A Simple and Fast Algorithm for Generating Correlation Matrices with a Known Average Correlation Coefficient

Abstract

This article describes a simple and fast algorithm for generating correlation matrices ( $\mathit{R})$ with a known average correlation. The algorithm should be useful for researchers desiring plausible $\mathit{R}$ matrices for substantive domains in which average correlations are known (at least approximately). The method is non iterative and it can solve relatively large problems (e.g., generate a $500\times 500$ $\mathit{R}$ matrix) in less than a second on a personal computer. It also has didactic value for introducing students to the convex set of feasible $\mathit{R}$ matrices of a fixed dimension. This Euclidean body is called an elliptope. The proposed method exploits the geometry of elliptopes to efficiently generate realistic $\mathit{R}$ matrices with a desired average correlation coefficient. R code for implementing the algorithm (and for reproducing all of the results of this article) is reported in an online supplement.

KEYWORDS:

• Correlation matrices
• Monte Carlo studies
• Elliptope geometry

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