From: 李俊杰 <klijunjie_at_gmail.com>

Date: Mon, 21 May 2007 23:14:14 +0800

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.

Thanks for your suggestion, and I am looking forward for your reply.

-----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
**> >
**> > 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
**> and provide commented, minimal, self-contained, reproducible code.
**>
*

-- 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 and provide commented, minimal, self-contained, reproducible code.Received on Mon 21 May 2007 - 15:25:48 GMT

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