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)$adj.r.squared does in R. I guess what you want me to derive is the formula in that book.
Though I know the formula of adjusted R2 for non-central moments, I still
want to know whether I am in the right way to compare *linear models with
intercept and those without intercept using maximizing adjs R^2 strategy.*
Actually, I consider the left column consisted of all 1 in predictor matrix Z as the intercept term. Then I apply maximizing adjs R^2 strategy to decide which variables to select. Z is the term in the model: Y=Zb+e.
Thanks for your suggestion, and I am looking forward for your reply.
> From: email@example.com
> [mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of ???
> Sent: Sunday, May 20, 2007 8:53 PM
> To: r-help_at_stat.math.ethz.ch
> Subject: [R] How to compare linear models with intercept and those
> withoutintercept using minimizing adjs R^2 strategy
> Dear R-list,
> I apologize for my many emails but I think I know how to desctribe my
> problem differently and more clearly.
> My question is how to compare linear models with intercept and those
> without intercept using maximizing adjusted R^2 strategy.
> Now I do it like the following:
> > library(leaps)
> > n=20
> > x=matrix(rnorm(n*3),ncol=3)
> > b=c(1,2,0)
> > intercept=1
> > y=x%*%b+rnorm(n,0,1)+intercept
> > var.selection=leaps(cbind(rep(1,n),x),y,int=F,method="adjr2")
> > ##### Choose the model with maximum adjr2
> > var.selection$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
> PLEASE do read the posting guide
> 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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