Berggren Mathias
Department of Psychology, Uppsala University.
Psychol Methods. 2024 Jul 18. doi: 10.1037/met0000681.
The coefficient of determination, ², also called the explained variance, is often taken as a proportional measure of the relative determination of model on outcome. However, while ² 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 ², and alternatives can therefore also be calculated by plugging in related estimates, such as the adjusted ². The third coefficient, new for this article, and here termed the CoD (the coefficient of determination in terms of standard deviations), or (-pi), equals ²/(²+1-²). It is argued that this coefficient most usefully captures the relative determination of the model. When the contribution of the error is times that of the model, the CoD equals 1/(1 + ), while ² equals 1/(1 + ²). (PsycInfo Database Record (c) 2024 APA, all rights reserved).
决定系数(R²)，也称为解释方差，通常被用作衡量模型对结果相对决定程度的比例指标。然而，尽管(R²)具有一些吸引人的统计特性，但其对平方变异（方差）的依赖可能会限制其作为该决定程度易于解释的描述性统计量的用途。在此，将讨论该系数在平方尺度上的特性，并将其推广到原始尺度上的三个相对度量。这些推广都可以表示为(R²)的变换形式，因此也可以通过代入相关估计值（如调整后的(R²)）来计算替代值。第三个系数是本文新提出的，在此称为CoD（标准差决定系数）或((-\pi))，等于(R²/(R² + 1 - R²))。有人认为，这个系数最能有效地体现模型的相对决定程度。当误差的贡献是模型贡献的(\times)倍时，CoD等于(1/(1 + ))，而(R²)等于(1/(1 + R²))。（PsycInfo数据库记录（c）2024美国心理学会，保留所有权利）
