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

[Ben Bolker]

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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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