[R-sig-ME] Fwd: Re: Wald F tests

[Ben Bolker]

  Does anyone out there have opinions on this subject?
How should one test hypotheses about fixed effects in
(G)LMMs, especially for small to moderate sample sizes?
(Please ignore issues of _estimation_ (PQL
vs Laplace vs AGQ vs ...)

  Should it amuse you to do so, you can vote at:

http://www.surveymonkey.com/s.aspx?sm=yLyfrV_2ftw6WGx2dEFLWnIw_3d_3d

(since we all know that scientific questions are settled
by a democratic process)

a hypothesis testing is soooo 20th century, don't bother
b likelihood ratio tests [ignore known anticonservatism]
c F tests (LMM) or Wald tests (GLMM) [ignore mismatch with hypothesized
null distributions]
d bootstrapped confidence intervals
e [mcmcsamp confidence intervals -- if available]
f randomization/simulation tests of nested null hypotheses
g AIC comparisons [ignore that prediction != hypothesis testing]

  Note that Wald Z tests [option c] are more or less what you're
doing, implicitly, if you just eyeball the estimated
parameter values and their standard errors.

  cheers
    Ben Bolker

-------- Original Message --------
Subject: [Fwd: Re: [R-sig-ME] Wald F tests]
Date: Tue, 07 Oct 2008 17:51:01 -0400
From: Ben Bolker <bolker at ufl.edu>
To: R Mixed Models <r-sig-mixed-models at r-project.org>


  But ... LRTs are non-recommended (anticonservative) for
comparing fixed effects of LMMs hence (presumably) for
GLMMs, unless sample size (# blocks/"residual" total sample
size) is large, no?

I just got through telling readers of
a forthcoming TREE (Trends in Ecology and Evolution) article
that they should use Wald Z, chi^2, t, or F (depending on
whether testing a single or multiple parameters, and whether
there is overdispersion or not), in preference to LRTs,
for testing fixed effects ... ?  Or do you consider LRT
better than Wald in this case (in which case as far as
we know _nothing_ works very well for GLMMs, and I might
just start to cry ...)  Or perhaps I have to get busy
running some simulations ...

  Where would _you_ go to find advice on inference
(as opposed to estimation) on estimated GLMM parameters?

  cheers
   Ben Bolker

Douglas Bates wrote:
> If I were using glmer to fit a generalized linear mixed model I would
> use likelihood ratio tests rather than Wald tests.  That is, I would
> fit a model including a particular term then fit it again without that
> term and calculate the difference in the deviance values, comparing
> that to a chi-square.
>
> I'm not sure how one would do this using the results from glmmPQL.
>
> On Fri, Oct 3, 2008 at 3:37 PM, Ben Bolker <bolker at ufl.edu> wrote:
>>  [forwarding to R-sig-mixed, where it is likely to get more
>> responses]
>>
>> Mark Fowler wrote:
>>
>> Hello,
>>        Might anyone know how to conduct Wald-type F-tests of the fixed
>> effects estimated by glmmPQL? I see this implemented in SAS (GLIMMIX),
>> and have seen it recommended in user group discussions, but haven't come
>> across any code to accomplish it. I understand the anova function treats
>> a glmmPQL fit as an lme fit, with the test assumptions based on maximum
>> likelihood, which is inappropriate for PQL. I'm using S-Plus 7. I also
>> have R 2.7 and S-Plus 8 if necessary.
>>
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