[R-sig-ME] Interpretation Inverse Gamma glmmTMB with interactions
Matteo Sebastianelli
m@tteo@@b@ @end|ng |rom gm@||@com
Fri Apr 24 16:20:36 CEST 2020
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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