变量选择方法
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方法显示了所有可能的回归方法的拟合 。
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) k <- ols\_all\_subset(model) plot(k)
最佳子集回归
选择在满足一些明确的客观标准时做得最好的预测变量的子集，例如具有最大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 Criteria plot model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) k <- ols\_best\_subset(model) plot(k)
逐步前进回归
从一组候选预测变量中建立回归模型，方法是逐步输入基于p值的预测变量，直到没有变量进入变量。该模型应该包括所有的候选预测变量。如果细节设置为TRUE，则显示每个步骤。
变量选择
#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)
