Hello again and Happy 2010!
I was looking back at this email because I need to do some additional
processing now. I was thinking that if I take the coef(ans) I get n+1
coefficients. I guess that the coef(ans)[1] is the constant term... Do I
need to add it when I calculate the estimated value for the outcome?
For example, lets say that I have divided my data into training data and
test data and I have the corresponding observed try_values and tey_values
(the real values for the samples that belong to the training set and the
test set respectively)
Here is my code:
*
library(MASS)
ridge.test=lm.ridge(tey_values~tedata,lambda)
est<-list()
yest<-numeric()
for(i in 1:length(tey_values)){
est[[i]]=coef(ridge.test)[-1]*tedata[i,]
yest[i]=sum(est[[i]])+coef(ridge.test)[1]
}*
On Wed, Dec 2, 2009 at 8:22 PM, Ravi Varadhan <rvarad...@jhmi.edu> wrote:
> The help page clearly states that ans$coef is "not on the original scale
> and
> are for use by the coef method". You also see that ans$scales gives you
> the
> scales used in the computation of ans$coef.
>
> So, to get coefficients on the original scale, you can either use coef(ans)
> or you can divide ans$coef by ans$scales.
>
> X1 <- runif(20)
> X2 <- runif(20)
> Y <- 2 * X1 - 2 * X2 + rnorm(20, sd=0.1)
>
> lam <- 10
> ans1 <- lm.ridge(Y ~ X1 + X2, lambda = lam)
>
> all.equal(ans1$coef / ans1$scales, coef(ans1)[2:3] )
>
> Hope this helps,
> Ravi.
>
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvarad...@jhmi.edu
>
> Webpage:
>
> http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
> tml<http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h%0Atml>
>
>
>
>
> ----------------------------------------------------------------------------
> --------
>
>
> -----Original Message-----
> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]
> On
> Behalf Of Ravi Varadhan
> Sent: Wednesday, December 02, 2009 12:25 PM
> To: 'David Winsemius'; 'Eleni Christodoulou'
> Cc: r-help@r-project.org
> Subject: Re: [R] Ridge regression
>
> You are right that the ans$coef and coef(ans) are different in ridge
> regression, where `ans' is the object from lm.ridge. It is the coef(ans)
> that yields the coefficients on the original scale. ans$coef is the
> coefficient of "X-scaled" and "Y-centered" version.
>
> Here is an example that illustrates the workings of ridge regression.
>
> First let us create some data:
>
> X1 <- runif(20)
> X2 <- runif(20)
> Y <- 2 * X1 - 2 * X2 + rnorm(20, sd=0.1)
>
> lam <- 10
> ans1 <- lm.ridge(Y ~ X1 + X2, lambda = lam)
> ans1$coef
> coef(ans1)
> # Note that these two are different
>
> # Now Let us scale the variables X1 and X2 and center Y
> #
> cY <- scale(Y, scale=FALSE)
> n <- length(Y)
> sX1 <- scale(X1) * sqrt(n/(n-1))
> sX2 <- scale(X2) * sqrt(n/(n-1))
>
> require(MASS)
>
> lam <- 10
> ans2 <- lm.ridge(cY ~ sX1 + sX2, lambda = lam)
>
> ans2$coef
> coef(ans2)
> # Now, see that the coefficients of sX1 and sX2 are the same
> # This is the connection!
>
> # Armed with this insight, we now compare the ans1$coef with scaled
> coefficients
> #
> ans1$coef
> c(coef(ans1)[2] * sd(X1), coef(ans1)[3] * sd(X2)) * sqrt((n-1)/n)
>
> # Now they are the same!
>
> I hope this is clear.
>
> Best,
> Ravi.
>
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvarad...@jhmi.edu
>
> Webpage:
>
> http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
> tml<http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h%0Atml>
>
>
>
>
> ----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]
> On
> Behalf Of David Winsemius
> Sent: Wednesday, December 02, 2009 11:04 AM
> To: Eleni Christodoulou
> Cc: r-help@r-project.org
> Subject: Re: [R] Ridge regression
>
>
> On Dec 2, 2009, at 10:42 AM, Eleni Christodoulou wrote:
>
> > Dear list,
> >
> > I have a couple of questions concerning ridge regression. I am using
> > the
> > lm.ridge(...) function in order to fit a model to my microarray data.
> > Thus *model=lm.ridge(...)*
> > I retrieve some coefficients and some scales for each gene. First of
> > all, I
> > would like to ask: the real coefficients of the model are not
> > included in
> > the first argument of the output but in the result of coef(model),
> > am I
> > right?
>
> Not exactly. coef(model) extracts the coefficients from the model but
> the coefficients do in the example instance I created following the
> help page happen to be in the first element of the model.
>
> eg:
> > long.rr$coef
> GNP Unemployed Armed.Forces Population Year
> Employed
> 25.3615288 3.3009416 0.7520553 -11.6992718 -6.5403380
> 0.7864825
> > long.rr[[1]]
> GNP Unemployed Armed.Forces Population Year
> Employed
> 25.3615288 3.3009416 0.7520553 -11.6992718 -6.5403380
> 0.7864825
>
> > Moreover, what does the scale argument represent? Which is its
> > connection with the coefficients? The R help file os not very
> > informative
> > for me...
>
> A plausible response to such a question might be that the help page is
> a sketchy substitute for the MASS book. However, I cannot find ridge
> regression in the table of contents or in the index of my copy, but I
> only have ed. 2 and the current edition is the 4th. So we will both
> need to wait for more knowledgeable (or with more recent editions of
> MASS) persons to answer that question.
>
> (And "scales" is not an argument, rather it's a returned value.)
>
> >
> > Thank you very much in advance,
> > Eleni Christodoulou
> >
>
>
> David Winsemius, MD
> Heritage Laboratories
> West Hartford, CT
>
> ______________________________________________
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>
> ______________________________________________
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> PLEASE do read the posting guide
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> and provide commented, minimal, self-contained, reproducible code.
>
>
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