, Volume 80, Issue 2, pp 365–378 | Cite as

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



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.

Key words

standardized regression coefficients multiple regression ADF, confidence intervals 

Supplementary material

11336_2013_9380_MOESM1_ESM.pdf (4.7 mb)
(PDF 44 kB)
11336_2013_9380_MOESM2_ESM.pdf (55 kb)
(PDF 133 kB)


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Copyright information

© The Psychometric Society 2013

Authors and Affiliations

  1. 1.Department of PsychologyUniversity of MinnesotaMinneapolisUSA

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