If you didn't post anonymously I would have made a suggestion. Full
names and affiliations should be given.
Frank
spime wrote:
Dear all,
I considered an ordinary ridge regression problem. I followed three
different ways:
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<-t(as.matrix(cbind(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 outputs for using the above three different
approaches, but which would been the same for all.
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.
regards.
--
Frank E Harrell Jr Professor and Chair School of Medicine
Department of Biostatistics Vanderbilt University
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
