Mark, Estimates of R values can be compared using Fishers r to z transform. Perhaps this will do what you wish to do. John
John Sorkin M.D., Ph.D. Chief, Biostatistics and Informatics Baltimore VA Medical Center GRECC, University of Maryland School of Medicine Claude D. Pepper OAIC, University of Maryland Clinical Nutrition Research Unit, and Baltimore VA Center Stroke of Excellence University of Maryland School of Medicine Division of Gerontology Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing) [EMAIL PROTECTED] >>> Duncan Murdoch <[EMAIL PROTECTED]> 09/13/07 2:31 PM >>> On 9/13/2007 2:18 PM, Leeds, Mark (IED) wrote: > I estimate two competing simple regression models, A and B where the LHS > is the same in both cases but the predictor is different ( > I handle the intercept issue based on other postings I have seen ). I > estimate the two models on a weekly basis over 24 weeks. > So, I end up with 24 RSquaredAs and 24 RsquaredBs, so essentally 2 time > series of Rsquareds. This doesn't have to be necessarily thought of as a > time series problem but, is there a usual way, given the Rsquared data, > to test > > H0 : Rsquared B = Rsquared A versus H1 : Rsquared B > Rsquared A > > so that I can map the 24 R squared numbers into 1 statistic. Maybe > that's somehow equivalent to just running 2 big regressions over the > whole 24 weeks and then calculating a statistic from those based on > those regressions ? The question doesn't make sense, if you're using standard notation. R^2 is a statistic, not a parameter, so one wouldn't test copies of it for equality. You can probably reframe the question in terms of E(R^2) so the statement parses, but then it doesn't really make sense from a subject matter point of view: unless model A is nested within model B, why would you ever expect the two fits to explain exactly the same amount of variation? If model A is really a special case of model B, then you're back to the standard hypothesis testing situation, but repeated 24 times. There's a lot of literature on how to handle such multiple testing problems, depending on what sort of alternatives you want to detect. (E.g. do you think all 24 cases will be identical, or is it possible that 23 will match but one doesn't?) Duncan Murdoch > > I broke things up into 24 weeks because I was thinking that the > stability of the performance difference of the two models could be > examined over time. Essentially these are simple time series regressions > X_t = B*X_t-1 + epsilon so I always need to consider > whether any type of behavior is stable. But now I am thinking that, if > I just want one overall number, then maybe I should be considering all > the data simultaneously ? > > In a nutshell, I am looking for any suggestions on the best way to test > whether Model B is better than Model A where > > Model A : X_t = Beta*X_t-1 + epsilon > > Model B : X_t = Betastar*Xstar_t-1 + epsilonstar > > > Thanks fo your help. > -------------------------------------------------------- > > This is not an offer (or solicitation of an offer) to buy/se...{{dropped}} > > ______________________________________________ > R-help@r-project.org 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. ______________________________________________ R-help@r-project.org 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. Confidentiality Statement: This email message, including any attachments, is for the so...{{dropped}} ______________________________________________ R-help@r-project.org 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.