Overdispersion in Beta GLMM with glmmTMMB

[pv272]

I specified a mixed model with Beta family and logit link to model the effect of treatment on the proportion of time (between 0 and 1) spent expressing a specific behaviour during an observation
Burrow_FS_1 <- glmmTMB(Burrowing_T ~ Treatment*Weight_C + DailySeen_C + (1|Colony) + (1|AnimalID), data = CS_FS_Burrow , family=beta_family())

I simulate the residuals and run the diagnostic plot

Simul_FS_Burrow <- simulateResiduals(fittedModel = Burrow_FS_1, n = 250) plot(Simul_FS_Burrow,quantreg = TRUE) testResiduals(Simul_FS_Burrow)

the diagnostic plot look as follow

and

I am mostly wondering whether it is an issue of concern that the dispersion test suggest overdipsersion, considering that models specifying a Beta distribution actually estimate the dispersion. If it is an issue, how should it be dealt with

[florianhartig]

Hi pv272,

the diagonal line in the upper right plot can probably be disregarded, see #78 - I hope that I can fix this issue in the next week, with an update of glmmTMB coming up that should close this issue.

I would interpret the underdispersion issue as a deviation from the model expectation though. It also fits together with this slight (albeit n.s.) shift in the distribution (qq plot, see also res ~ pred lower left).

My best guess is that the reason is that the residual distribution simply cannot be perfectly described by a beta. Yes, the beta has in some sense a variable dispersion, but the MLE for the beta will not necessarily have the right dispersion if the distribution doesn't follow a beta.

Practically, you don't have many alternatives to the beta in this case. You could see if switching on variable dispersion or zero-inflation helps (I think that's possible for the beta in glmmTMB, but not sure). You could also check if you see patterns of res ~ predictors - this could be a reason for such a misfit.

If neither of this helps, I wouldn't trouble myself too much over this - a slight deviation shouldn't create too much error, and underdispersion has usually conservative effects on p-values.