[R-sig-ME] Emmeans & effects packages: Post-hoc tests for Tweedie glmmTMB model

[Fox, John]

Dear Niall,

> On Apr 20, 2020, at 6:11 PM, Millar, Niall <niall.millar using wsu.edu> wrote:
> 
> Dear John,
> 
> Thanks very much for reply. I'd just like to clarify a few points and make sure I understand. Do you mean that the effects package calculates these asymptotic confidence intervals by assuming that the distribution of the parameters (not the data) is normal? If so, can I then generate hypothesis tests with these confidence intervals by assuming some uncertainty in the parameter values?

Yes, the estimated fixed-effects coefficients and the estimated effects, which are linear combinations of the estimated coefficients, are asymptotically normal, and the confidence intervals reported are either based on the normal or t-distribution, depending on the model. 

But it's not obvious to me that the point-wise confidence intervals for the effects correspond to hypotheses that you want to test. The object returned by Effect(), however, contains not only the estimated effects, their standard errors, and confidence limits, but also their full covariance matrix. Consequently, you should be able to formulate a Wald test for *any* linear combination of the effects of interest, or even, by the delta method, a test for a nonlinear function of the fixed effects.

Best,
 John

> 
> Thanks,
> -Niall
> From: Fox, John <jfox using mcmaster.ca>
> Sent: 17 April 2020 14:03
> To: Millar, Niall <niall.millar using wsu.edu>; r-sig-mixed-models using r-project.org <r-sig-mixed-models using r-project.org>
> Subject: RE: Emmeans & effects packages: Post-hoc tests for Tweedie glmmTMB model
>  
> Dear Niall,
> 
> I've not seen applications of GLMMs using the Tweedie Family, but don't see why that should matter. The "effects" computed by the functions in the effects package are linear functions of the estimated fixed-effects parameters, and their asymptotic standard errors are computed from the estimated covariance matrix of the fixed effects. The default (asymptotic) confidence intervals are computed pointwise and so don't adjust for simultaneous inference, but there is an option to compute Scheffe intervals.
> 
> By the way, the fixed-effects part of your model is more compactly Shoot.weight ~ N.Level*Rhiz*Species.
> 
> I hope this helps,
>  John
> 
> --------------------------------------
> John Fox, Professor Emeritus
> McMaster University
> Hamilton, Ontario, Canada
> Web: socialsciences.mcmaster.ca/jfox/
> 
> 
> 
> > -----Original Message-----
> > From: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> On
> > Behalf Of Millar, Niall
> > Sent: Friday, April 17, 2020 4:52 PM
> > To: r-sig-mixed-models using r-project.org
> > Subject: [R-sig-ME] Emmeans & effects packages: Post-hoc tests for Tweedie
> > glmmTMB model
> > 
> > Are there any problems with using the effects and emmeans packages to
> > interpret glmmTMB models with Tweedie distributions?
> > 
> > I have glmmTMB models using the Tweedie distribution, and I want to draw
> > inference about the direction and magnitude of the predicted effects. In
> > the model given below:
> > 
> > glmmTMB(Shoot.weight ~ Species + N.Level + Rhiz + Species:N.Level +
> > Species:Rhiz + N.Level:Rhiz + N.Level:Rhiz:Species + (1|Block) + (1|Acc),
> > family=tweedie, data=DcleanSOY)
> > 
> > I have a significant effect of the N.Level:Rhiz:Species interaction term
> > (based on a likelihood ratio test). N level is a continuous predictor, and
> > Rhiz and Species are both two-level factors.
> > 
> > I have used the effects package to make a plot with 95% confidence
> > intervals to interpret this 3-way interaction. I have also made separate
> > models for each level of the N level predictor, and used emmeans to get
> > pairwise Tukey contrasts of the Rhiz and Species predictors at each N
> > level.
> > 
> > Can I base my inference on these 95% confidence intervals and/or emmeans
> > contrasts, or are these methods not supported for Tweedie glmmTMB models?
> > 
> > Thanks! -Niall
> > 
> > 
> > Niall Millar
> > PhD Candidate
> > Porter Lab
> > School of Biological Sciences
> > 
> > Washington State University Vancouver
> > 14204 NE Salmon Creek Ave
> > Vancouver, WA  98686
> > 360-784-9816
> > niall.millar using wsu.edu
> > 
> >        [[alternative HTML version deleted]]
> > 
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