Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

For a fixed set of standardized regression coefficients and a fixed coefficient of determination (R-squared), an infinite number of predictor correlation matrices will satisfy the implied quadratic form. I call such matrices fungible correlation matrices. In this article, I describe an algorithm for generating positive definite (PD), positive semidefinite (PSD), or indefinite (ID) fungible correlation matrices that have a random or fixed smallest eigenvalue. The underlying equations of this algorithm are reviewed from both algebraic and geometric perspectives. Two simulation studies illustrate that fungible correlation matrices can be profitably used in Monte Carlo research. The first study uses PD fungible correlation matrices to compare penalized regression algorithms. The second study uses ID fungible correlation matrices to compare matrix-smoothing algorithms. R code for generating fungible correlation matrices is presented in the supplemental materials.

Original languageEnglish (US)
Pages (from-to)554-568
Number of pages15
JournalMultivariate Behavioral Research
Volume51
Issue number4
DOIs
StatePublished - Jul 3 2016

Keywords

  • Monte Carlo
  • Random correlation matrices
  • matrix smoothing
  • multiple regression
  • penalized regression

Fingerprint

Dive into the research topics of 'Fungible Correlation Matrices: A Method for Generating Nonsingular, Singular, and Improper Correlation Matrices for Monte Carlo Research'. Together they form a unique fingerprint.

Cite this