MULTIPLE-REGRESSION FOR PHYSIOLOGICAL DATA-ANALYSIS - THE PROBLEM OF MULTICOLLINEARITY
MULTIPLE-REGRESSION FOR PHYSIOLOGICAL DATA-ANALYSIS - THE PROBLEM OF MULTICOLLINEARITY
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DOI：
10.1152/ajpregu.1985.249.1.r1
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发表时间：
1985-01-01
影响因子：
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通讯作者：
GLANTZ, SA
中科院分区：
文献类型：
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作者：
SLINKER, BK;GLANTZ, SA
多元线性回归，其中几个预测变量与一个响应变量相关，是一种强大的统计工具，可以定量地了解体内复杂的生理系统。为了使这些见解正确，所有预测变量必须是不相关的。在许多生理实验中，预测变量不能被精确控制和并行变化(即它们高度相关)。关于响应的信息存在冗余，这种情况称为多重共线性，这导致在估计回归方程中的参数时出现数值问题；参数的大小或符号往往不正确，或者具有较大的标准误差。虽然好的实验设计可以避免多重共线性，但并不是所有有趣的生理学问题都可以在不遇到多重共线性的情况下进行研究。在这些情况下，已经提出了各种特别程序来缓解多重共线性。虽然这些程序中的许多都是有争议的，但它们可以帮助将多元线性回归应用于一些生理问题。
Multiple linear regression, in which several predictor variables are related to a response variable, is a powerful statistical tool for gaining quantitative insight into complex in vivo physiological systems. For these insights to be correct, all predictor variables must be uncorrelated. In many physiological experiments the predictor variables cannot be precisely controlled and change in parallel (i.e., they are highly correlated). There is a redundancy of information about the response, a situation called multicollinearity, that leads to numerical problems in estimating the parameters in regression equations; the parameters are often of incorrect magnitude or sign, or have large standard errors. Although multicollinearity can be avoided with good experimental design, not all interesting physiological questions can be studied without encountering multicollinearity. In these cases various ad hoc procedures have been proposed to mitigate multicollinearity. Although many of these procedures are controversial, they can be helpful in applying multiple linear regression to some physiological problems.