Coefficients of Determination in Logistic Regression Models-A New Proposal: The Coefficient of Discrimination
Coefficients of Determination in Logistic Regression Models-A New Proposal: The Coefficient of Discrimination
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DOI：
10.1198/tast.2009.08210
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发表时间：
2009-11-01
影响因子：
1.8
通讯作者：
Tjur, Tue
中科院分区：
文献类型：
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作者：
Tjur, Tue
在逻辑回归的背景下，人们提出了许多与普通回归模型中的决定系数 R(2) 类似的方法。我们的出发点是研究与变异的二次测度相关的三个定义。我们讨论了这些统计数据的属性，并表明该系列可以通过第四个统计数据以自然的方式扩展，其解释更为简单，即分别成功和失败的拟合值平均值之间的差异。我们建议将此统计数据命名为“歧视系数”，并建议将其用作解释力的标准衡量标准。在直观的解释中，这个量与 R(2) 的经典版本没有直接关系，但事实证明它通过两个精确关系与这些相关，这意味着所有这些统计量都是渐近等价的。
Many analogues to the coefficient of determination R(2) in ordinary regression models have been proposed in the context of logistic regression. Our starting point is a study of three definitions related to quadratic measures of variation. We discuss the properties of these statistics, and show that the family can be extended in a natural way by a fourth statistic with an even simpler interpretation, namely the difference between the averages of fitted values for successes and failures, respectively. We propose the name "the coefficient of discrimination" for this statistic, and recommend its use as a standard measure of explanatory power. In its intuitive interpretation, this quantity has no immediate relation to the classical versions of R(2), but it turns out to be related to these by two exact relations, which imply that all these statistics are asymptotically equivalent.