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

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  • Niels G. Waller

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.

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  • Niels G. Waller, 2025. "A Simple and Fast Algorithm for Generating Correlation Matrices with a Known Average Correlation Coefficient," The American Statistician, Taylor & Francis Journals, vol. 79(1), pages 23-29, January.
    • Handle: RePEc:taf:amstat:v:79:y:2025:i:1:p:23-29
    DOI: 10.1080/00031305.2024.2350449
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