[R-sig-ME] t-distributed residuals [was Re: sandwich variance estimation using glmer?]

[Whit Armstrong]

Do you have a winbugs example of the model you would like to fit?

If it is as simple as using a t-dist prior for your coefficients, then
it's pretty simple to do that in winbugs or PyMC.

Of course I'd like to plug my own project which is a c++ equivalent of
winbugs, now directly callable from R via inline.

I'm happy to translate a winbugs model and post the cppbugs equivalent.

-Whit


On Fri, Nov 5, 2010 at 12:25 PM, Ben Bolker <bbolker at gmail.com> wrote:
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> On 10-11-05 12:12 PM, David Atkins wrote:
>>
>> On 11/4/10 3:06 PM, Andrew Robinson wrote:
>>> 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.
>>
>> Andrew--
>>
>> You are, of course, absolutely correct.  I use R almost exclusively, and
>> for the most part, not having robust SE doesn't really cause any
>> problems for me (in general, or with respect to checking diagnostics...
>> actually, I love it!).
>>
>> From my own experience, I have seen the HLM's software use of both be
>> helpful in the following way: I have several times had colleagues /
>> students come to me with output from HLM, noting the discrepancy between
>> SE and wondering what this means?  In essence, b/c that software puts
>> both of them in front of you, it's hard to miss when they are different
>> (esp. since p-values will then be radically different).
>>
>> These times tend to be "teachable moments" in terms of what it is saying
>> about the model and data (and fit).  More often that not, the outcome
>> has been some form of count variable (which lurk quite commonly in
>> psychological/psychiatric waters), and thus we can talk about
>> distributional properties of the outcome vs. model, etc. (And I think
>> the mean-variance relationship of the Poisson tends to lead to large
>> adjustments with the robust SE.)
>>
>> I would in no way suggest that lme4 should follow suit with the HLM
>> software, and I honestly doubt whether it would serve a similar purpose,
>> as more novice statistical users tend to be intimidated by R (given lack
>> of menus, GUI, etc.).
>>
>> As I mentioned before, what I *would* be interested in are robust
>> approaches a la incorporating t-distribution in prior or likelihood.  I
>> am currently working with a colleague on an analysis of a small number
>> of groups, where we have discused this -- he's exploring WinBUGS as an
>> option at present (to follow-up on our analyses with glmer and MCMCglmm).
>>
>> For what it's worth (and realizing it ain't all that much about R...).
>>
>
>  Channeling Dave Fournier here for a few moments ...
>
>  For that particular project, I would recommend that you give AD Model
> Builder and (to plug my own project and make things a little more R-ish)
> the R2ADMB package a try. AD Model Builder is fast, flexible, uses
> Laplace approximation for mixed modeling, and allows you to do post-hoc
> MCMC sampling around the estimated modes; changing from a Gaussian to
> t-distributed residual/likelihood calculations is in principle just a
> matter of adding a parameter and changing the line of code that does the
> likelihood calculation.  And ADMB is now open source.
>  The downside is that you have to learn a new system (objective
> functions in ADMB are written in a superset of C++). Overall I would say
> that the effort, and the payoff, of learning ADMB are on the same order
> of magnitude as learning WinBUGS/JAGS ...
>
>  Ben Bolker
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