This is an intellectual musing; not one I am currently in need of.

I finally went through @matti’s excellent tutorial on zero-one-inflated Beta models for VAS scales: https://vuorre.netlify.com/post/2019/02/18/analyze-analog-scale-ratings-with-zero-one-inflated-beta-models/

It left me wondering if the rate of extreme ratings (0s and 1s) could be though of as a “catch all more extreme than this threshold” just like the extreme categories in ordinal regression? I find it likely that participants map the VAS response option to a narrow region on the Beta distribution, e.g., [0.2, 0.7], and everything more extreme than that “rounded in” to the nearest response option (here [0, 0.2[ becomes 0).

That way, maybe the model could be parametarized as the Beta parameters + thresholds. I.e.:

- precision,
- mean [0, 1],
- lower threshold [0, upper]
- upper threshold [lower, 1].

Since the Beta parameters are generative of ALL data in this model, these parameters should be estimated with greater precision, and perhaps even greater validity. As I understand it, the ZOIB “discards” 0s and 1s as a different process, but I think that a whole bunch of 1s should actually be taken as evidence that the beta-mean is higher.

So I’m wondering (1) if this is even possible to model, and (2) is there already a way to model it? If so, this would def be worth a tutorial, and perhaps a paper! It could be generalized to much more than beta.