logistic回归中自变量相对重要性的相对权重估计

目的将相对权重指标扩展应用于logistic回归分析,以更精确评价自变量的相对重要性。方法原始变量通过最小二乘正交变换获得一组独立不相关但与原变量最大相关的新变量集,并对因变量关于新变量集作回归分析获取一组标准回归系数β,再通过分析正交变量对原变量的回归作用返回至原变量集获取一组相关系数λ,最后对这两组估计参数平方乘积和所得结果就是自变量成比例贡献于因变量的重要性。结果相对权重总和等于模型的总变异R2,有效地分配了每个自变量对因变量的贡献大小。结论当存在共线性问题时,相对权重是评价自变量相对重要性的精确量化指标,为许多分类资料分析中希望确定自变量相对重要性的研究者提供一个可行的估计方法 。

Estimation of Relative Weights for Quantifying the Independent Variables Importance in Logistic Regression

Objective The work proposes an extension of relative weights index to apply in logistic regression analysis for evaluating more accurately the relative importance of independent variables. Methods Firstly create a new set of uncorrelated variables that are the maximally related to original predictors by least squares orthogonal transformation.Then obtain the coefficients linking the new orthogonal variables to dependent variable,then rescale back to the original variables and derive a new set of coefficients by regressing the original variables on their orthogonal variables.Finally produce an estimate of the proportionate contribution for each independent variable by multiplying the two previously computed squared coefficients. ResultsThe sum of the relative weights is equal to the model’s squared multiple correlation,they portion the contribution size associated with each independent variable validly. Conclusion When it exist collinearity among the various variables,the relative weights are more accurate tools for quantifying the relative importance of independent variables,also relative weights provide a feasible measure for researchers wishing to estimate the relative importance of each variable in the logistic regression model.