# 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 23:14:14 +0800

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.

-----Original Message-----
> From: r-help-bounces@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
> >
> > ##### Choose the model with maximum 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,
>
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>
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> and provide commented, minimal, self-contained, reproducible code.
>

```--
Junjie Li,                  klijunjie_at_gmail.com
Undergranduate in DEP of Tsinghua University,

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