{"title":"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。","authors":"Mathias Berggren","doi":"10.1037/met0000681","DOIUrl":null,"url":null,"abstract":"<p><p>The coefficient of determination, <i>R</i>², also called the explained variance, is often taken as a proportional measure of the relative determination of model on outcome. However, while <i>R</i>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 <i>R</i>², and alternatives can therefore also be calculated by plugging in related estimates, such as the adjusted <i>R</i>². The third coefficient, new for this article, and here termed the CoD<sub>SD</sub> (the coefficient of determination in terms of standard deviations), or <i>R</i><sub>π</sub> (<i>R</i>-pi), equals <i>R</i>²/(<i>R</i>²+1-<i>R</i>²). It is argued that this coefficient most usefully captures the relative determination of the model. When the contribution of the error is <i>c</i> times that of the model, the CoD<sub>SD</sub> equals 1/(1 + <i>c</i>), while <i>R</i>² equals 1/(1 + <i>c</i>²). (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>","PeriodicalId":20782,"journal":{"name":"Psychological methods","volume":" ","pages":""},"PeriodicalIF":7.6000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coefficients of determination measured on the same scale as the outcome: Alternatives to R² that use standard deviations instead of explained variance.\",\"authors\":\"Mathias Berggren\",\"doi\":\"10.1037/met0000681\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The coefficient of determination, <i>R</i>², also called the explained variance, is often taken as a proportional measure of the relative determination of model on outcome. However, while <i>R</i>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 <i>R</i>², and alternatives can therefore also be calculated by plugging in related estimates, such as the adjusted <i>R</i>². The third coefficient, new for this article, and here termed the CoD<sub>SD</sub> (the coefficient of determination in terms of standard deviations), or <i>R</i><sub>π</sub> (<i>R</i>-pi), equals <i>R</i>²/(<i>R</i>²+1-<i>R</i>²). It is argued that this coefficient most usefully captures the relative determination of the model. When the contribution of the error is <i>c</i> times that of the model, the CoD<sub>SD</sub> equals 1/(1 + <i>c</i>), while <i>R</i>² equals 1/(1 + <i>c</i>²). (PsycInfo Database Record (c) 2024 APA, all rights reserved).</p>\",\"PeriodicalId\":20782,\"journal\":{\"name\":\"Psychological methods\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":7.6000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Psychological methods\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://doi.org/10.1037/met0000681\",\"RegionNum\":1,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PSYCHOLOGY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Psychological methods","FirstCategoryId":"102","ListUrlMain":"https://doi.org/10.1037/met0000681","RegionNum":1,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PSYCHOLOGY, MULTIDISCIPLINARY","Score":null,"Total":0}
Coefficients of determination measured on the same scale as the outcome: Alternatives to R² that use standard deviations instead of explained variance.
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).
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.