Multivariate distributions of correlated binary variables generated by pair-copulas

Huihui Lin () and N. Rao Chaganty ()
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Huihui Lin: Department of Mathematics & Statistics, Old Dominion University
N. Rao Chaganty: Department of Mathematics & Statistics, Old Dominion University

Journal of Statistical Distributions and Applications, 2021, vol. 8, issue 1, 1-14

Abstract: Abstract Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) and the multivariate probit (MP) model are two of the popular methods for analyzing such data. However, both methods have some significant drawbacks. The GEEs may not have an underlying likelihood and the MP model may fail to generate a multivariate binary distribution with specified marginals and bivariate correlations. In this paper, we study multivariate binary distributions that are based on D-vine pair-copula models as a superior alternative to these methods. We elucidate the construction of these binary distributions in two and three dimensions with numerical examples. For higher dimensions, we provide a method of constructing a multidimensional binary distribution with specified marginals and equicorrelated correlation matrix. We present a real-life data analysis to illustrate the application of our results.

Keywords: D-vine; Mutivariate binary distributions; Multivariate probit model; Pair-copulas (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1186/s40488-021-00118-z

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