[RsR] glmrob - fit statistics: R^2 - r-squared ?

[Martin Maechler]

>>>>> F... F... <.... using gmail.com>  on Tue, 31 Jan 2017 20:17:31 -0500 writes:

    > Dear Prof. Maechler:
    > I am using the glmrob function from your package and am interested in
    > having fit statistics (r-squared). Summary doesn't give me that. Is there
    > another way to obtain it?

I'm replying to the dedicated mailing list, "robust statistics with R",
(BCC'ing to F.F. who asked me in private):

Even standard R's   glm()  does not provide an R^2 for
generalized linear models, because it is doubtful how it should
be defined outside of least squares and the normal distribution
assumption.

But of course, other goodness-of-fit (GOF) measures do make
sense, and summary(glm(..)) provides deviances, dispersion
parameter estimates and AIC  aiming in that direction.


For linear models with the 'normal' family, we typically use lmrob(),
and there, the summary method now has been providing a _robust_
version of R^2, thanks to this research paper (and code contribution),

     Renaud, O. and Victoria-Feser, M.-P. (2010).  A robust coefficient
     of determination for regression, _Journal of Statistical Planning
     and Inference_ *140*, 1852-1862.

we now have

> mod1 <- lmrob(stack.loss ~ ., data = stackloss)
> summary(mod1)

Call:
lmrob(formula = stack.loss ~ ., data = stackloss)
 \--> method = "MM"
Residuals:
      Min        1Q    Median        3Q       Max 
-10.50974  -1.43819  -0.09134   1.02503   7.23113 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -41.52462    5.29780  -7.838 4.82e-07 ***
Air.Flow      0.93885    0.11743   7.995 3.68e-07 ***
Water.Temp    0.57955    0.26296   2.204   0.0416 *  
Acid.Conc.   -0.11292    0.06989  -1.616   0.1246    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Robust residual standard error: 1.912 
Multiple R-squared:  0.9593,	Adjusted R-squared:  0.9521 
^^^^^^^^^^^^^^^^^^              ^^^^^^^^^^^^^^^^^^

[.............]
[.............]

and the help page explains:

r.squared: robust “R squared” or R^2, a coefficient of determination:
          This is the consistency corrected robust coefficient of
          determination by Renaud and Victoria-Feser (2010).

-----------------------------

I have not known of similar research / proposals for
non-Gaussian robustified GLMs, and so there hasn't been anything
in "summary(glmrob(..))" in the robustbase package,
but maybe there are proposals out there which the readers of
R-SIG-robust know about ?

We would be interested to know...

Martin Maechler
ETH Zurich