Dear all,
For an ordinary ridge regression problem, I followed three different
approaches:
1. estimate beta without any standardization
2. estimate standardized beta (standardizing X and y) and then again convert
back
3. estimate beta using lm.ridge() function
X<-matrix(c(1,2,9,3,2,4,7,2,3,5,9,1),4,3)
y<-as.matrix(c(2,3,4,5))
n<-nrow(X)
p<-ncol(X)
#Without standardization
intercept <- rep(1,n)
Xn <- cbind(intercept, X)
K<-diag(c(0,rep(1.5,p)))
beta1 <- solve(t(Xn)%*%Xn+K)%*%t(Xn)%*%y
beta1
#with standardization
ys<-scale(y)
Xs<-scale(X)
K<-diag(1.5,p)
bs <- solve(t(Xs)%*%Xs+K)%*%t(Xs)%*%ys
b<- sd(y)*(bs/sd(X))
intercept <- mean(y)-sum(as.matrix(colMeans(X))*b)
beta2<-rbind(intercept,b)
beta2
#Using lm.ridge function of MASS package
beta3<-lm.ridge(y~X,lambda=1.5)
I'm getting three different results using above described approaches:
> beta1
[,1]
intercept 3.4007944
0.3977462
0.2082025
-0.4829115
> beta2
[,1]
intercept 3.3399855
0.1639469
0.0262021
-0.1228987
> beta3
X1 X2 X3
3.35158977 0.19460958 0.03152778 -0.15546775
It will be very helpful to me if anybody can help me regarding why the
outputs are coming different.
I am extremely sorry for my previous anonymous post.
regards.
-----
Sabyasachi Patra
PhD Scholar
Indian institute of Technology Kanpur
India.
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