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

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Abstract

This article describes a simple and fast algorithm for generating correlation matrices ((Formula presented.) 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.

Original languageEnglish (US)
JournalAmerican Statistician
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
© 2024 American Statistical Association.

Keywords

  • Correlation matrices
  • Elliptope geometry
  • Monte Carlo studies

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