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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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  • Jeff Jones
  • Niels Waller

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. Copyright The Psychometric Society 2015

Suggested Citation

  • Jeff Jones & Niels Waller, 2015. "The Normal-Theory and Asymptotic Distribution-Free (ADF) Covariance Matrix of Standardized Regression Coefficients: Theoretical Extensions and Finite Sample Behavior," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 365-378, June.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:365-378
    DOI: 10.1007/s11336-013-9380-y
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    References listed on IDEAS

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    1. Niels Waller & Jeff Jones, 2011. "Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of Predictors," Psychometrika, Springer;The Psychometric Society, vol. 76(3), pages 410-439, July.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Niels Waller & Jeff Jones, 2010. "Correlation Weights in Multiple Regression," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 58-69, March.
    4. Niels Waller, 2011. "The Geometry of Enhancement in Multiple Regression," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 634-649, October.
    5. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, September.
    6. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    7. Allen Fleishman, 1978. "A method for simulating non-normal distributions," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 521-532, December.
    8. Kelley, Ken, 2007. "Confidence Intervals for Standardized Effect Sizes: Theory, Application, and Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i08).
    9. Ke-Hai Yuan & Wai Chan, 2011. "Biases and Standard Errors of Standardized Regression Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 670-690, October.
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    Citations

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    Cited by:

    1. Paul Dudgeon, 2017. "Some Improvements in Confidence Intervals for Standardized Regression Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 928-951, December.
    2. José A. Fernández-Archilla & José M. Aguilar-Parra & Joaquín F. Álvarez-Hernández & Antonio Luque de la Rosa & Gerardo Echeita & Rubén Trigueros, 2020. "Validation of the Index for Inclusion Questionnaire for Parents of Non-University Education Students," IJERPH, MDPI, vol. 17(9), pages 1-13, May.
    3. Jeff Jones & Niels Waller, 2016. "Erratum to: The Normal-Theory and Asymptotic Distribution-Free (ADF) Covariance Matrix of Standardized Regression Coefficients: Theoretical Extensions and Finite Sample Behavior," Psychometrika, Springer;The Psychometric Society, vol. 81(1), pages 249-249, March.
    4. José A. Fernández-Archilla & Joaquín F. Álvarez & José M. Aguilar-Parra & Rubén Trigueros & Isabel D. Alonso-López & Gerardo Echeita, 2020. "Validation of the Index for Inclusion Questionnaire for Compulsory Secondary Education Students," Sustainability, MDPI, vol. 12(6), pages 1-11, March.

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