Melbourne School of Psychological Sciences, The University of Melbourne, Parkville, VIC, 3010, Australia.
Psychometrika. 2017 Dec;82(4):928-951. doi: 10.1007/s11336-017-9563-z. Epub 2017 Mar 13.
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.
袁和陈（心理测量学 76:670-690，2011 年。doi：10.1007/S11336-011-9224-6）在固定和随机分数假设下为标准化回归系数推导出一致的置信区间。琼斯和沃勒（心理测量学 80:365-378，2015 年。doi：10.1007/S11336-013-9380-Y）通过检查基于 Browne 的置信区间，将这些发展扩展到数据非正态的情况（Br J Math Stat Psychol 37:62-83，1984 年。doi：10.1111/j.2044-8317.1984.tb00789.x）渐近分布自由（ADF）理论。本研究考察了七种不同的异方差一致（HC）估计量，作为构建非正态标准化回归系数置信区间的潜在更好解决方案。在蒙特卡罗模拟中评估了正态理论、ADF 和 HC 估计量。研究结果证实，HC3（MacKinnon 和 White，J Econ 35:305-325，1985 年。doi：10.1016/0304-4076（85）1985.10.1007/s10182-010-0141-2）和 HC5（Cribari-Neto 和 Da Silva，Adv Stat Anal 95:129-146，2011 年。doi：10.1007/s10182-010-0141-2）区间估计在所有研究条件下均优于琼斯和沃勒的 ADF 估计量，也优于正态理论方法。在 HC3 估计量的一组受限条件下，HC5 估计量更稳健。考虑将 HC 估计量扩展到其他效应大小度量的一些可能的扩展，以用于未来的发展。
