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

[Ben Bolker]

On 10-11-04 10:18 AM, Doran, 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?

   I would say there are two issues here, one philosophical and one
technical/pragmatic.

  Philosophical: how should one divide one's time and effort between
trying to come up with better parametric models vs. admitting that 'all
models are wrong' and coming up instead with robust alternatives that
perform reasonably well across a broad range of (unknown/unspecified)
parametric models?

  Technical/pragmatic: taking your case of t-distributions of residuals
-- this could be reasonably straightforward to implement in a framework
that is closer to a brute force computational solution (MCMC, AD Model
Builder), but I wouldn't know where to begin trying to implement it in
the elegant/computationally efficient lme4 framework ...

  cheers
    Ben Bolker