[R] ridge regression

From: Daniel <daniel_at_sintesys.com.ar>
Date: Sat 20 Aug 2005 - 00:54:54 EST

 

Hello, I have the following doubts related with lm.ridge. I take the Longley example.
First: I think coefficients from lm(Employed~.,data=longley) should be equal coefficients from lm.ridge(Employed~.,data=longley, lambda=0) why it does not happen?
Second: if I have for example
Ridge<-lm.ridge(Employed~., data=longley, lambda = seq(0,0.1,0.001)), I suppose intercept coefficients is defined implicit, why it does not appear in Ridge$coef?  

Third: I suppose that if I define y<-longley$Employed and X<-as.matrix(cbind(1,Longley[,1:6]) and I as the identity the following should be true:

         Coef=(X'X+kI)^(-1) X'y and if a take k=Ridge$kHKV, the coefficients should be approx equal to Ridge$Coef[near value of kHKV] and it does not happen, why?  

Numbers:
> Ridge$kHKB

[1] 0.004275357  

Using the calculation above:
Coef=

                      [,1]
  1            -0.095492310
  GNP.deflator -0.052759002
  GNP           0.070993540
  Unemployed   -0.004244391
  Armed.Forces -0.005725582
  Population   -0.413341544
  Year          0.048420107
 

And if I take from Ridge&coef:  

Ridge$coef[0.004]
GNP.deflator -0.03098507
GNP -1.32553151
Unemployed -1.53237769
Armed.Forces -0.63334911
Population -0.88690241
Year 6.82105049  

Any help, suggestion or orientation?
Thanks in advance
Daniel Rozengardt  

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