[R] How to compare linear models with intercept and those withoutintercept using minimizing adjs R^2 strategy
=?GB2312?B?wO6/ob3c?=
klijunjie at gmail.com
Thu May 24 08:29:54 CEST 2007
2007/5/24, Lucke, Joseph F <Joseph.F.Lucke at uth.tmc.edu>:
>
>
>
> ------------------------------
> *From:* Àî¿¡½Ü [mailto:klijunjie at gmail.com]
> *Sent:* Monday, May 21, 2007 8:12 PM
> *To:* Lucke, Joseph F
> *Subject:* Re: [R] How to compare linear models with intercept and those
> withoutintercept using minimizing adjs R^2 strategy
>
>
>
>
> 2007/5/22, Lucke, Joseph F <Joseph.F.Lucke at uth.tmc.edu>:
> >
> > Bottom line:
> > You use the adjusted R2 with the intercept in your leaps(). If the case
> > arises that the the intercept-only model (no other predictors) is the result
> > of you leaps(), then you may test for whether the intercept itself is zero.
> >
> >
> > You cannot compare models with predictors for intercept versus no
> > intercept as this violates marginality.
> >
>
> I've wrote my question in pdf file. Sorry for my slow understanding.
>
>
> > ------------------------------
> > *From:* Àî¿¡½Ü [mailto:klijunjie at gmail.com]
> > *Sent: *Monday, May 21, 2007 11:34 AM
> > *To:* Lucke, Joseph F
> > *Cc:* r-help at stat.math.ethz.ch
> > *Subject:* Re: [R] How to compare linear models with intercept and those
> > withoutintercept using minimizing adjs R^2 strategy
> >
> >
> > So when I am using the adjusted R2 and as a penalized optimality
> > criterion, and I have to compare models with intercept and those without
> > intercept to decide the final model selected, does my crierion in my
> > first email make sense?
> >
> > Because we know that in leaps(leaps), if we want to select a model by
> > the adjusted R2 criterion, we have to decide whether the intercept should be
> > added in advance. But with my adjusted R2 criterion, we don't have to decide
> > that in advance.
> >
> > Thank you so much for your patient clarification.
> >
> >
> >
> > 2007/5/22, Lucke, Joseph F <Joseph.F.Lucke at uth.tmc.edu>:
> > >
> > > You don't have to embed model selection as hypothesis testing. You
> > > are using the adjusted R2 and as a penalized optimality criterion.
> > >
> > > ------------------------------
> > > *From:* Àî¿¡½Ü [mailto:klijunjie at gmail.com]
> > > *Sent: *Monday, May 21, 2007 10:43 AM
> > > *To:* Lucke, Joseph F
> > > *Cc:* r-help at stat.math.ethz.ch
> > > *Subject:* Re: [R] How to compare linear models with intercept and
> > > those withoutintercept using minimizing adjs R^2 strategy
> > >
> > >
> > > I have a question about what you've wrote in your pdf file. Why must
> > > we view my problem in the viewpoint of hypothesis testing? Is testing the
> > > original philosophy of maximizing Fisher's A-statistic to choose a optimum
> > > model?
> > >
> > > Thanks.
> > >
> > >
> > > 2007/5/21, Lucke, Joseph F <Joseph.F.Lucke at uth.tmc.edu>:
> > > >
> > > > I taken the conversation offline and used a pdf file to better
> > > > display equations.
> > > >
> > > > ------------------------------
> > > > *From:* Àî¿¡½Ü [mailto:klijunjie at gmail.com]
> > > > *Sent: *Monday, May 21, 2007 10:14 AM
> > > > *To:* Lucke, Joseph F
> > > > *Cc:* r-help at stat.math.ethz.ch
> > > > *Subject:* Re: [R] How to compare linear models with intercept and
> > > > those withoutintercept using minimizing adjs R^2 strategy
> > > >
> > > >
> > > >
> > > >
> > > > 2007/5/21, Lucke, Joseph F <Joseph.F.Lucke at uth.tmc.edu>:
> > > > >
> > > > > One issue is whether you want your estimators to be based on
> > > > > central
> > > > > moments (covariances) or on non-central moments. Removing the
> > > > > intercept
> > > > > changes the statistics from central to non-central moments. The
> > > > > adjusted R2, by which I think you mean Fisher's adjusted R2, is
> > > > > based on
> > > > > central moments (ratio of unbiased estimators of
> > > > > variances---central
> > > > > moments). So if you remove the intercept, you must re-derive the
> > > > > adjusted R2 for non-central moments --- you can't just plug in the
> > > > > number of independent variables as zero.
> > > >
> > > >
> > > > I have consulted A.J. Miller's Subset Selection in Regression(1990),
> > > > and I found what I was talking about adjusted R^2 was exactly as you
> > > > said--Fisher's A-statisitc. The formula of adjusted R^2 without the
> > > > intercept in that book was also the same as what summary(lm)$adj.r.squared
> > > > does in R. I guess what you want me to derive is the formula in that book.
> > > >
> > > > Though I know the formula of adjusted R2 for non-central moments, I
> > > > still want to know whether I am in the right way to compare *linear
> > > > models with intercept and those without intercept using maximizing adjs R^2
> > > > strategy. *
> > > > **
> > > > Actually, I consider the left column consisted of all 1 in
> > > > predictor matrix Z as the intercept term. Then I apply maximizing
> > > > adjs R^2 strategy to decide which variables to select. Z is the term in the
> > > > model: Y=Zb+e.
> > > >
> > > > Thanks for your suggestion, and I am looking forward for your reply.
> > > >
> > > >
> > > >
> > > > -----Original Message-----
> > > > > From: r-help-bounces at stat.math.ethz.ch
> > > > > [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of ???
> > > > > Sent: Sunday, May 20, 2007 8:53 PM
> > > > > To: r-help at stat.math.ethz.ch
> > > > > Subject: [R] How to compare linear models with intercept and those
> > > > >
> > > > > withoutintercept using minimizing adjs R^2 strategy
> > > > >
> > > > > Dear R-list,
> > > > >
> > > > > I apologize for my many emails but I think I know how to desctribe
> > > > > my
> > > > > problem differently and more clearly.
> > > > >
> > > > > My question is how to compare linear models with intercept and
> > > > > those
> > > > > without intercept using maximizing adjusted R^2 strategy.
> > > > >
> > > > > Now I do it like the following:
> > > > >
> > > > > > library(leaps)
> > > > > > n=20
> > > > > > x=matrix(rnorm(n*3),ncol=3)
> > > > > > b=c(1,2,0)
> > > > > > intercept=1
> > > > > > y=x%*%b+rnorm(n,0,1)+intercept
> > > > > >
> > > > > > var.selection=leaps(cbind(rep(1,n),x),y,int=F,method="adjr2")
> > > > > > ##### Choose the model with maximum adjr2
> > > > > > var.selection$which[var.selection$adjr2==max(var.selection$adjr2
> > > > > ),]
> > > > > 1 2 3 4
> > > > > TRUE TRUE TRUE FALSE
> > > > >
> > > > >
> > > > > Actually, I use the definition of R-square in which the model is
> > > > > without
> > > > > a intercept term.
> > > > >
> > > > > Is what I am doing is correct?
> > > > >
> > > > > Thanks for any suggestion or correction.
> > > > > --
> > > > > Junjie Li, klijunjie at gmail.com
> > > > > Undergranduate in DEP of Tsinghua University,
> > > > >
> > > > > [[alternative HTML version deleted]]
> > > > >
> > > > > ______________________________________________
> > > > > R-help at stat.math.ethz.ch mailing list
> > > > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > > > PLEASE do read the posting guide
> > > > > http://www.R-project.org/posting-guide.html<http://www.r-project.org/posting-guide.html>
> > > > > and provide commented, minimal, self-contained, reproducible code.
> > > > >
> > > > >
> > > >
> > > >
> > > >
> > > > --
> > > > Junjie Li, klijunjie at gmail.com
> > > > Undergranduate in DEP of Tsinghua University,
> > > >
> > > >
> > >
> > >
> > > --
> > > Junjie Li, klijunjie at gmail.com
> > > Undergranduate in DEP of Tsinghua University,
> > >
> >
> >
> >
> > --
> > Junjie Li, klijunjie at gmail.com
> > Undergranduate in DEP of Tsinghua University,
> >
>
>
>
> --
> Junjie Li, klijunjie at gmail.com
> Undergranduate in DEP of Tsinghua University,
>
>
--
Junjie Li, klijunjie at gmail.com
Undergranduate in DEP of Tsinghua University,
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