An efficient algorithm is derived for generating systems of correlated binary data. The procedure allows for the specification of all pairwise correlations within each system. Intercorrelations between systems can be specified qualitatively.The procedure requires the simultaneous solution of a system of equations for obtaining the threshold probabilities to generate each system of binary data. A numerical example is provided to demonstrate that the procedure generates correlated binary variables that yield correlations in close agreement with the specified population correlations.
Headrick, Todd C. "A Method for Simulating Systems of Correlated Binary Data." (Winter 2002).