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LAR(最小角回归)
LAR(最小角回归)
chenlongzhen
Sunday, March 01, 2015
LAR过程
LAR图解
R的lar包使用longley
数据(具有高度共线性)
用最小角度算最小二乘解,确定变量过程
library(lars)
## Warning: package 'lars' was built under R version 3.1.2
## Loaded lars 1.2
head(longley)
## GNP.deflator GNP Unemployed Armed.Forces Population Year Employed
## 1947 83.0 234.289 235.6 159.0 107.608 1947 60.323
## 1948 88.5 259.426 232.5 145.6 108.632 1948 61.122
## 1949 88.2 258.054 368.2 161.6 109.773 1949 60.171
## 1950 89.5 284.599 335.1 165.0 110.929 1950 61.187
## 1951 96.2 328.975 209.9 309.9 112.075 1951 63.221
## 1952 98.1 346.999 193.2 359.4 113.270 1952 63.639
w <- as.matrix(longley)
#col1为y,col2-7为x
laa <- lars(w[,2:7], w[,1])
laa
##
## Call:
## lars(x = w[, 2:7], y = w[, 1])
## R-squared: 0.993
## Sequence of LASSO moves:
## GNP Year Armed.Forces Unemployed Employed Population Year Employed
## Var 1 5 3 2 6 4 -5 -6
## Step 1 2 3 4 5 6 7 8
## Employed Year Employed Employed
## Var 6 5 -6 6
## Step 9 10 11 12
plot(laa)
summary(laa)
## LARS/LASSO
## Call: lars(x = w[, 2:7], y = w[, 1])
## Df Rss Cp
## 0 1 1746.86 1210.0561
## 1 2 1439.51 996.6871
## 2 3 32.31 12.6400
## 3 4 23.18 8.2425
## 4 5 22.91 10.0505
## 5 6 22.63 11.8595
## 6 7 18.04 10.6409
## 7 6 14.74 6.3262
## 8 5 13.54 3.4848
## 9 6 13.27 5.2974
## 10 7 13.01 7.1189
## 11 6 12.93 5.0624
## 12 7 12.84 7.0000
Cp
衡量多重共线性严重程度越小越好
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LAR(最小角回归)
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