IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i2p365-378.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9380-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9380-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Max Auerswald & Morten Moshagen, 2015. "Generating Correlated, Non-normally Distributed Data Using a Non-linear Structural Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 920-937, December.
    3. Mohan D. Pant & Todd C. Headrick, 2017. "Simulating Uniform- and Triangular- Based Double Power Method Distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(1), pages 1-1.
    4. Emanuela Raffinetti & Pier Alda Ferrari, 2021. "A dependence measure flow tree through Monte Carlo simulations," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(2), pages 467-496, April.
    5. Al-Subaihi, Ali A., 2004. "Simulating Correlated Multivariate Pseudorandom Numbers," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 9(i04).
    6. M Hashem Pesaran & Takashi Yamagata, 2012. "Testing CAPM with a Large Number of Assets," Discussion Papers 12/05, Department of Economics, University of York.
    7. Pasquale Dolce & Cristina Davino & Domenico Vistocco, 2022. "Quantile composite-based path modeling: algorithms, properties and applications," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(4), pages 909-949, December.
    8. Ke-Hai Yuan & Peter Bentler, 2002. "On robusiness of the normal-theory based asymptotic distributions of three reliability coefficient estimates," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 251-259, June.
    9. repec:jss:jstsof:09:i04 is not listed on IDEAS
    10. Njål Foldnes & Steffen Grønneberg, 2015. "How General is the Vale–Maurelli Simulation Approach?," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1066-1083, December.
    11. Hakan Demirtas, 2016. "A Note on the Relationship Between the Phi Coefficient and the Tetrachoric Correlation Under Nonnormal Underlying Distributions," The American Statistician, Taylor & Francis Journals, vol. 70(2), pages 143-148, May.
    12. Reinartz, Werner & Haenlein, Michael & Henseler, Jörg, 2009. "An empirical comparison of the efficacy of covariance-based and variance-based SEM," International Journal of Research in Marketing, Elsevier, vol. 26(4), pages 332-344.
    13. Pesaran, M. H. & Yamagata, T., 2012. "Testing CAPM with a Large Number of Assets (Updated 28th March 2012)," Cambridge Working Papers in Economics 1210, Faculty of Economics, University of Cambridge.
    14. Headrick, Todd C. & Sheng, Yanyan & Hodis, Flaviu-Adrian, 2007. "Numerical Computing and Graphics for the Power Method Transformation Using Mathematica," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i03).
    15. Mahul, Olivier, 2002. "Hedging Price Risk in the Presence of Crop Yield and Revenue Insurance," 2002 International Congress, August 28-31, 2002, Zaragoza, Spain 24881, European Association of Agricultural Economists.
    16. Shaobo Jin & Fan Yang-Wallentin, 2017. "Asymptotic Robustness Study of the Polychoric Correlation Estimation," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 67-85, March.
    17. Rainer Schlittgen & Marko Sarstedt & Christian M. Ringle, 2020. "Data generation for composite-based structural equation modeling methods," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(4), pages 747-757, December.
    18. repec:jss:jstsof:19:i03 is not listed on IDEAS
    19. Hakan Demirtas & Robab Ahmadian & Sema Atis & Fatma Ezgi Can & Ilker Ercan, 2016. "A nonnormal look at polychoric correlations: modeling the change in correlations before and after discretization," Computational Statistics, Springer, vol. 31(4), pages 1385-1401, December.
    20. Clintin Davis-Stober, 2011. "A Geometric Analysis of When Fixed Weighting Schemes Will Outperform Ordinary Least Squares," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 650-669, October.
    21. Theo Dijkstra & Karin Schermelleh-Engel, 2014. "Consistent Partial Least Squares for Nonlinear Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 585-604, October.
    22. Gary van Vuuren & Riaan de Jongh, 2017. "A comparison of risk aggregation estimates using copulas and Fleishman distributions," Applied Economics, Taylor & Francis Journals, vol. 49(17), pages 1715-1731, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:365-378. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.