IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v36y2009i6p647-657.html
   My bibliography  Save this article

A copula-based Markov chain model for the analysis of binary longitudinal data

Author

Listed:
  • Gabriel Escarela
  • Luis Carlos Perez-Ruiz
  • Russell Bowater

Abstract

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.

Suggested Citation

  • Gabriel Escarela & Luis Carlos Perez-Ruiz & Russell Bowater, 2009. "A copula-based Markov chain model for the analysis of binary longitudinal data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(6), pages 647-657.
    • Handle: RePEc:taf:japsta:v:36:y:2009:i:6:p:647-657
    DOI: 10.1080/02664760802499287
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760802499287
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760802499287?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Xue‐Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320, June.
    2. Azari, Rahman & Li, Lexin & Tsai, Chih-Ling, 2006. "Longitudinal data model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3053-3066, July.
    3. Patrick J. Heagerty, 2002. "Marginalized Transition Models and Likelihood Inference for Longitudinal Categorical Data," Biometrics, The International Biometric Society, vol. 58(2), pages 342-351, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huihui Lin & N. Rao Chaganty, 2021. "Multivariate distributions of correlated binary variables generated by pair-copulas," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-14, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Furman, Edward & Landsman, Zinoviy, 2010. "Multivariate Tweedie distributions and some related capital-at-risk analyses," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 351-361, April.
    2. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    3. Jaeun Choi & A. James O'Malley, 2017. "Estimating the causal effect of treatment in observational studies with survival time end points and unmeasured confounding," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 159-185, January.
    4. Philipp Arbenz, 2013. "Bayesian Copulae Distributions, with Application to Operational Risk Management—Some Comments," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 105-108, March.
    5. Azam, Kazim, 2014. "Effects of Marginal Specifcations on Copula Estimation," Economic Research Papers 270230, University of Warwick - Department of Economics.
    6. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    7. 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.
    8. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Technical Working Papers 0331, National Bureau of Economic Research, Inc.
    9. Kenneth J. Wilkins & Garrett M. Fitzmaurice, 2006. "A Hybrid Model for Nonignorable Dropout in Longitudinal Binary Responses," Biometrics, The International Biometric Society, vol. 62(1), pages 168-176, March.
    10. Smith, Michael Stanley & Shively, Thomas S., 2018. "Econometric modeling of regional electricity spot prices in the Australian market," Energy Economics, Elsevier, vol. 74(C), pages 886-903.
    11. M.J. Daniels & C. Wang & B.H. Marcus, 2014. "Fully Bayesian inference under ignorable missingness in the presence of auxiliary covariates," Biometrics, The International Biometric Society, vol. 70(1), pages 62-72, March.
    12. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    13. 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.
    14. Minji Lee & Sun Ju Chung & Youngjo Lee & Sera Park & Jun-Gun Kwon & Dai Jin Kim & Donghwan Lee & Jung-Seok Choi, 2020. "Investigation of Correlated Internet and Smartphone Addiction in Adolescents: Copula Regression Analysis," IJERPH, MDPI, vol. 17(16), pages 1-12, August.
    15. Zichen Ma & Shannon W. Davis & Yen‐Yi Ho, 2023. "Flexible copula model for integrating correlated multi‐omics data from single‐cell experiments," Biometrics, The International Biometric Society, vol. 79(2), pages 1559-1572, June.
    16. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    17. Mendes, Beatriz Vaz de Melo & Arslan, Olcay, 2006. "Multivariate Skew Distributions Based on the GT-Copula," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 26(2), November.
    18. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    19. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    20. Mai, Qing & Zou, Hui, 2015. "Sparse semiparametric discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 175-188.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:36:y:2009:i:6:p:647-657. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.