I am using a Poisson GLMM with glmer() from lme4 package in R. My data is ecological count data, and the model has one random effect (site id, because I have repeated measures) and up to twelve fixed effects (model selection will be used to determine the best combination of fixed effects).
Analysis overview: I am analysing the count of observations per day of certain mammal species at 12 different sites. My dataset consists of ~120 days of observations at each of the different sites. For each site, I have a total of 12 potential fixed effects (explanatory variables) which are essentially the structural and environmental characteristics of the sites monitored. The aim is to understand which of these characteristics affect use of a site by mammals. Only the relative magnitude of the fixed effects are important, and whether they drive more or less usage of a site.
Example code for the global model (all twelve fixed effects):
library(lme4)
m1 <- glmer(use ~ . + (1|SiteID), data = mydata, family = poisson(link = "log"))
The check_overdispersion() function from performance package indicates my data is definitely over-dispersed with p<0.001, but the dispersion ratio (which should be equal to 1) is 1.246 - so fairly minor over-dispersion compared to other examples I've seen.
library(performance)
check_overdispersion(m1)
# Overdispersion test
dispersion ratio = 1.246
Pearson's Chi-Squared = 1692.832
p-value = < 0.001
Overdispersion detected.
Similarly, overdisp_fun() produced these results:
chisq ratio rdf p
1.692832e+03 1.245645e+00 1.359000e+03 1.293849e-09
I am familiar with the options for dealing with over-dispersion (quasi-poisson, observation-level random effect, negative binomial appear to be the main options). However, I don't want to over-complicate the model unnecessarily, so I am interested as to whether such minor levels of over-dispersion are deemed "acceptable" to proceed with standard poisson glmm and would not affect model output? Or is the fact alone that over-dispersion exists enough to warrant addressing it?
From what I have read online, there is little consensus on a maximum dispersion ratio although I did see a ratio of 1.4 mentioned somewhere.
