. (1991). Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association. Biometrika, 78:153–160. CrossrefGoogle Scholar

  • [12] Madsen, R. W. (1993). Generalized binomial distribution. Comm. Statist. Theory Methods, 22:3065–3086. CrossrefGoogle Scholar

  • [13] Mai, J.-M. and Scherer, M. (2012). Simulating Copulas; Stochastic Models, Sampling Algorithms and Applications. Series in Quantitative Finance: Volume 4. World Scientific Publishing Company, New York. Web of ScienceGoogle Scholar

  • [14] Nikoloulopoulos, A. K. and Karlis, D. (2008). Multivariate logit copula model with an application to dental data. Stat. Med., 27:6393–6406. CrossrefWeb of SciencePubMedGoogle Scholar

  • [15] Ochi, Y. and Prentice, R. L. (1984). Likelihood inference in a correlated probit regression model. Biometrika, 71:531–542. CrossrefGoogle Scholar

  • [16] Pals, S. L., Beaty, B. L., Posner, S. F., and Bull, S. (2009). Estimates of intraclass correlation for variables related to behavioral hiv/std prevention in a predominantly african american and hispanic sample of young women. Health Education & Behavior, 36:182–194. Web of ScienceGoogle Scholar

  • [17] Ridout, M. S., Demétrio, C. G. B., and Firth, D. (1999). Estimating intraclass correlation for binary data. Biometrics, 55:137– 148. CrossrefPubMedGoogle Scholar

  • [18] Saha, K. K. (2012). Profile likelihood-based confidence interval of the intraclass correlation for binary outcome data sampled from clusters. Stat. Med., 31:3982–4002. Web of ScienceCrossrefPubMedGoogle Scholar

  • [19] Shoukri, M. M., Kumar, P., and Colak, D. (2011). Analyzing dependent proportions in cluster randomized trials: Modeling inter-cluster correlation via copula function. Comput. Statist. Data Anal., 55:1226–1235. CrossrefWeb of ScienceGoogle Scholar

  • [20] Stefanescu, C. and Turnbull, B. W. (2003). Likelihood inference for exchangeable binary data with varying cluster sizes. Biometrics, 59:18–24. PubMedCrossrefGoogle Scholar

  • [21] Turner, R. M., Omar, R. Z., and Thompson, S. G. (2001). Bayesian methods of analysis for cluster randomized trials with binary outcome data. Stat. Med., 20:453–472. PubMedCrossrefGoogle Scholar

  • [22] Turner, R. M., Omar, R. Z., and Thompson, S. G. (2006). Constructing intervals for the intracluster correlation coefficient using bayesian modelling, and application in cluster randomized trials. Stat. Med., 25:1443–1456. PubMedCrossrefGoogle Scholar

  • [23] Williams, D. A. (1975). The analysis of binary response from toxicological experiments involving reproduction and teratogenicity. Biometrics, 31:949–952. PubMedCrossrefGoogle Scholar

  • [24] Williams, D. A. (1982). Extra-binomial variation in logistic linear models. J. Appl. Statist., 31:305–309. Google Scholar

  • [25] Zou, G. and Donner A., (2004). Confidence interval estimation of the intraclass correlation coefficient for binary outcome data. Biometrics., 60:807–811.CrossrefPubMedGoogle Scholar

About the article

Received: 2014-05-12

Accepted: 2014-10-16

Published Online: 2014-12-01

Citation Information: Dependence Modeling, Volume 2, Issue 1, ISSN (Online) 2300-2298, DOI: https://doi.org/10.2478/demo-2014-0006.

Export Citation

© 2014 Fodé Tounkara, Louis-Paul Rivest. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Fodé Tounkara and Louis-Paul Rivest
Biometrics, 2015, Volume 71, Number 3, Page 721

Comments (0)

Please log in or register to comment.
Log in