I'm running a generalised linear mixed model with beta family on the effect of overhead cover (proportion ∈ (0,1)) on the proportion of birds scavenging from carrion left out in nature (proportion ∈ (0,1)), with Area as random factor (factor w/ 6 levels).
> myglmm <- glmmTMB(ProportionBirdsScavenging ~ OverheadCover + (1|Area), data = df_prop_birds_eating, beta_family(link = "logit"), weights = pointWeight_scaled) > summary(myglmm) Family: beta ( logit ) Formula: ProportionBirdsScavenging ~ OverheadCover + (1 | Area) Data: df_prop_birds_eating Weights: pointWeight_scaled AIC BIC logLik deviance df.resid -5.3 0.8 6.7 -13.3 30 Random effects: Conditional model: Groups Name Variance Std.Dev. Area (Intercept) 1.198e-10 1.094e-05 Number of obs: 34, groups: Area, 6 Overdispersion parameter for beta family (): 5.17 Conditional model: Estimate Std. Error z value Pr(>|z|) (Intercept) 1.7869 0.7196 2.483 0.013017 * OverheadCover -4.7387 1.2661 -3.743 0.000182 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The overdispersion parameter is 5.17. I have tried to find some information about this parameter for beta models, but I could not find much. Most of what I found was about the poisson or binomial distribution, and tests about significance e.g.
AER::dispersiontest only test for Poisson GLMs. My question is whether this overdispersion parameter value of 5.17 is too high? Does this mean that the model assumptions are not met and the output can not be trusted? If so, is there a way of fixing this, so that my model yields reliable results?
About overdispersion in Poisson models I frequently read that adding a dispersion parameter would 'fix' the overdispersion, but in the beta model I am using there already is a dispersion parameter. Can somebody elaborate on this?