[Fwd: Re: Wald F tests]

  Somewhat off-topic, but relevant to the larger question:
is there a good way to hack profile confidence limits for
[g]lmer fits?  (Nothing obvious springs to the eye ...) Has
anyone tried it?

Murray Jorgensen wrote:

Not that Doug needs my support but his support of the likelihood ratio
as the right thing to be looking at regardless of any calibration
difficulties strikes a chord with me. There is a famous Tukey quote that
I can perhaps bend into service here:

"Far better an approximate answer to the right question, than the exact
answer to the wrong question, which can always be made precise."

In this context I take the "right question" to be interpretation of the
likelihood ratio and the "wrong question" to be the local properties of
the fitted "larger" model.

Murray Jorgensen

Douglas Bates wrote:

On Tue, Oct 7, 2008 at 4:51 PM, Ben Bolker <bolker at ufl.edu> wrote:

 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 ...

My reasoning, based on my experiences with nonlinear regression models
and other nonlinear models, is that a test that involves fitting the
alternative model and the null model then comparing the quality of the
fit will give more realistic results than a test that only involves
fitting the alternative model and using that fit to extrapolate to
what the null model fit should be like.

We will always use approximations in statistics but as we get more
powerful computing facilities some of the approximations that we
needed to use in the past can be avoided.  I view Wald tests as an
approximation to the quantity that we want to use to compare models,
which is some measure of the comparative fit.  The likelihood ratio or
the change in the deviance seems to be a reasonable way of comparing
the fits of two nested models.  There may be problems with calibrating
that quantity (i.e. converting it to a p-value) in which case we may
want to use a bootstrap or some other simulation-based method like
MCMC.  However, I don't think this difficulty would cause me to say
that it is better to use an approximation to the model fit under the
null hypothesis than to go ahead and fit it.

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

I'm not sure.  As I once said to Martin, my research involves far too
much "re" and far too little "search".  Probably because of laziness I
tend to try to reason things out instead of conducting literature
reviews.

 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.