Coefficients of determination measured on the same scale as the outcome: Alternatives to R² that use standard deviations instead of explained variance.

IF 7.6 1区 心理学 Q1 PSYCHOLOGY, MULTIDISCIPLINARY
Mathias Berggren
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引用次数: 0

Abstract

The coefficient of determination, R², also called the explained variance, is often taken as a proportional measure of the relative determination of model on outcome. However, while R² has some attractive statistical properties, its reliance on squared variations (variances) may limit its use as an easily interpretable descriptive statistic of that determination. Here, the properties of this coefficient on the squared scale are discussed and generalized to three relative measures on the original scale. These generalizations can all be expressed as transformations of R², and alternatives can therefore also be calculated by plugging in related estimates, such as the adjusted R². The third coefficient, new for this article, and here termed the CoDSD (the coefficient of determination in terms of standard deviations), or Rπ (R-pi), equals R²/(R²+1-R²). It is argued that this coefficient most usefully captures the relative determination of the model. When the contribution of the error is c times that of the model, the CoDSD equals 1/(1 + c), while R² equals 1/(1 + c²). (PsycInfo Database Record (c) 2024 APA, all rights reserved).

以与结果相同的尺度衡量的决定系数:R² 的替代品,使用标准差代替解释方差。
判定系数 R²,也称为解释方差,通常被用作衡量模型对结果的相对判定的比例。然而,虽然 R² 具有一些吸引人的统计特性,但它对平方差(方差)的依赖可能会限制其作为一种易于解释的判定系数描述性统计量的使用。在此,我们将讨论该系数在平方标度上的特性,并将其归纳为原始标度上的三个相对测量值。这些概括都可以表示为 R² 的变换,因此也可以通过插入相关估计值(如调整后的 R²)来计算替代系数。第三个系数是本文新增的,在此称为 CoDSD(以标准差表示的判定系数),或 Rπ (R-pi),等于 R²/(R²+1-R²)。有观点认为,该系数能最有效地反映模型的相对确定性。当误差贡献是模型贡献的 c 倍时,CoDSD 等于 1/(1 + c),而 R² 等于 1/(1 + c²)。(PsycInfo Database Record (c) 2024 APA,保留所有权利)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Psychological methods
Psychological methods PSYCHOLOGY, MULTIDISCIPLINARY-
CiteScore
13.10
自引率
7.10%
发文量
159
期刊介绍: Psychological Methods is devoted to the development and dissemination of methods for collecting, analyzing, understanding, and interpreting psychological data. Its purpose is the dissemination of innovations in research design, measurement, methodology, and quantitative and qualitative analysis to the psychological community; its further purpose is to promote effective communication about related substantive and methodological issues. The audience is expected to be diverse and to include those who develop new procedures, those who are responsible for undergraduate and graduate training in design, measurement, and statistics, as well as those who employ those procedures in research.
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