[R-sig-ME] sandwich variance estimation using glmer?

[David Atkins]

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 at u.washington.edu

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