I am trying to model tooth loss among human populations before modern surgery (i. e. extraction at the dentist :-) ). I have a empirical data-set with individuals and tooth-loss as binary variable per tooth-possition (i.e. canine, molars etc.). The most important predicting variable is the age of the respective individual.
In the first run of models, and disregarding the information on tooth-position, the data-set is reduced to the number of lost teeth vs. the number of still observable tooth positions (which vary) per individual.
A simple logistic regression (model 1) with binomial probability distribution reveals strong overdispersion:
fit <- glm(formula = cbind(lost_teeth, tooth_positions - lost_teeth) ~ age, family = binomial, data = data_tooth_loss)
AIC(fit)
2123.05
DHARMa::simulateResiduals(fittedModel = fit, plot = T)
If the individuals are added (model 2), the AIC improves substantially but now the plot shows strong underdispersion. Strangely, the dispersion test is not significant.
fit <- glm(formula = cbind(lost_teeth, tooth_positions - lost_teeth) ~ age + individual_no, family = binomial, data = data_tooth_loss)
AIC(fit)
920.4828
simulationOutput <- DHARMa::simulateResiduals(fittedModel = fit, plot = T)
DHARMa::testDispersion(simulationOutput)
DHARMa nonparametric dispersion test via sd of residuals fitted vs. simulated
data: simulationOutput
dispersion = 0.95687, p-value = 0.064
alternative hypothesis: two.sided
A betabinominal model (model 3) takes care of the overdispersion. I use the function betabin of the package aod for that. Despite the fact that DHARMa provides no built-in support for aod, thanks to the vignette, I was able to add a custom function for creating a DHARMa object. There is no overdispersion anymore and the plot of the residual looks fine in my view.
I now face the problem that model 2 has the lowest AIC but that model 3 appears far more elegant and does not suffer from underdispersion. In the vignette and, for example, here you state that underdispersion is less of an issue than overdispersion so I am not sure on what ground I can reject model 2in favour of model 3. Model 2seems clearly overfitted from looking at the figures but is there a measure to read this result from, especially as the dispersion test is not significant?
First of all: Many thanks for the great package!
I am trying to model tooth loss among human populations before modern surgery (i. e. extraction at the dentist :-) ). I have a empirical data-set with individuals and tooth-loss as binary variable per tooth-possition (i.e. canine, molars etc.). The most important predicting variable is the age of the respective individual.
In the first run of models, and disregarding the information on tooth-position, the data-set is reduced to the number of lost teeth vs. the number of still observable tooth positions (which vary) per individual. A simple logistic regression (
model 1) with binomial probability distribution reveals strong overdispersion:If the individuals are added (
model 2), the AIC improves substantially but now the plot shows strong underdispersion. Strangely, the dispersion test is not significant.A betabinominal model (
model 3) takes care of the overdispersion. I use the functionbetabinof the packageaodfor that. Despite the fact thatDHARMaprovides no built-in support foraod, thanks to the vignette, I was able to add a custom function for creating aDHARMaobject. There is no overdispersion anymore and the plot of the residual looks fine in my view.I now face the problem that
model 2has the lowest AIC but thatmodel 3appears far more elegant and does not suffer from underdispersion. In the vignette and, for example, here you state that underdispersion is less of an issue than overdispersion so I am not sure on what ground I can rejectmodel 2in favour ofmodel 3.Model 2seems clearly overfitted from looking at the figures but is there a measure to read this result from, especially as the dispersion test is not significant?Any advice is much appreciated!