IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v82y2017i4d10.1007_s11336-017-9563-z.html
   My bibliography  Save this article

Some Improvements in Confidence Intervals for Standardized Regression Coefficients

Author

Listed:
  • Paul Dudgeon

    (The University of Melbourne)

Abstract

Yuan and Chan (Psychometrika 76:670–690, 2011. doi: 10.1007/S11336-011-9224-6 ) derived consistent confidence intervals for standardized regression coefficients under fixed and random score assumptions. Jones and Waller (Psychometrika 80:365–378, 2015. doi: 10.1007/S11336-013-9380-Y ) extended these developments to circumstances where data are non-normal by examining confidence intervals based on Browne’s (Br J Math Stat Psychol 37:62–83, 1984. doi: 10.1111/j.2044-8317.1984.tb00789.x ) asymptotic distribution-free (ADF) theory. Seven different heteroscedastic-consistent (HC) estimators were investigated in the current study as potentially better solutions for constructing confidence intervals on standardized regression coefficients under non-normality. Normal theory, ADF, and HC estimators were evaluated in a Monte Carlo simulation. Findings confirmed the superiority of the HC3 (MacKinnon and White, J Econ 35:305–325, 1985. doi: 10.1016/0304-4076(85)90158-7 ) and HC5 (Cribari-Neto and Da Silva, Adv Stat Anal 95:129–146, 2011. doi: 10.1007/s10182-010-0141-2 ) interval estimators over Jones and Waller’s ADF estimator under all conditions investigated, as well as over the normal theory method. The HC5 estimator was more robust in a restricted set of conditions over the HC3 estimator. Some possible extensions of HC estimators to other effect size measures are considered for future developments.

Suggested Citation

  • Paul Dudgeon, 2017. "Some Improvements in Confidence Intervals for Standardized Regression Coefficients," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 928-951, December.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-017-9563-z
    DOI: 10.1007/s11336-017-9563-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-017-9563-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-017-9563-z?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. P. M. Bentler & Sik-Yum Lee, 1983. "Covariance Structures Under Polynomial Constraints: Applications to Correlation and Alpha-Type Structural Models," Journal of Educational and Behavioral Statistics, , vol. 8(3), pages 207-222, September.
    3. 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).
    4. Francisco Cribari-Neto & Wilton Silva, 2011. "A new heteroskedasticity-consistent covariance matrix estimator for the linear regression model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(2), pages 129-146, June.
    5. Cribari-Neto, Francisco, 2004. "Asymptotic inference under heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 215-233, March.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. 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).
    8. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
    9. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    10. Gerhard Arminger & Ronald Schoenberg, 1989. "Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 409-425, September.
    11. Niels Waller & Jeff Jones, 2010. "Correlation Weights in Multiple Regression," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 58-69, March.
    12. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    13. 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.
    14. Headrick, Todd C., 2002. "Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 685-711, October.
    15. 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.
    16. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    17. Jeffrey J. Hoogland & Anne Boomsma, 1998. "Robustness Studies in Covariance Structure Modeling," Sociological Methods & Research, , vol. 26(3), pages 329-367, February.
    18. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    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. Clemens Koob, 2021. "Determinants of content marketing effectiveness: Conceptual framework and empirical findings from a managerial perspective," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-25, April.

    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. Hartigan, Luke, 2018. "Alternative HAC covariance matrix estimators with improved finite sample properties," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 55-73.
    2. 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.
    3. Katarzyna Jabłońska, 2018. "Dealing With Heteroskedasticity Within The Modeling Of The Quality Of Life Of Older People," Statistics in Transition New Series, Polish Statistical Association, vol. 19(3), pages 423-452, September.
    4. Cheng, Tsung-Chi, 2012. "On simultaneously identifying outliers and heteroscedasticity without specific form," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2258-2272.
    5. Romano, Joseph P. & Wolf, Michael, 2017. "Resurrecting weighted least squares," Journal of Econometrics, Elsevier, vol. 197(1), pages 1-19.
    6. Michael O'Hara & Christopher F. Parmeter, 2013. "Nonparametric Generalized Least Squares in Applied Regression Analysis," Pacific Economic Review, Wiley Blackwell, vol. 18(4), pages 456-474, October.
    7. Eric S. Lin & Ta-Sheng Chou, 2018. "Finite-sample refinement of GMM approach to nonlinear models under heteroskedasticity of unknown form," Econometric Reviews, Taylor & Francis Journals, vol. 37(1), pages 1-28, January.
    8. repec:jss:jstsof:16:i09 is not listed on IDEAS
    9. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
    10. José Curto & José Pinto & Ana Morais & Isabel Lourenço, 2011. "The heteroskedasticity-consistent covariance estimator in accounting," Review of Quantitative Finance and Accounting, Springer, vol. 37(4), pages 427-449, November.
    11. Jabłońska Katarzyna, 2018. "Dealing With Heteroskedasticity Within The Modeling Of The Quality Of Life Of Older People," Statistics in Transition New Series, Statistics Poland, vol. 19(3), pages 433-452, September.
    12. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
    13. Richard H. Spady & Sami Stouli, 2018. "Simultaneous Mean-Variance Regression," Bristol Economics Discussion Papers 18/697, School of Economics, University of Bristol, UK.
    14. Pötscher, Benedikt M. & Preinerstorfer, David, 2021. "Valid Heteroskedasticity Robust Testing," MPRA Paper 107420, University Library of Munich, Germany.
    15. Zeileis, Achim, 2006. "Implementing a class of structural change tests: An econometric computing approach," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 2987-3008, July.
    16. A. Colin Cameron & Douglas L. Miller, 2010. "Robust Inference with Clustered Data," Working Papers 106, University of California, Davis, Department of Economics.
    17. Pötscher, Benedikt M. & Preinerstorfer, David, 2023. "How Reliable Are Bootstrap-Based Heteroskedasticity Robust Tests?," Econometric Theory, Cambridge University Press, vol. 39(4), pages 789-847, August.
    18. Francisco Cribari-Neto & Maria da Gloria Lima, 2010. "Approximate inference in heteroskedastic regressions: A numerical evaluation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(4), pages 591-615.
    19. repec:jss:jstsof:42:c01 is not listed on IDEAS
    20. Cyrus J. DiCiccio & Joseph P. Romano & Michael Wolf, 2016. "Improving weighted least squares inference," ECON - Working Papers 232, Department of Economics - University of Zurich, revised Nov 2017.
    21. Charles, Amelie & Darne, Olivier, 2006. "Large shocks and the September 11th terrorist attacks on international stock markets," Economic Modelling, Elsevier, vol. 23(4), pages 683-698, July.
    22. repec:jss:jstsof:11:i10 is not listed on IDEAS
    23. Packalen, Mikko & Wirjanto, Tony S., 2012. "Inference about clustering and parametric assumptions in covariance matrix estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 1-14, January.

    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:82:y:2017:i:4:d:10.1007_s11336-017-9563-z. 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.