Some Improvements in Confidence Intervals for Standardized Regression Coefficients

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: non-normality; robust confidence intervals; standardized regression coefficients.