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

Author

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Dimitris Karlis & Naushad Mamode Khan & Yuvraj Sunecher, 2024. "The Negative Binomial INAR(1) Process under Different Thinning Processes: Can We Separate between the Different Models?," Stats, MDPI, vol. 7(3), pages 1-15, July.
    2. 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.

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