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 <dialvac-r@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]]
>
>
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> 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.
538280@gmail.com
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