[R] robust model selection criteria

[Prof Brian Ripley]

On Fri, 29 Apr 2005, Berton Gunter wrote:

>
>
> -- Bert Gunter
> Genentech Non-Clinical Statistics
> South San Francisco, CA
>
> "The business of the statistician is to catalyze the scientific learning
> process."  - George E. P. Box
>
>
>
>> -----Original Message-----
>> From: r-help-bounces at stat.math.ethz.ch
>> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of
>> Carsten.Colombier at efv.admin.ch
>> Sent: Friday, April 29, 2005 9:26 AM
>> To: r-help at stat.math.ethz.ch
>> Subject: [R] robust model selection criteria
>>
>> Dear R-help-team,
>>
>> do you know if there is a package for R available that
>> contains a function,
>> which calculates a robust model selection criterium like
>
>> robust AIC and has
>> a robust selection function like "step" for lm-objects, for
>> an  rlm-object.
>> Unfortunately, functions like "step" or "stepAIC" cannot be applied to
>> rlm-objects. Moreover, these functions do not use  robust AIC.
>>
>
> ??? How could this be meaningful? The robust "likelihood" need not increase
> as more parameters are added because of the robust reweighting (points would
> be downweighted differently in the different models). How do you account for
> the number of "parameters" in a robust model given that it is in essence
> nonlinear?
>
> (This comment subject to correction/expansion by wiser heads than me)

More fundamentally, `AIC' is about maximum-likelihood fitting of true 
models.  Now rlm does usually correspond to ML fitting of a non-normal 
linear model, so it would be possible to compute a likelihood and hence 
AIC.  The point however is that the model is assumed to be false.  There 
are AIC-like criteria for that situation, but they are essentially 
impossible to compute accurately as they depend on fine details of the 
unknown true error distribution (and still assume a linear model).

>
> -- Bert Gunter
> Genentech Non-Clinical Statistics
> South San Francisco, CA
>
> "The business of the statistician is to catalyze the scientific learning
> process."  - George E. P. Box
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595