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

Jorge A. Sefair (), Oscar Guaje and Andrés L. Medaglia
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Jorge A. Sefair: Arizona State University
Oscar Guaje: Universidad de los Andes
Andrés L. Medaglia: Universidad de los Andes

OR Spectrum: Quantitative Approaches in Management, 2021, vol. 43, issue 3, No 8, 777-808

Abstract: 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.

Keywords: Correlated random vectors; Iman–Conover method; Spearman rank correlation; Pearson product-moment correlation; Kendall coefficient of concordance; Phi correlation coefficient; Relative risk; Simulation; Data imputation (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00291-021-00620-5

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