Coefficients of determination for multiple logistic regression analysis
Coefficients of determination for multiple logistic regression analysis
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DOI：
10.2307/2685605
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发表时间：
2000-02-01
影响因子：
1.8
通讯作者：
Menard, S
中科院分区：
文献类型：
--
作者：
Menard, S
分析了逻辑回归中连续预测值（R-2类似物）的决定系数与普通最小二乘回归中熟悉的R-2统计量的概念和数学相似性，并将其与离散预测值（预测效率指标）的决定系数进行了比较。本文提出了一个由实质性问题驱动的例子，并使用了来自全国家庭概率样本的经验数据，以说明在评估模型时不同决定系数的行为，包括具有不同基本率的因变量，即具有“积极”结果的不同比例的案例或观察。从概念上与普通最小二乘决定系数相似，以及相对独立于基准比率而言，一种R-2类比似乎比其他类比更可取。此外，在选择预测效率指标时，还应考虑基础率。正如预期的那样，基于R-2类似物的结论不一定与基于预测效率的结论一致，即给定模型对几种结果中的哪一种预测更好。
Coefficients of determination for continuous predicted values (R-2 analogs) in logistic regression are examined for their conceptual and mathematical similarity to the familiar R-2 statistic from ordinary least squares regression, and compared to coefficients of determination for discrete predicted values (indexes of predictive efficiency). An example motivated by substantive concerns and using empirical data from a national household probability sample is presented to illustrate the behavior of the different coefficients of determination in the evaluation of models including dependent variables with different base rates-that is, different proportions of cases or observations with "positive" outcomes. One R-2 analog appears to be preferable to the others both in terms of conceptual similarity to the ordinary least squares coefficient of determination, and in terms of its relative independence from the base rate. In addition, base rate should also be considered when selecting an index of predictive efficiency. As expected, the conclusions based on R-2 analogs are not necessarily consistent with conclusions based on predictive efficiency, with respect to which of several outcomes is better predicted by a given model.