重新审视用于估算粗略或调整比值比的判别函数方法。

IF 1.8 4区 数学 Q1 STATISTICS & PROBABILITY
Robert H Lyles, Ying Guo, Andrew N Hill
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引用次数: 0

摘要

假定结果是二元的,逻辑回归是估计与连续预测因子相对应的粗略或调整后的几率比的最常用方法。我们重新研究了一种称为判别函数的方法,它可以得到闭式估计值和相应的标准误差。在其最吸引人的应用中,我们表明该方法建议对结果和其他协变量的连续预测因子进行多元线性回归,以取代传统的逻辑回归模型。如果标准诊断支持该线性回归模型的假设(包括误差的正态性),那么与通常的逻辑回归最大似然估计法相比,该估计法具有明显的优势。这些优势包括基于对数几率比的最小方差无偏估计器在偏差和效率方面的改进,以及在逻辑回归因数据点分离而无法收敛时提供估计值。在此介绍的多变量分析中使用判别函数方法所需的假设条件没有历史上受到批评的那么严格,当与特定连续预测因子相关的调整后几率比是主要关注点时,这种方法值得考虑。模拟和案例研究可以说明这些问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Fresh Look at the Discriminant Function Approach for Estimating Crude or Adjusted Odds Ratios.

Assuming a binary outcome, logistic regression is the most common approach to estimating a crude or adjusted odds ratio corresponding to a continuous predictor. We revisit a method termed the discriminant function approach, which leads to closed-form estimators and corresponding standard errors. In its most appealing application, we show that the approach suggests a multiple linear regression of the continuous predictor of interest on the outcome and other covariates, in place of the traditional logistic regression model. If standard diagnostics support the assumptions (including normality of errors) accompanying this linear regression model, the resulting estimator has demonstrable advantages over the usual maximum likelihood estimator via logistic regression. These include improvements in terms of bias and efficiency based on a minimum variance unbiased estimator of the log odds ratio, as well as the availability of an estimate when logistic regression fails to converge due to a separation of data points. Use of the discriminant function approach as described here for multivariable analysis requires less stringent assumptions than those for which it was historically criticized, and is worth considering when the adjusted odds ratio associated with a particular continuous predictor is of primary interest. Simulation and case studies illustrate these points.

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来源期刊
American Statistician
American Statistician 数学-统计学与概率论
CiteScore
3.50
自引率
5.60%
发文量
64
审稿时长
>12 weeks
期刊介绍: Are you looking for general-interest articles about current national and international statistical problems and programs; interesting and fun articles of a general nature about statistics and its applications; or the teaching of statistics? Then you are looking for The American Statistician (TAS), published quarterly by the American Statistical Association. TAS contains timely articles organized into the following sections: Statistical Practice, General, Teacher''s Corner, History Corner, Interdisciplinary, Statistical Computing and Graphics, Reviews of Books and Teaching Materials, and Letters to the Editor.
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