In reply to KeJon Poole.

Yes, this simulation requires some care. Section 9.2 of Simulating Data with SAS (Wicklin, 2013) discusses the Emrich and Piedmonte (1991) algorithm for simulating from multivariate correlated binary variables and implements the algorithm in SAS/IML. To get the correct correlations, you need to solve an intermediate equation that involves the bivariate normal CDF. Also, be aware that not all correlation matrices are feasible.