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Some Improvements in Confidence Intervals for Standardized Regression Coefficients

Published online by Cambridge University Press:  01 January 2025

Paul DudgeonOpen the ORCID record for Paul Dudgeon[Opens in a new window]
Paul Dudgeon*
Affiliation:
The University of Melbourne
*
Correspondence should be made to Paul Dudgeon, Melbourne School of Psychological Sciences, The University of Melbourne, Parkville, VIC 3010, Australia. Email: dudgeon@unimelb.edu.au
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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.

Keywords

standardized regression coefficientsrobust confidence intervalsnon-normality

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Type
Original Paper
Information
Psychometrika , Volume 82 , Issue 4 , December 2017, pp. 928 - 951
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-017-9563-z) contains supplementary material, which is available to authorized users.

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