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

[Fox, John]

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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> >
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> 
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