Variance model

[maxbiostat]

Can you show predictions under both models?

[linas]

Green Ash, normal

White Ash, normal

Green Ash, normal+logit

White Ash, normal+logit

[maxbiostat]

Nice. So it seems the normal model predicts things quite well. I share your sentiment that it’d be better to have a model which gave predictions in (0,1) almost surely, but since your hack didn’t quite work, it suggests a more complicated model is needed. One that properly accommodates the endpoints. Now it’s up to you whether you want to invest the extra effort into treating the idiosyncrasies in the data. If the goal is to predict either in sample or over a short horizon, the normal model might be just fine.

[linas]

Actually I would like to invest the extra time. Could you please provide guidance?

[maxbiostat]

Now that’s an attitude I rarely see! Cool!

Now, as discussed here, if your goal was to simply understand what predicts canopy loss, a simpler model would be fine. Since you want actual predictions, you might have to go into dangerous of zero-one-inflated beta regression models.

See this and this discussions here on the forum and try to work out how to incorporate these things into your current model.

One thing I’d try first is @bgoodri’s “hack”:

Zero one inflated beta regression in STAN

There is the cdfquantreg R package that has likelihoods that put positive mass on 0 and / or 1, but it does not use Stan. I started to incorporate it into RStanArm but didn’t finish it. In the meantime you could transform your y with (y * (n - 1) + .5) / n to force it interior, where n is the number of observations.

Maybe also @saudiwin can share some insight into some of the stuff he’s done, but that’d entail discretising your response variable.

[linas]

Observed response variable is discrete anyway in the increments of 10. True canopy is continuous variable.

[linas]

It seems there was a bug. Below are corrected fits. They look very similar. I wonder if there is some Bayesian way to compare fits.
beta, adjust 0/1 data values by 1e-5 so they conform to beta distribution

normal

logit: adjust 0/1 data values to make logit transformation possible

[maxbiostat]

You might want to look into LOO. There’s a helpful FAQ as well.

[martinmodrak]

An aside beyond what others said (which is good) if the outcome is discretized and ordered you may also want to try to model it as ordinal regression (i.e. ordered_logistic_lpmf). This would even accommodate if the response is somewhat non-linear in predictors…