[R] Goodness of fit with robust regression

[Bert Gunter]

Hi:

Just a few additional comments to Spencer's.

1. There is an R-SIG-Robust group that you may wish to post your
question to if you have not already done so. There you **should** find
experts to help you, of which I'm also not one.

2. The situation regarding the effectiveness of robust techniques is
not so grim as Spencer seems to imply. Heuristics have been backed up
by more than 30 years of simulations and asymptotic work. Asymptotic
optimality (which may or may not be all that useful) has been shown
for certain approaches in certain situations. Generally and vaguely
speaking, many "standard" (e.g. M-estimators) robust estimation
methods (e.g. Tukey biweight) have been found to be fairly harmless
(little loss of efficiency) when the data are "well-behaved" and
potentially lots better when they are not.

3. A big problem in establishing reference distributions (for
inference) for the various approaches is that robustness weights
depend on data and fitting parameters. If you can automate the
selection of these in some way, simulation can always be used -- and
is, I believe, what is generally recommended for inference.

4. Probably the most important and difficult issue in applying robust
methods is finding good starting values. That's why MASS's rlm
function has a well thought-out strategy of using a very low
efficiency but high resistance (and typically computationally
intensive) estimator to produce "safe" initial starting guesses from
which an M-estimator than iterates to a solution (typically very
quickly). This is also something that needs to be automated (as rlm
does) for simulation/bootstrap based inference.

But again: Please refer to (1) above. All of my "advice" is subject to
modification by the folks there.

Cheers,
Bert


On Mon, Mar 14, 2011 at 8:54 AM, Spencer Graves
<spencer.graves at structuremonitoring.com> wrote:
>      I'm not an expert on robust modeling.  However, as far as I know, most
> robust regression procedures are based on heuristics, justified by claims
> that "it seems to work" rather than reference to assumptions about a
> probability model that makes the procedures "optimal".  There may be
> exceptions for procedures that assume a linear model plus noise that follows
> a student's t distribution or a contaminated normal.  Thus, if you can't get
> traditional R-squares from a standard robust regression function, it may be
> because the people who wrote the function thought that R-squared (as,
> "percent of variance explained") did not make sense in that context.  This
> is particularly true for robust general linear models.
>
>
>      Fortunately, the prospects are not as grim as this explanation might
> seem:  The summary method for an "lmrob" object (from the robustbase
> package) returned for me the standard table with estimated, standard errors,
> t values, and p values for the regression coefficients.  The robustbase
> package also includes an anova method for two nested lmrob models.  This
> returns pseudoDF (a replacement for the degrees of freedom), Test.Stat
> (analogous to 2*log(likelihood ratio)), Df, and Pr(>chisq).  In addition to
> the 5 References in the lmrob help page, help(pac=robustbase) says, it is '
> "Essential" Robust Statistics.  The goal is to provide tools allowing to
> analyze data with robust methods.  This includes regression methodology
> including model selections and multivariate statistics where we strive to
> cover the book "Robust Statistics, Theory and Methods" by Maronna, Martin
> and Yohai; Wiley 2006.'
>
>
>      I chose to use lmrob, because it seemed the obvious choice from a
> search I did of Jonathan Baron's database of contributed R packages:
>
>
> library(sos)
> rls <- findFn('robust fit') # 477 matches;  retrieved 400
> rls.m <- findFn('robust model')# 2404 matches;  retrieved 400
> rls. <- rls|rls.m # union of the two searchs
> installPackages(rls.)
> # install missing packages with many matches
> # so we can get more information about those packages
> writeFindFn2xls(rls.)
> # Produce an Excel file with a package summary
> # as well a table of the individual matches
>
>
>      Hope this helps.
>      Spencer Graves
>
>
> p.s.  The functions in MASS are very good.  I did not use rlm in this case
> primarily because MASS was package number 27 in the package summary in the
> Excel file produced by the above script.  Beyond that, methods(class='rlm')
> identified predict, print, se.contrast, summary and vcov methods for rlm
> objects, and showMethods(class='rlm') returned nothing.  Conclusion:  If
> there is an anova method for rlm objects, I couldn't find it.
>
>
> On 3/14/2011 7:00 AM, agent dunham wrote:
>>
>> I also have the same problem, can anybody help?
>>
>> and I would also like to see the p-values associated with the t-value of
>> the
>> coefficients.
>>
>> At present I type summary (mod1.rlm) and neither of these things appear.
>>
>> Thanks, user at host.com
>>
>> --
>> View this message in context:
>> http://r.789695.n4.nabble.com/R-Goodness-of-fit-with-robust-regression-tp809412p3353919.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help at 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 at 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.
>



-- 
Bert Gunter
Genentech Nonclinical Biostatistics
467-7374
http://devo.gene.com/groups/devo/depts/ncb/home.shtml