A column-oriented optimization approach for the generation of correlated random vectors

Abstract

To induce a desired correlation structure among random variables, widely popular simulation software relies upon the method of Iman and Conover (IC). The underlying premise is that the induced Spearman rank correlation is a meaningful way to approximate other correlation measures among the random variables (e.g., Pearson’s correlation). However, as expected, the desired a posteriori correlation structure often deviates from the Spearman correlation structure. Rooted in the same principle of IC, we propose an alternative distribution-free method based on mixed-integer programming to induce a Pearson correlation structure to bivariate or multivariate random vectors. We also extend our distribution-free method to other correlation measures such as Kendall’s coefficient of concordance, Phi correlation coefficient, and relative risk. We illustrate our method in four different contexts: (1) the simulation of a healthcare facility, (2) the analysis of a manufacturing tandem queue, (3) the imputation of correlated missing data in statistical analysis, and (4) the estimation of the budget overrun risk in a construction project. We also explore the limits of our algorithms by conducting extensive experiments using randomly generated data from multiple distributions.