TY - JOUR
T1 - Easily simulated multivariate binary distributions with given positive and negative correlations
AU - Oman, Samuel D.
PY - 2009/2/15
Y1 - 2009/2/15
N2 - 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 C 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.
AB - 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 C 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.
UR - http://www.scopus.com/inward/record.url?scp=58549117280&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2008.11.017
DO - 10.1016/j.csda.2008.11.017
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AN - SCOPUS:58549117280
SN - 0167-9473
VL - 53
SP - 999
EP - 1005
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 4
ER -