Thanks for the feedback!
You’re correct about the binomial specification of choice with the probability of “success” as inv\_logit(mug\_utils - pen\_utils). I’ve since transitioned the model to an aggregated version of the problem, and re-written the if statements explicitly (which is much cleaner, ultimately).
Regarding the constraints on 1-lambda, lambda is taken as the loss aversion parameter which is assumed non-negative in the literature. I did have an upper bound on the parameter block so that 0\leq \lambda \leq 6, since a \lambda>5 is theoretically implausible, but perhaps this is not the right way to model this constraint. That said, the lognormal distribution set as a prior have almost no mass above 5.
The second question regarding the known treatment effect is a good one, and it helped me clarify what I’m hoping to achieve, so thanks! The way I’m thinking about it is that the model for utility is known (I’m assuming people behave according to this KR model of reference-dependence), and the observed choices follow this structural model (with logit noise) on the basis of 2 latent variables: \lambda and the relative utility of pens. Since the treatment is embedded into the model, I know how it interacts with choice behavior. So I can use experimental variation in treatments to help identify the distribution of these latent variables, the \lambda and “consumption utils”.
Thanks again for helping me understand the set up better. I’ve run into a new problem which I think warrants a separate thread as it has to do with a BFMI -Low warning and sample sizes in binomial models. Will edit a link it once I’ve submitted it in case it’s helpful to anyone.