underdispersion in nbinominal GLMM

[NimoLululu]

Hi @florianhartig,

First of all, thank you for bringing DHARMa to our work – it's been incredibly helpful!

I have encountered dispersion issues while fitting a GLMM using glmmTMB. Initially, I aimed to explore the relationship between prevalence (defined as infectedbird / totalbird) and explanatory variables. I started with the following code:

modelone <-gimmtmB(cbind(infectedbird, totalbird - infectedbird) ~ latitude + longitude + season*route + (1 | ID)+(1 | birdsp),family= binomial(link ="logit")),

However, an overdispersion issue was detected. To address this, I adjusted the model to a negative binomial GLMM:

modeltwo<- glmmTMB(infectedbird ~ latitude + longitude + season * route + (1 | birdsp) + (1 | ID)+offset(log(totalbird)),family = nbinom2(link = "log")).

After running the dispersion test, I found an underdispersion issue instead:

testDispersion(modeltwo)
DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated
data: simulationOutput
dispersion = 0.23962, p-value = 0.44

I would appreciate any insights into addressing the underdispersion.

TIA,
Nimo