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

[Fox, John]

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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