I am currently in the process of trying to complete a poisson GLMM analysis with two fixed (with an interaction) and two random effects using the glmer() function of the lme4 package. Using the testDispersion() function of the package DHARMa I found my data to be significantly over-dispersed (ratio = 1.877, p-value = <2.2e-16) so as a result attempted to use the glmer.nb() function in order to account for this over-dispersion by using the negative binomial distribution. My problem is that the model using this function still produced a significant dispersion test (ratio = 0.8817, p-value = 0.024). Should I still use this method to account for over-dispersion or is there a better way to account for it? The code for each of my models took the following forms:
Poisson: model1<-glmer(y~x1*x2 + (1|R1) + (1|R2), family = "poisson", data = dataset)
Negative binomial: model2<-glmer.nb(y~x1*x2 + (1|R1) + (1|R2), data = dataset)
DHARMa::simulateResiduals
and plot the residuals to get a better idea of how severe the problem is instead of focusing on ratio tests. A $p$-value of 0.024 is "non-issue" if the model adheres well to our modelling assumptions/research question. $\endgroup$ – usεr11852 Aug 9 '20 at 13:25