Posterior predictive tail / ceiling effects in logit

I’ve analyzed binomial data (hit/miss) from an experiment and looked at the distribution of the data vs. posterior predictive samples. As you can see below, the right tail of the original data has higher values than the posterior predictive samples. I have ceiling effects from some participants. Should I be worried about it?


I looked around and found that a Tobit model might be a better way to go about this. Would you recommend it? How can I easily implement such a transform?

I think a censor model would better handle cases like this.

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Thanks I modeled it with a potential function like the parametrizations outlined here

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