原文链接：http://tecdat.cn/?p=5453
原文出处：拓端数据部落公众号
变量抉择办法
所有可能的回归
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols\_all\_subset(model)
## # A tibble: 15 x 6
## Index N Predictors \`R-Square\` \`Adj. R-Square\` \`Mallow's Cp\`
##
## 1 1 1 wt 0.75283 0.74459 12.48094
## 2 2 1 disp 0.71834 0.70895 18.12961
## 3 3 1 hp 0.60244 0.58919 37.11264
## 4 4 1 qsec 0.17530 0.14781 107.06962
## 5 5 2 hp wt 0.82679 0.81484 2.36900
## 6 6 2 wt qsec 0.82642 0.81444 2.42949
## 7 7 2 disp wt 0.78093 0.76582 9.87910
## 8 8 2 disp hp 0.74824 0.73088 15.23312
## 9 9 2 disp qsec 0.72156 0.70236 19.60281
## 10 10 2 hp qsec 0.63688 0.61183 33.47215
## 11 11 3 hp wt qsec 0.83477 0.81706 3.06167
## 12 12 3 disp hp wt 0.82684 0.80828 4.36070
## 13 13 3 disp wt qsec 0.82642 0.80782 4.42934
## 14 14 3 disp hp qsec 0.75420 0.72786 16.25779
## 15 15 4 disp hp wt qsec 0.83514 0.81072 5.00000该 plot 办法显示了所有可能的回归办法的拟合。
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
k <- ols\_all\_subset(model)
plot(k)
最佳子集回归
抉择在满足一些明确的主观规范时做得最好的预测变量的子集，例如具备最大 R2 值或最小 MSE，Cp 或 AIC。
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
ols\_best\_subset(model)
## Best Subsets Regression
## ------------------------------
## Model Index Predictors
## ------------------------------
## 1 wt
## 2 hp wt
## 3 hp wt qsec
## 4 disp hp wt qsec
## ------------------------------
##
## Subsets Regression Summary
## -------------------------------------------------------------------------------------------------------------------------------
## Adj. Pred
## Model R-Square R-Square R-Square C(p) AIC SBIC SBC MSEP FPE HSP APC
## -------------------------------------------------------------------------------------------------------------------------------
## 1 0.7528 0.7446 0.7087 12.4809 166.0294 74.2916 170.4266 9.8972 9.8572 0.3199 0.2801
## 2 0.8268 0.8148 0.7811 2.3690 156.6523 66.5755 162.5153 7.4314 7.3563 0.2402 0.2091
## 3 0.8348 0.8171 0.782 3.0617 157.1426 67.7238 164.4713 7.6140 7.4756 0.2461 0.2124
## 4 0.8351 0.8107 0.771 5.0000 159.0696 70.0408 167.8640 8.1810 7.9497 0.2644 0.2259
## -------------------------------------------------------------------------------------------------------------------------------
## AIC: Akaike Information Criteria
## SBIC: Sawa's Bayesian Information Criteria
## SBC: Schwarz Bayesian Criteria
## MSEP: Estimated error of prediction, assuming multivariate normality
## FPE: Final Prediction Error
## HSP: Hocking's Sp
## APC: Amemiya Prediction Criteriaplot
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
k <- ols\_best\_subset(model)
plot(k)
逐渐后退回归
从一组候选预测变量中建设回归模型，办法是逐渐输出基于 p 值的预测变量，直到没有变量进入变量。该模型应该包含所有的候选预测变量。如果细节设置为TRUE，则显示每个步骤。
变量抉择
# 向前逐步回归
model <- lm(y ~ ., data = surgical)
ols\_step\_forward(model)
## We are selecting variables based on p value...
## 1 variable(s) added....
## 1 variable(s) added...
## 1 variable(s) added...
## 1 variable(s) added...
## 1 variable(s) added...
## No more variables satisfy the condition of penter: 0.3
## Forward Selection Method
##
## Candidate Terms:
##
## 1 . bcs
## 2 . pindex
## 3 . enzyme_test
## 4 . liver_test
## 5 . age
## 6 . gender
## 7 . alc_mod
## 8 . alc_heavy
##
## ------------------------------------------------------------------------------
## Selection Summary
## ------------------------------------------------------------------------------
## Variable Adj.
## Step Entered R-Square R-Square C(p) AIC RMSE
## ------------------------------------------------------------------------------
## 1 liver_test 0.4545 0.4440 62.5119 771.8753 296.2992
## 2 alc_heavy 0.5667 0.5498 41.3681 761.4394 266.6484
## 3 enzyme_test 0.6590 0.6385 24.3379 750.5089 238.9145
## 4 pindex 0.7501 0.7297 7.5373 735.7146 206.5835
## 5 bcs 0.7809 0.7581 3.1925 730.6204 195.4544
## ------------------------------------------------------------------------------
model <- lm(y ~ ., data = surgical)
k <- ols\_step\_forward(model)
## We are selecting variables based on p value...
## 1 variable(s) added....
## 1 variable(s) added...
## 1 variable(s) added...
## 1 variable(s) added...
## 1 variable(s) added...
## No more variables satisfy the condition of penter: 0.3
plot(k)
参考文献
1.R 语言多元 Logistic 逻辑回归 利用案例
2. 面板平滑转移回归 (PSTR) 剖析案例实现剖析案例实现 ”)
3.matlab 中的偏最小二乘回归（PLSR）和主成分回归（PCR）
4.R 语言泊松 Poisson 回归模型剖析案例
5.R 语言回归中的 Hosmer-Lemeshow 拟合优度测验
6.r 语言中对 LASSO 回归，Ridge 岭回归和 Elastic Net 模型实现
7. 在 R 语言中实现 Logistic 逻辑回归
8.python 用线性回归预测股票价格
9.R 语言如何在生存剖析与 Cox 回归中计算 IDI，NRI 指标