[R-sig-ME] [R] Checking modeling assumptions in a binomial GLMM

[Ben Bolker]

On 14-07-17 05:19 PM, Ravi Varadhan wrote:
> Thank you very much, Ben.
> 
> I have one more question:  you have function for computing
> overdispersion, overdisp.glmer() in "RVAideMemoire" package.  This is
> useful, I suppose.  Why is it not part of lme4, or, equivalently why
> doesn't glmer() not provide this information?
> 
> Thanks, Ravi

RVAideMemoire is not our package: it's by Maxime Hervé.

We probably didn't add the overdispersion calculation to lme4
because (1) we didn't get around to it; (2) for GLMMs it's an
even-more-approximate estimate of overdispersion than it is
for GLMs; (3) it's easy enough for users to implement themselves
(another version is listed at
http://glmm.wikidot.com/faq#overdispersion_est,
and the aods3::gof() function also does these calculations
(although looking at it, there may be some issues with the
using the results of lme4::deviance() for these purposes -- it returns
something different from the sum of squares of the deviance
residuals ...)

  The summary statement of glmer models probably *should* include this
information.  Feel free to post an issue at
https://github.com/lme4/lme4/issues ...

This somewhat simpler expression replicates the results of
RVAideMemoire's function, although not quite as prettily:

library(lme4)
example(glmer)

c(dev <- sum(residuals(gm1)^2),
  dfr <- df.residual(gm1),
  ratio <- dev/dfr)

RVAideMemoire::overdisp.glmer(gm1)

> 
> -----Original Message----- From: Ben Bolker
> [mailto:bbolker at gmail.com] Sent: Thursday, July 17, 2014 4:40 PM To:
> Ravi Varadhan Cc: r-sig-mixed-models at r-project.org Subject: Re: [R]
> Checking modeling assumptions in a binomial GLMM
> 
> On 14-07-17 10:05 AM, Ravi Varadhan wrote:
> 
>> Dear Ben,
> 
>> Thank you for the helpful response.  I had posted the question to
> r-sig-mixed last week, but I did not hear from anyone.  Perhaps, the 
> moderator never approved my post.  Hence, the post to r-help.
> 
> [cc'ing to r-sig-mixed-models now]
> 
>> My example has repeated binary (0/1) responses at each visit of a
> clinical trial (it is actually the schizophrenia trial discussed in 
> Hedeker and Gibbons' book on longitudinal analysis).  My impression 
> was that diagnostics are quite difficult to do, but was interested in
> seeing if someone had demonstrated this.
> 
> 
>> I have some related questions: the glmer function in "lme4" does
>> not
> handle nAGQ > 1 when there are more than 1 random effects.  I know 
> this is a curse of dimensionality problem, but I do not see why it 
> cannot handle nAGQ up to 9 for 2-3 dimensions.  Is Laplace's 
> approximation sufficiently accurate for multiple random effects?  Is 
> mcmcGLMM the way to go for binary GLMM with multiple random effects?
> 
> 
> To a large extent AGQ is not implemented for multiple random effects
> (or, in lme4 >= 1.0.0, for vector-valued random effects) because we
> simply haven't had the time and energy to implement it.  Doug Bates
> has long felt/stated that AGQ would be infeasibly slow for multiple
> random effects.  To be honest, I don't know if he's basing that on
> better knowledge than I (or anyone!) have about the internals of lme4
> (e.g. trying to construct the data structures necessary to do AGQ
> would lead to a catastrophic loss of sparsity) or whether it's just
> that his focus is usually on gigantic data sets where
> multi-dimensional AGQ truly would be infeasible.
> 
> Certainly MCMCglmm, or going outside the R framework (to SAS PROC
> GLIMMIX, or Stata's GLLAMM
> <http://www.stata-press.com/books/mlmus3_ch10.pdf>), would be my
> first resort when worrying about whether AGQ is necessary. 
> Unfortunately, I know of very little discussion about how to
> determine in general whether AGQ is necessary (or what number of
> quadrature points is sufficient), without actually doing it -- most
> of the examples I've seen (e.g.
> <http://www.stata-press.com/books/mlmus3_ch10.pdf> or Breslow 2003)
> just check by brute force (see http://rpubs.com/bbolker/glmmchapter
> for another example).  It would be nice to figure out a score test,
> or at least graphical diagnostics, that could suggest (without
> actually doing the entire integral) how much the underlying densities
> departed from those assumed by the Laplace approximation.  (The
> zeta() function in http://lme4.r-forge.r-project.org/JSS/glmer.Rnw
> might be a good starting point ...)
> 
> cheers Ben Bolker
>