Also see fortune(254) and others about r-squared in general.
On Thu, Jul 11, 2013 at 3:35 PM, Greg Snow <538...@gmail.com> wrote: > One way to get standardized beta coefficients is to center and scale all > of the x variables (subtract the mean then divide by the standard > deviation), then fit the regression on the standardized x's. You could do > the same thing with a robust regression (these values may not be meaningful > if there are outliers in the x variables). > > You can calculate the sum of squares residuals by squaring the residuals > (difference between observed and predicted values) and summing them up. > You can calculate the sum of squares regression by summing the squares of > the distances between the predicted values and a measure of center, the > measure of center for OLS is just the mean, for a robust regression you may > want to use the estimated intercept when fitting an intercept only model > using the same robust function. You can then find the sum of squares total > by summing the squared differences between the observed values and the > measure of center (if you do not use the mean then don't expect that SSE + > SSR = SST). Using these values (and degrees of freedom) you can compute > things that you could call R-squared, adjusted R-squared and an F ratio. > Though in the robust model I would be very surprised if the F-ratio (even > if you can figure out the correct degrees of freedom) followed an F > distribution or non-central F distribution, and the r-squared values are > probably even less meaningful than they are for OLS (and since some argue > that R-squared for OLS is pretty meaningless to begin with, that is saying > something). > > It would be better to decide what question(s) you are really trying to > answer, then find the method that will answer the question(s), possibly > using a bootstrap or permutation approach, or something more appropriate > rather than trying to force a square peg into a hole that you have not even > checked to see if it is round, square, or something else. > > > On Tue, Jul 9, 2013 at 2:20 AM, D. Alain <dialva...@yahoo.de> wrote: > >> Dear R-List, >> >> due to outliers in my data I wanted to carry out a robust regression. >> According to APA standards, reporting OLS regression results should >> include >> >> 1. unstandardized beta coefficients >> 2. standardized beta coefficients >> 3. SE >> 4. t values >> 5. r squared >> 6. r squared adjusted >> 7. F (df.num/df.den) >> >> Now I tried the robust version using lmrob (package="robustbase") >> >> lmrob.fit<-lmrob(y~x1+x2+x3,data=mydat) >> >> I got >> 1. unstandardized beta coef >> 3. SE >> 4. t values >> >> What about? >> 2. standardized beta coef >> 5. r squared >> 6. r squared adjusted >> 7. F (df.num/df.den) >> >> I have read in an R-threat ( >> http://tolstoy.newcastle.edu.au/R/e5/help/08/11/7271.html) that R2 is >> only valid in the context of least-square methods. Is there no equivalent I >> could report for non-least-square methods? Then why does lmrob-output not >> include standardized beta coefs and F statistic? How can I compute both of >> them? >> >> Then I realized that ltsReg (package="robustbase") does actually report >> almost everything I would need, but I could not find "standardized beta >> coefficients" (does anyone know how I could compute these coefs?) >> Though, the authors of the package "strongly recommend using lmrob() >> instead of ltsReg". Is this due to inefficiency or are the coefs biased? >> >> Finally I found lmRob (package="robust") which does report at least a >> multiple R2, but which is apparently biased and needs correction as I found >> in a threat of Renaud & Victoria-Feser >> https://stat.ethz.ch/pipermail/r-sig-robust/2010/000290.html >> >> where the authors recommend to correct R2 for bias (Renaud, O. & >> Victoria-Feser, M.-P. (2010). A robust coefficient of determination for >> regression. Journal of Statistical Planning and Inference, 140, 1852-1862. >> http://dx.doi.org/10.1016/j.jspi.2010.01.008). Does that mean, that >> "multiple r squared" can be reported even though it is not a least square >> method, but should be corrected for bias? Then, what does that mean for the >> rest of lmRob-output (e.g. t-values)? >> >> I must confess that I am somewhat confused and I would be very thankful >> for any clarification in this matter. >> Thank you in advance and sorry for my question if it reveals some serious >> lack of knowledge on my side. >> >> Best wishes. >> >> Alain >> >> [[alternative HTML version deleted]] >> >> >> ______________________________________________ >> 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. >> >> > > > -- > Gregory (Greg) L. Snow Ph.D. > 538...@gmail.com > -- Gregory (Greg) L. Snow Ph.D. 538...@gmail.com [[alternative HTML version deleted]] ______________________________________________ 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.
