That's an interesting point, Dave.  Surely, however, there are better model
diagnostics?  By 'better' I mean more likely to pinpoint the source of lack
of fit within a model?

Personally I wouldn't rely on the concordance between robust and asymptotic
SE as an indicator of model appropriateness.  I don't see how it adds
anything important to the diagnostic process.

1) if the match is bad, I'll examine the diagnostics, but

2) if the match is good, I'll examine the diagnostics anyway, as part of due
diligence.

Also I don't know of any theory that suggests that deviation between robust
and asymptotic standard error estimates *always* indicates a model problem.
If anyone does, I'm happy to learn about it.

On the other hand, robust SE are (likely to be) larger than asymptotic SE.
So, if I see a deviation, it could be because (a) there's a problem with my
model, and (b) the model is fine but I'm paying a price for robustness.

All of which raises an interesting question: if we observe a deviation
between the estimate and hunt through the model diagnostics to find a cause,
but can't --- then what do we do?

Cheers

Andrew


On Fri, Nov 5, 2010 at 2:59 AM, David Atkins <datkins@u.washington.edu>wrote:

>
> One slightly different perspective on robust SE in mixed models:
>
> The place where I have seen these used regularly is in the HLM software
> (popular in education and psychology circles).  HLM *always* reports both
> "standard" and robust SE.
>
> What I find interesting is that if you read Raudenbush and Bryk (and the
> HLM manual), they suggest using the robust SE as a model diagnostic (my
> term).  That is, when there is a discrepancy between SE, they rightly note
> that something is amiss, and you should do further detective work related to
> the random-effects specification.
>
> That seems like a very valid use of robust SE, though I fully acknowledge
> such info (ie, model isn't fitting well) could be got other ways.
>
> [BTW, I'd love to see other robust approaches, such as t-distributed error
> and/or priors, but as Ben notes that's an awfully high bar to implement --
> either in lmer or MCMCglmm.  The heavy package is an initial attempt, but
> seems to be "stalled out" at the moment.]
>
> For what it's worth.
>
> cheers, Dave
>
>
>
> Harold wrote:
>
> Let me push on this just a bit to spark further discussion. The OP was
> interested in robust standard errors given misspecification in the
> likelihood. So, one possible avenue was to explore Huber-White standard
> errors, or the sandwich estimator, to account for this misspecification and
> obtain "better" standard errors, but still use the point estimates of the
> fixed effects as given.
>
> Some discussion on this has noted that the misspecification occurs in many
> ways, sometimes given that distributional assumptions were not met. Let's
> assume someone was willing and skilled to code up the HW as a possible
> solution within lmer to account for not meeting certain distributional
> assumptions.
>
> My question is now why not directly code up models that permit for
> different distributional assumptions, such as t-distributions of residuals
> (random effects) or whatever the case might be? In other words, why not
> write code that addresses the problems directly (misspecification of the
> likelihood) rather than focusing on HW estimates.
>
> Isn't it a better use of time and energy to focus on properly specifying
> the likelihood and estimating parameters from that model rather than HW?
>
> --
> Dave Atkins, PhD
> Research Associate Professor
> Department of Psychiatry and Behavioral Science
> University of Washington
> datkins@u.washington.edu
>
> Center for the Study of Health and Risk Behaviors (CSHRB)
> 1100 NE 45th Street, Suite 300
> Seattle, WA  98105
> 206-616-3879
> http://depts.washington.edu/cshrb/
> (Mon-Wed)
>
> Center for Healthcare Improvement, for Addictions, Mental Illness,
>  Medically Vulnerable Populations (CHAMMP)
> 325 9th Avenue, 2HH-15
> Box 359911
> Seattle, WA 98104
> http://www.chammp.org
> (Thurs)
>
> _______________________________________________
> R-sig-mixed-models@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>



-- 
Andrew Robinson
Program Manager, ACERA
Senior Lecturer in Applied Statistics                      Tel:
+61-3-8344-6410
Department of Mathematics and Statistics            Fax: +61-3-8344 4599
University of Melbourne, VIC 3010 Australia
Email: a.robinson@ms.unimelb.edu.au    Website: http://www.ms.unimelb.edu.au

	[[alternative HTML version deleted]]


