[R-sig-ME] p-values glmer in lme4

[Douglas Bates]

My favorite Oscar Wilde quote is "Consistency is the last refuge of the
unimaginative".

On Wed, Jul 19, 2017 at 4:53 PM Phillip Alday <phillip.alday at mpi.nl> wrote:

> And to add to the mix: MixedModels.jl labels the the (mean/stderr)
> column 'z' for LMM and provides p-values, which is an interesting
> development from the Doug Bates' R FAQ entry on the lack of p-values in
> lme4. (And the default estimation is once again ML and not REML.) None
> of it terribly surprising based on DB's comments here and elsewhere over
> the years, but an interesting course nonetheless.
>
> Phillip
>
> On 07/19/2017 11:18 PM, Ben Bolker wrote:
> >
> >    I agree that the label should go according to the inference used. The
> > funny (??) thing is that in base lmer (not in the lmerTest extension
> > package) *the summary doesn't print p-values at all*, so according to
> > the rubric above we can't tell whether the (mean/stderr) column should
> > be labeled 'z' or 't'. (We could label that column 'mean/std.err.', but
> > then some users would ask "why doesn't the summary print either z or t
> > values?" :-( )
> >
> >
> > On 17-07-19 03:58 PM, Fox, John wrote:
> >> Hi Ben,
> >>
> >> I'm glad that you chimed in on this question.
> >>
> >> Of course, what you say about (virtually) all the p-values being
> >> approximations is correct. My own preference would be to use
> >> "t-value" when you look up a p-value (approximate or not) for a Wald
> >> statistic in a t-distribution and "z-value" when you look up (an
> >> asymptotic approximation to) a p-value in the standard-normal
> >> distribution. Frankly, however, this seems a bit like splitting
> >> hairs, and so I think that what you do now is fine.
> >>
> >> Best, John
> >
> >>> -----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
> >>>>>
> >>>>> [[alternative HTML version deleted]]
> >>>>>
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