# Confused about over dispersion for my beta distribution

I have percentage data so I am using a beta distribution and I want to do a mixed-effect model so I am still trying to decide between glmmTMD or the brm packages. I saw somewhere that some distribution types are affected by overdispersion more like Poisson however they said Beta isn't that much of a concern (is that true?). For the glmmTMB, I have two models one is looking at just random intercept model and the other is looking at the random slope intercept

glmmTMB(Redecimal ~ Region+food+genus +Region:food + Region:genus + genus:food + (1|sample), family = beta_family(link = "logit"), data = REdata)

glmmTMB(Redecimal ~ Region+food+genus +Region:food + Region:genus + genus:food + (1+food|sample), family = beta_family(link = "logit"), data = REdata_with_Pro_NA)


When I run the summary for these models I get very different overdispersion parameters. For the random intercept model I get a score of 26.9

Family: beta  ( logit )
Formula:
Redecimal ~ Region + food + genus + Region:food + Region:genus +
genus:food + (1 | sample)
Data: REdata_with_Pro_NA

AIC      BIC   logLik deviance df.resid
-670.3   -608.3    353.2   -706.3      214

Random effects:

Conditional model:
Groups Name        Variance Std.Dev.
sample (Intercept) 0.05991  0.2448
Number of obs: 232, groups:  sample, 48

Overdispersion parameter for beta family (): 26.9


and for the random slope model I get a crazy high number (also warnings about convergence but that's another problem since I am missing data for one group

Family: beta  ( logit )
Formula:
Redecimal ~ Region + food + genus + Region:food + Region:genus +
genus:food + (1 + food | sample)
Data: REdata_with_Pro_NA

AIC      BIC   logLik deviance df.resid
NA       NA       NA       NA      200

Random effects:

Conditional model:
Groups Name        Variance Std.Dev. Corr
sample (Intercept) 0.3329   0.5770
foodHNA     0.7688   0.8768   -0.63
foodLNA     1.0893   1.0437   -0.59  0.82
foodPro     0.3381   0.5815   -0.67  0.61  0.51
foodSyn     0.6385   0.7990   -0.68  0.55  0.45  0.79
Number of obs: 232, groups:  sample, 48

Overdispersion parameter for beta family (): 1.42e+08


then I was using the DHARMa package

res <-simulateResiduals(glmmtbm, plot = T)
testDispersion(res)


for the intercept model score 26.9 I got these plots

DHARMa nonparametric dispersion test via sd of residuals fitted
vs. simulated

data:  simulationOutput
ratioObsSim = 1.1623, p-value = 0.008
alternative hypothesis: two.sided


and then for the slope model which had an overdispersion value of 1.42^8 I got

DHARMa nonparametric dispersion test via sd of residuals fitted
vs. simulated

data:  simulationOutput
ratioObsSim = 0.99052, p-value = 0.92
alternative hypothesis: two.sided


I am confused at why the intercept model that had a much lower value for the overdispersion parameter was significant using the DHARMa package and the slope model was not. My main question is should I worry about the value for beta distribution and if so what should I do. This is my first time trying to do any generalized mixed-effects modeling. And also for the brm package how would I go about testing it for overdispersion since the summary doesn't give a parameter value like glmmtmb