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Easily simulated multivariate binary distributions with given positive and negative correlations

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  • Oman, Samuel D.

Abstract

We consider the problem of defining a multivariate distribution of binary variables, with given first two moments, from which values can be easily simulated. Oman and Zucker [Oman, S.D., Zucker, D.M., 2001. Modelling and generating correlated binary variables. Biometrika 88, 287-290] have done this when the correlation matrix of the binary variables is the Schur product of a parametric correlation matrix appropriate for normal variables (intraclass, moving average or autoregressive), having non-negative entries, with a matrix whose entries comprise the Fréchet upper bounds on the pairwise correlations of the binary variables. We extend their method to include negative correlations; moreover, we extend the range of positive correlations allowed in the moving-average case. We present algorithms for simulation of data from these distributions, and examine the ranges of correlations obtained.

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  • Oman, Samuel D., 2009. "Easily simulated multivariate binary distributions with given positive and negative correlations," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 999-1005, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:999-1005
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    References listed on IDEAS

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    1. N. Rao Chaganty & Harry Joe, 2006. "Range of correlation matrices for dependent Bernoulli random variables," Biometrika, Biometrika Trust, vol. 93(1), pages 197-206, March.
    2. Guosheng Yin & Yu Shen, 2005. "Adaptive Design and Estimation in Randomized Clinical Trials with Correlated Observations," Biometrics, The International Biometric Society, vol. 61(2), pages 362-369, June.
    3. N. Rao Chaganty & Harry Joe, 2004. "Efficiency of generalized estimating equations for binary responses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 851-860, November.
    4. Bahjat F. Qaqish, 2003. "A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations," Biometrika, Biometrika Trust, vol. 90(2), pages 455-463, June.
    5. Molin Wang & John M. Williamson, 2005. "Generalization of the Mantel–Haenszel Estimating Function for Sparse Clustered Binary Data," Biometrics, The International Biometric Society, vol. 61(4), pages 973-981, December.
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    5. Li, Gaorong & Lian, Heng & Feng, Sanying & Zhu, Lixing, 2013. "Automatic variable selection for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 174-186.

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