R语言做岭回归

ridge regression可以用来处理下面两类问题：一是数据点少于变量个数；二是变量间存在共线性。

当变量间存在共线性的时候，最小二乘回归得到的系数不稳定，方差很大。这是因为系数矩阵X与它的转置矩阵相乘得到的矩阵不能求得其逆矩阵，而ridge regression通过引入参数lambda，使得该问题得到解决。在R语言中，MASS包中的函数lm.ridge()可以很方便的完成。它的输入矩阵X始终为n x p 维，不管是否包含常数项。

Usage

lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,

         x = FALSE, y = FALSE, contrasts = NULL, ...)

 

> install.packages("MASS")

> library('MASS')

> longley 

> names(longley)[1] <- "y"

> lm.ridge(y ~ ., longley)

                             GNP              Unemployed   Armed.Forces    Population       Year              Employed 

2946.85636017    0.26352725    0.03648291    0.01116105       -1.73702984   -1.41879853    0.23128785 

> plot(lm.ridge(y ~ ., longley, lambda = seq(0,0.1,0.001)))

> select(lm.ridge(y ~ ., longley, lambda = seq(0,0.1,0.0001)))

modified HKB estimator is 0.006836982 

modified L-W estimator is 0.05267247 

smallest value of GCV  at 0.0057