Re: [R] Goodness of fit with robust regression

From: Spencer Graves <spencer.graves_at_structuremonitoring.com>
Date: Mon, 14 Mar 2011 08:54:41 -0700

       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.
>
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