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

G Escarela, L Carlos Perez-Ruiz, Russell Bowater

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)647-657
    Number of pages11
    JournalJournal of Applied Statistics
    Volume36
    Issue number6
    DOIs
    Publication statusPublished - 1 Jan 2009

    Keywords

    • discrete time series
    • maximum likelihood
    • serial correlation
    • Markov regression models
    • copula
    • probit regression model

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