logistic回归模型总结.docx
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logistic回归模型总结.docx
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logistic回归模型总结
[]logistic回归模型总结
logistic回归模型是最成熟也是应用最广泛的分类模型,通过学习和实践拟通过从入门、进阶到高级的过程对其进展总结,以便加深自己的理解也为对此有兴趣者提供学习的便利。
一、有关logistic的根本概念
logistic回归主要用来预测离散因变量与一组解释变量之间的关系
最常用的是二值型logistic。
即因变量的取值只包含两个类别
例如:
好、坏;发生、不发生;常用Y=1或Y=0表示*表示解释变量则
P〔Y=1|*〕表示在*的条件下Y=1的概率,logistic回归的数学表达式为:
log〔p/1-p〕=A+B*=L其中p/1-p称为优势比〔ODDS〕即发生与不发生的概率之比
可以根据上式反求出P〔Y=1|*〕=1/〔1+e^-L〕
根据样本资料可以通过最大似然估计计算出模型的参数
然后根据求出的模型进展预测
下面介绍logistic回归在SAS中的实现以及输出结果的解释
二、logistic回归模型初步
SAS中logistic回归输出结果主要包括预测模型的评价以及模型的参数
预测模型的评价与多元线性回归模型的评价类似主要从以下几个层次进展
〔1〕模型的整体拟合优度
主要评价预测值与观测值之间的总体一致性。
可以通过以下两个指标来进展检验
1、Hosmer-Lemeshowz指标
HL统计量的原假设Ho是预测值和观测值之间无显著差异,因此HL指标的P-Value的值越大,越不能拒绝原假设,即说明模型很好的拟合了数据。
在SAS中这个指标可以用LACKFIT选项进展调用
2、AIC和SC指标即池雷准则和施瓦茨准则
与线性回归类似AIC和SC越小说明模型拟合的越好
〔2〕从整体上看解释变量对因变量有无解释作用
相当于多元回归中的F检验在logistic回归中可以通过似然比〔likelihoodratio
test〕进展检验
〔3〕解释变量解释在多大程度上解释了因变量
与线性回归中的R^2作用类似
在logistic回归中可以通过Rsquare和C统计量进展度量
在SAS过RSQ来调用Rsquare,C统计量自动输出
(4)
模型评价指标汇总
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mso-border-top-alt: solidwindowte*t.5pt;mso-border-left-alt: solidwindowte*t.5pt; mso-border-alt: solidwindowte*t.5pt;padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri;mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast; mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">似然比卡方 none;border-left: none;border-bottom: solidwindowte*t1.0pt; border-right: solidwindowte*t1.0pt;mso-border-top-alt: solidwindowte*t.5pt; mso-border-left-alt: solidwindowte*t.5pt;mso-border-alt: solidwindowte*t.5pt; padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">越大 none;border-left: none;border-bottom: solidwindowte*t1.0pt; border-right: solidwindowte*t1.0pt;mso-border-top-alt: solidwindowte*t.5pt; mso-border-left-alt: solidwindowte*t.5pt;mso-border-alt: solidwindowte*t.5pt; padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">越好 117.9pt;border-top: none;border-left: none;border-bottom: solidwindowte*t1.0pt;border-right: solidwindowte*t1.0pt; mso-border-top-alt: solidwindowte*t.5pt;mso-border-left-alt: solidwindowte*t.5pt; mso-border-alt: solidwindowte*t.5pt;padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">类似与多元回归中的回归平方和 106.3pt;border-top: none;border-left: none;border-bottom: solidwindowte*t1.0pt;border-right: solidwindowte*t1.0pt; mso-border-top-alt: solidwindowte*t.5pt;mso-border-left-alt: solidwindowte*t.5pt; mso-border-alt: solidwindowte*t.5pt;padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">自动输出 73.75pt;border-top: none;border-left: none;border-bottom: solidwindowte*t1.0pt;border-right: solidwindowte*t1.0pt; mso-border-top-alt: solidwindowte*t.5pt;mso-border-left-alt: solidwindowte*t.5pt; mso-border-alt: solidwindowte*t.5pt;padding: 0cm5.4pt0cm5.4pt"> P 宋体; mso-ascii-font-family: Calibri;mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin">值越小越好RSQUARE none;border-left: none;border-bottom: solidwindowte*t1.0pt; border-right: solidwindowte*t1.0pt;mso-border-top-alt: solidwindowte*t.5pt; mso-border-left-alt: solidwindowte*t.5pt;mso-border-alt: solidwindowte*t.5pt; padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">越大 none;border-left: none;border-bottom: solidwindowte*t1.0pt; border-right: solidwindowte*t1.0pt;mso-border-top-alt: solidwindowte*t.5pt; mso-border-left-alt: solidwindowte*t.5pt;mso-border-alt: solidwindowte*t.5pt; padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">越好 117.9pt;border-top: none;border-left: none;border-bottom: solidwindowte*t1.0pt;border-right: solidwindowte*t1.0pt; mso-border-top-alt: solidwindowte*t.5pt;mso-border-left-alt: solidwindowte*t.5pt; mso-border-alt: solidwindowte*t.5pt;padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-fareast-theme-font: minor-fareast;mso-hansi-font-family: Calibri;mso-hansi-theme-font: minor-latin">类似与多元回归中的R^2 106.3pt;border-top: none;border-left: none;border-bottom: solidwindowte*t1.0pt;border-right: solidwindowte*t1.0pt; mso-border-top-alt: solidwindowte*t.5pt;mso-border-left-alt: solidwindowte*t.5pt; mso-border-alt: solidwindowte*t.5pt;padding: 0cm5.4pt0cm5.4pt"> 宋体;mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin;mso-fareast-font-family: 宋体;mso-far
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