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xlaa <- 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