# Re: [R] How to compare linear models with intercept and those withoutintercept using minimizing adjs R^2 strategy

From: 李俊杰 <klijunjie_at_gmail.com>
Date: Mon, 21 May 2007 23:42:33 +0800

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:* 李俊杰 [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@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,

[[alternative HTML version deleted]]

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Received on Mon 21 May 2007 - 15:59:35 GMT

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