p-values glmer in lme4

-----Original Message-----
From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-project.org]
On Behalf Of Ben Bolker
Sent: Wednesday, July 19, 2017 3:29 PM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] p-values glmer in lme4


  This diagnosis sounds correct, and I agree that calling these numbers "z
values" is probably the best way to make the reviewers happy.

It opens an interesting terminological can of worms.  My initial reaction to
John's post was "oh, I guess glmer should print 'z value'
rather than 't value' even for fits using families with an estimated dispersion
parameter". Then I thought "but if that's true shouldn't lmer also print 'z value'
rather than 't value', since it provides essentially the same numbers?" Then I
thought "if we switch lmer to printing 'z value' will everyone start asking 'why
does lmer provide z values rather than t values?"  Sigh.

  The point is that most of this, while unfairly confusing, is just convention.  "z
values" and "t values" are the same thing - MLEs (or REML estimates) of the
parameters divided by their estimated standard deviations. Of the common
(G)LMM applications, the *only* case in which these values are actually known
to follow a t distribution exactly is for linear mixed models (Gaussian
conditional distribution), in the classic case of a balanced, nested design (and,
implied by John below, that the fit uses REML). Otherwise it becomes a
question of which approximations you're happy with.

  And the sampling distributions of these values are never Normal (even in the
perfect theoretical world where all model assumptions are true), except
asymptotically.


On 17-07-19 02:50 PM, Fox, John wrote:

Dear Leen Catrysse,

I'm going to assume that you used the glmer() function in the lme4 package

to fit your gamma GLMM. I notice that the summary() for a gamma model fit by
glmer() reports a "t value" for each fixed-effect coefficient  -- simply the Wald
statistics given by the ratio of the estimated coefficient to its estimated
asymptotic standard error -- followed by a "Pr(>|z|)".

I suspect that the Wald statistic is labelled as a "t value" because the gamma

GLMM has an estimated dispersion parameter, but because there are no
degrees of freedom calculated for the estimated dispersion (as there could be,
for example, for a LMM fit by REML), I think that it would probably be
preferable to call the Wald statistic a "z value." In any event, the notation
"Pr(>|z|)" suggests that the standard normal distribution is used to obtain a p-
value.

So, to satisfy the reviewer, why not just call the Wald statistics "z-values"

rather than a "t-values"?

I hope this helps,
 John

-----------------------------
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
Web: socserv.mcmaster.ca/jfox

-----Original Message-----
From: R-sig-mixed-models
[mailto:r-sig-mixed-models-bounces at r-project.org]
On Behalf Of Catrysse Leen
Sent: Wednesday, July 19, 2017 7:21 AM
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] p-values glmer in lme4

Dear,

I used GLMM to analyse eye-tracking data with the gamma distribution
and the log link. P-values were automatically computed in the output
(based on the asymptotic Wald tests).
We received a comment of a reviewer that the output of our GLMM is
inconsistent, as we report a t-value from the output and the p-value
based on the asymptotic Wald tests.
Does anyone has some feedback on how we can deal with this comment?

Thanks in advance,
Leen Catrysse

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