[RsR] Prediction Intervals for Robust Regression

[Martin Maechler]

>>>>> Stromberg, Arnold <astro11 using uky.edu>
>>>>>     on Mon, 16 Feb 2015 20:14:06 +0000 writes:

    > Jonathan,
    > Seems straightforward theoretically, let's see if anyone has implemented them in R.

    > Arny

    > Arnold J. Stromberg
    > Professor and Chair, Department of Statistics, University of Kentucky
    [ ........... ]

Well,  the predict() method for lmrob() fits (package
'robustbase') has built in.
I wonder why nobody has seen that and mentioned it here.

In the mean time, Jonathan has also asked on R-help
and got some advice there...
and now has found predict.lmrob  "in some way" and asked me (as
'robustbase' maintainer) about it.

I'm taking the liberty of answering here -- so others are also
helped in the future, *and* this thread is somewhat decently
closed within the R-SIG-robust list :

>>>>> Burns, Jonathan (NONUS) <Jonathan.Burns1 using GDIT.com>
>>>>>     on Thu, 19 Feb 2015 21:37:26 +0000 writes:

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

    > I am interested in creating prediction intervals for the robust regression models.  I tried to use the function predict.lmrob(); however, R gave me an error - could not find function "predict.lmrob".  I thought perhaps this was because I was using an older version of the package.  I updated the package and I still get the error.  I am using R version 3.1.0.

    > I also got the same error with the function print.lmrob, plot.lmrob() and anova.lmrob().  Lmrob() itself works fine.

    > This is the result that I get when I list the functions in robustbase:

    >> ls("package:robustbase")
    > [1] "adjbox"              "adjboxStats"         "adjOutlyingness"
    > [4] "aircraft"            "airmay"              "alcohol"
    ......................
    ......................
    > [103] "vaso"                "wagnerGrowth"        "wgt.himedian"
    > [106] "wood"

print(), predict() etc are all generic functions,
their   lmrob S3 methods *are* called  print.lmrob(), predict.lmrob(), etc,
but they are *hidden* and you do not see them normally.

Rather you should use  print(..), predict(...), etc.

If you really need to see them you can use
  getAnywhere("predict.lmrob")
etc.

{This is all general R knowledge - somewhat intermediate level -
 about using S3 methods in R packages and namespaces}

Note that you've also asked about this on the R-help mailing list on
Feb 11, and you got two answers, the second one by Prof Brian
Ripley explained to you  that matters *are* actually more complicated:

If you use robustness for a good reason, it seems a bit
optimistic to assume that a future observation has normal errors,
(rather than a mixture of normal + "outlier") and so the
standard assumptions about prediction intervals would be doubtful.

But I agree (with you I assume) that sometimes you *want* to
make this somewhat optimistic assumption.... and for that case,
everything is ready for you on a silver plate :

Why did you not just read the help page for predict.lmrob ?
Even though the object is hidden -- because you should call predict() --
it still has nice help page {well, that can be improved, and I
will for the next version of robustbase}, and that help
*does* answer your question on how to compute prediction intervals: 

Andreas Ruckstuhl, the author of the function does provide them
(under the optimistic assumption), in the exact same way as the
predict() method for lm  {called "predict.lm"} does.

==> Just use  predict( <fitted lmrob object>,  interval = "prediction")
(or a variant where you specify new data, weights, etc).


Best regards,
Martin


    > -----Original Message-----
    > From: R-SIG-Robust [mailto:r-sig-robust-bounces using r-project.org] On Behalf Of Jonathan Burns
    > Sent: Wednesday, February 11, 2015 12:42 PM
    > To: r-sig-robust using r-project.org
    > Subject: [RsR] Prediction Intervals for Robust Regression

    > I have created robust regression models using least trimmed squares and MM- regression (using robustbase).

    > I am now looking to create prediction intervals for the predicted results.  While I have seen some discussion in the literature about confidence intervals on the estimates for robust regression, I haven’t had much success on prediction intervals for the results.  I was wondering anyone would be able to provide some direction on how to create these prediction intervals in the robust regression setting.

    > Thanks,
    > Jonathan Burns
    > Sr. Statistician
    > General Dynamics Information Technology
    > Medicare & Medicaid Solutions
    > One West Pennsylvania Avenue
    > Baltimore, MD 21204
    > Jonathan.Burns1 using gdit.com
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