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The Normal-Theory and Asymptotic Distribution-Free (ADF) Covariance Matrix of Standardized Regression Coefficients: Theoretical Extensions and Finite Sample Behavior

Published online by Cambridge University Press:  01 January 2025

Jeff A. Jones  and
Niels G. Waller
Jeff A. Jones
Affiliation:
University of Minnesota-Twin Cities
Niels G. Waller*
Affiliation:
University of Minnesota-Twin Cities
*
Requests for reprints should be sent to Niels G. Waller, Department of Psychology, University of Minnesota, 75 East River Road, Minneapolis, MN, 55455, USA. E-mail: nwaller@umn.edu
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Abstract

Yuan and Chan (Psychometrika, 76, 670–690, 2011) recently showed how to compute the covariance matrix of standardized regression coefficients from covariances. In this paper, we describe a method for computing this covariance matrix from correlations. Next, we describe an asymptotic distribution-free (ADF; Browne in British Journal of Mathematical and Statistical Psychology, 37, 62–83, 1984) method for computing the covariance matrix of standardized regression coefficients. We show that the ADF method works well with nonnormal data in moderate-to-large samples using both simulated and real-data examples. R code (R Development Core Team, 2012) is available from the authors or through the Psychometrika online repository for supplementary materials.

Keywords

standardized regression coefficientsmultiple regressionADFconfidence intervals

Information

Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 2 , June 2015 , pp. 365 - 378
Copyright
Copyright © 2013 The Psychometric Society

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Footnotes

Electronic Supplementary Material The online version of this article (doi:10.1007/s11336-013-9380-y) contains supplementary material, which is available to authorized users.

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The Normal-Theory and Asymptotic Distribution-Free (ADF) Covariance Matrix of Standardized Regression Coefficients: Theoretical Extensions and Finite Sample Behavior
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