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 <[EMAIL PROTECTED]>: > > I taken the conversation offline and used a pdf file to better display > equations. > > ------------------------------ > *From:* Àî¿¡½Ü [mailto:[EMAIL PROTECTED] > *Sent:* Monday, May 21, 2007 10:14 AM > *To:* Lucke, Joseph F > *Cc:* r-help@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 <[EMAIL PROTECTED]>: > > > > 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)$adj.r.squared > does in R. I guess what you want me to derive is the formula in that book. > > Though I know the formula of adjusted R2 for non-central moments, I still > want to know whether I am in the right way to compare *linear models with > intercept and those without intercept using maximizing adjs R^2 strategy. > * > ** > Actually, I consider the left column consisted of all 1 in predictor > matrix Z as the intercept term. Then I apply maximizing adjs R^2 strategy > to decide which variables to select. Z is the term in the model: Y=Zb+e. > > Thanks for your suggestion, and I am looking forward for your reply. > > > > -----Original Message----- > > From: [EMAIL PROTECTED] > > [mailto:[EMAIL PROTECTED] On Behalf Of ??? > > Sent: Sunday, May 20, 2007 8:53 PM > > To: r-help@stat.math.ethz.ch > > Subject: [R] How to compare linear models with intercept and those > > withoutintercept using minimizing adjs R^2 strategy > > > > Dear R-list, > > > > I apologize for my many emails but I think I know how to desctribe my > > problem differently and more clearly. > > > > My question is how to compare linear models with intercept and those > > without intercept using maximizing adjusted R^2 strategy. > > > > Now I do it like the following: > > > > > library(leaps) > > > n=20 > > > x=matrix(rnorm(n*3),ncol=3) > > > b=c(1,2,0) > > > intercept=1 > > > y=x%*%b+rnorm(n,0,1)+intercept > > > > > > var.selection=leaps(cbind(rep(1,n),x),y,int=F,method="adjr2") > > > ##### Choose the model with maximum adjr2 > > > var.selection$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, [EMAIL PROTECTED] > > Undergranduate in DEP of Tsinghua University, > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@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, [EMAIL PROTECTED] > Undergranduate in DEP of Tsinghua University, > > -- Junjie Li, [EMAIL PROTECTED] Undergranduate in DEP of Tsinghua University, [[alternative HTML version deleted]]
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