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

Niels G. Waller

The American Statistician, 2025, vol. 79, issue 1, 23-29

Abstract: This article describes a simple and fast algorithm for generating correlation matrices (R) with a known average correlation. The algorithm should be useful for researchers desiring plausible 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 × 500 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 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 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.

Date: 2025
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DOI: 10.1080/00031305.2024.2350449

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