I may have sent this only to Harold yesterday by accident. Sorry Harold.


On Wed, Nov 3, 2010 at 8:57 AM, Doran, Harold <HDoran@air.org> wrote:

> Out of curiosity, why would you want a sandwich estimator from lmer? That
> estimator is typically used when the likelihood is misspecified, but you
> still want standard errors that account for correlations among units within
> a cluster.
>
> Since this is what lmer standard errors already account for, is there a
> need for the sandwich?
>
>

I think robust standard errors might be useful as a diagnostic. This is
Raudenbush and Bryk’s take (2002:278):



“The robust variance estimates can be highly diagnostic. The analyst can
examine discrepancies between model-based and robust standard errors. Large
discrepancies typically signal model misspecification. For example, when
slope heterogeneity exists but is not modeled, we typically find
discrepancies between the model-based and robust standard errors.
Incorporating the slope heterogeneity will, in this case, eliminate the
discrepancy.”



Also see:



Maas, C. J.M, and J. J Hox. 2004. “The influence of violations of
assumptions on multilevel parameter estimates and their standard
errors.” *Computational
Statistics & Data Analysis* 46:427–440.



Abstract:

A crucial problem in the statistical analysis of hierarchically structured
data is the dependence of the observations at the lower levels. Multilevel
modeling programs account for this dependence and in recent years these
programs have been widely accepted. One of the major assumptions of the
tests of significance used in the multilevel programs is normality of the
error distributions involved. Simulations were used to assess how important
this assumption is for the accuracy of multilevel parameter estimates and
their standard errors. Simulations varied the number of groups, the group
size, and the intraclass correlation, with the second level residual errors
following one of three non-normal distributions. In addition asymptotic
maximum likelihood standard errors are compared to robust (Huber/White)
standard errors.



The results show that non-normal residuals at the second level of the model
have little or no effect on the parameter estimates. For the fixed
parameters, both the maximum likelihood-based standard errors and the robust
standard errors are accurate. For the parameters in the random part of the
model, the maximum likelihood-based standard errors at the lowest level are
accurate, while the robust standard errors are often overcorrected. The
standard errors of the variances of the level-two random effects are highly
inaccurate, although the robust errors do perform better than the maximum
likelihood errors. For good accuracy, robust standard errors need at least
100 groups. *Thus, using robust standard errors as a diagnostic tool seems
to be preferable to simply relying on them to solve the problem.*



-----------------------------------------------------------------------------------------------------------------



Personally, I’ve recently come across some less than ideal kurtosis, and I’d
like to compare the model standard errors against the robust standard errors
in lmer.
-Jeremy

On Thu, Nov 4, 2010 at 11:59 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)
>
> _______________________________________________
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>



-- 
Jeremy Pais
Doctoral Candidate
Department of Sociology
University at Albany, SUNY

jeremy.pais01@albany.edu
jpais.albany@gmail.com
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