[R-sig-ME] Interpretation Inverse Gamma glmmTMB with interactions

[Matteo Sebastianelli]

Hi all,

I have been running an inverse Gamma glmm in glmmTMB and I am facing some
interpretation issues. DHARMa validation QQplot shows strong deviation when
using a gaussian model. The full model has a 3-way interaction. Here is the
output:

>
Cand.mod[[2]]<-glmmTMB(PRP~logEVI+logLAI+logVCF+logSRTM+phenotype*zone*mindist+
(1|Location/Bird_ID),control=glmmTMBControl(profile=quote(length(parameters$beta)>=5)),family=Gamma(link="inverse"),
contact)
> summary(Cand.mod[[2]])
 Family: Gamma  ( inverse )
Formula:          PRP ~ logEVI + logLAI + logVCF + logSRTM + phenotype *
zone *      mindist + (1 | Location/Bird_ID)
Data: contact

     AIC      BIC   logLik deviance df.resid
 -2510.0  -2406.4   1278.0  -2556.0      647

Random effects:

Conditional model:
 Groups           Name        Variance Std.Dev.
 Bird_ID:Location (Intercept) 0.007765 0.08812
 Location         (Intercept) 0.001286 0.03586
Number of obs: 670, groups:  Bird_ID:Location, 607; Location, 149

Dispersion estimate for Gamma family (sigma^2): 0.00149

Conditional model:
                                        Estimate Std. Error z value
Pr(>|z|)
(Intercept)                            2.0804378  0.1703550  12.212  <
2e-16 ***
logEVI                                -0.0903489  0.0458202  -1.972
0.048631 *
logLAI                                 0.0006268  0.0237269   0.026
0.978926
logVCF                                 0.0476667  0.0186172   2.560
0.010457 *
logSRTM                                0.0181225  0.0142313   1.273
0.202867
phenotypeyellow-fronted               -0.4409140  0.0445983  -9.886  <
2e-16 ***
zone2                                 -0.1888145  0.0651436  -2.898
0.003750 **
zone3                                  0.0542872  0.0453511   1.197
0.231289
zone4                                 -0.1738887  0.0525499  -3.309
0.000936 ***
mindist                                0.0266960  0.0221012   1.208
0.227088
phenotypeyellow-fronted:zone2          0.4846604  0.0690797   7.016
2.28e-12 ***
phenotypeyellow-fronted:zone3          0.2510780  0.0497183   5.050
4.42e-07 ***
phenotypeyellow-fronted:zone4          0.0867471  0.0640485   1.354
0.175609
phenotypeyellow-fronted:mindist       -0.0367038  0.0229506  -1.599
0.109765
zone2:mindist                          0.0608414  0.0342409   1.777
0.075591 .
zone3:mindist                          0.0641069  0.0247138   2.594
0.009487 **
zone4:mindist                          0.0248087  0.0334446   0.742
0.458217
phenotypeyellow-fronted:zone2:mindist -0.0616859  0.0363812  -1.696
0.089973 .
phenotypeyellow-fronted:zone3:mindist -0.0646249  0.0276774  -2.335
0.019547 *
phenotypeyellow-fronted:zone4:mindist -0.0292554  0.0442657  -0.661
0.508673
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


What we want to understand is how to to interpret a three way interaction
model. Which factors are meaningful? If we have a three way interaction
phenotype x zone x mindist, are the P values given correct or do we
estimate them by extrapolation from the main effects and two way
interaction estimates? Are the main effects and two-way interaction effects
telling us anything meaningful, e.g. phenotype x zone or phenotype x
mindist?

Also, when we run 4 models for each zone we get some significant effects
that we can't see in the model with the 4 zones together (e.g. there is a
strong interaction effect between distance and phenotype in one of the
zone, estimate = -0.114, st.err = .03,  p=.0001). Is there a way to
extrapolate such effects from the full model?

Looking forward to hear from you.

All the best,

Matteo

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