Summarizing the predictive power of a generalized linear model
Summarizing the predictive power of a generalized linear model
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DOI：
10.1002/1097-0258(20000715)19:13
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发表时间：
2000-07-15
影响因子：
2
通讯作者：
Agresti, A
中科院分区：
文献类型：
--
作者：
Zheng, BY;Agresti, A
本文研究了广义线性模型预测能力的概括度量，特别关注普通线性回归的多重相关系数的推广。总体值是响应与其给定预测变量的条件期望之间的相关性，样本值是观察到的响应与模型预测值之间的相关性。我们在偏差、均方误差和过度参数化情况下的行为方面比较了四个测量估计量。样本估计器和折刀估计器通常表现良好，但交叉验证估计器具有较大的负偏差和较大的均方误差。人们可以使用引导方法来构建相关性度量的总体值的置信区间，并估计模型选择过程可以提供实际预测能力的过度乐观度量的程度。版权所有 (C) 2000 John Wiley & Sons, Ltd.
This paper studies summary measures of the predictive power of a generalized linear model, paying special attention to a generalization of the multiple correlation coefficient from ordinary linear regression. The population value is the correlation between the response and its conditional expectation given the predictors, and the sample value is the correlation between the observed response and the model predicted value. We compare four estimators of the measure in terms of bias, mean squared error and behaviour in the presence of overparameterization. The sample estimator and a jack-knife estimator usually behave adequately, but a cross-validation estimator has a large negative bias with large mean squared error. One can use bootstrap methods to construct confidence intervals for the population value of the correlation measure and to estimate the degree to which a model selection procedure may provide an overly optimistic measure of the actual predictive power. Copyright (C) 2000 John Wiley & Sons, Ltd.