# Interpreting dispersion parameters of poisson GLMM with count data

I am working with count data and trying to understand if my model fit is acceptable for this poisson Generalized Linear Mixed Model:

Richness.glmer<-glmer(Richness ~ Unit.type + plot.type + (1|NFI.Point), family = poisson, data = PartA.data.Birds )

I ran a dispersion test using overdisp_fun and got the following result:

chisq = 55.90, ratio = 0.65, p = 0.995, logp = -0.00489

With a ratio of 0.65, does this mean my model is acceptable? Or is it underdispersed? I also made the following residual plot of my data, which appears to be okay, but I am not sure if the combination of this residual plot that the 0.65 dispersion ratio indicates a good model fit or not

I understand what I would do if I was running a Generalized Linear Model that had overdispersion issues (which seems to be the most common problem). But in my case with my GLMM I am uncertain of:

1). If my model fit is acceptable, and, if not 2). What to do about it.

Note also that your random intercept has very low variance, so you might try comparing the model with a regular glm() and also using Conway-Maxwell-Poisson regression, available in the compoisson package for R, which specifically handles under-dispersed count data.