Posted by Improvements on the Development of Correlated Input Variables for Monte Carlo Simulation
From the Journal of Cost Analysis and Parametrics: Volume 10 | Issue 1 | October 2021
Downloadable file: JCAPv10i1-CorrelatedInputVariablesMonteCarlo-Henke
Abstract: In this paper, the development of model inputs with specified correlation is explored. Input variable correlation is an influential driver of final cost risk distributions; especially so for highly positively or negatively correlated inputs. If not captured appropriately between inputs, significant errors in resultant cost risk distribution will occur. In general, the further away from a 50% confidence level cost value, the greater the error will be when input data does not reflect accurate correlation. The widely adopted Iman-Conover (IC) Method for inducing desired rank correlation on a multivariate input for modeling by Monte Carlo simulation is reviewed. The IC method culminates in the re-ordering of the values of each input vector such that the resultant correlation of the vectors is close to the desired correlation. This paper provides insights into how the IC Method, devised as a method for inducing a desired rank correlation, can be equally if not more powerful for inducing desired Pearson product-moment (linear) correlation on inputs. Spearman’s rank correlation and linear correlation values that result from the IC Method are compared to the desired correlation values ranging from -1 to 1. Insights into the mechanics of the algorithm are presented in order to provide a richer understanding of the process and to inform aspects of work when the algorithm is employed. Extending this IC method to an iterative process described in this paper shows that the resulting set of variates would more accurately reflect the desired correlation in all cases for the calculated linear correlation. Conversely, for highly skewed distributions, the iteration process resulted in increasing the error of the calculated Spearman’s rank correlation. The iteration process is explained with examples to illustrate improved linear correlation accuracy for both symmetric and highly skewed distributions.
Author: Douglas Henke served in the U. S. Coast Guard from 1980 to 2004. His service included tours as Chief Engineer on the Coast Guard Cutter CAMPBELL, Associate Professor in the Coast Guard Academy’s Engineering Department and final tour as Program Manager for recapitalizing the Coast Guard’s aging fleet of ships and boats. Since retirement in 2004, he’s been a consultant to Program Managers in the Coast Guard’s Acquisition Directorate; providing a variety of services including financial and statistical analysis and modeling.