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Mar 15 at 15:18 comment added Galen @SextusEmpiricus Yes, all good concerns to have (+1). In Bayesian workflow it is common to fit models in an experimental fashion as a way of learning what is important; essentially a form of sensitivity analysis. I think it would be a good idea to try out a variety of distinct priors to see how sensitive the resulting posterior is to the choice of priors.
Mar 15 at 7:36 comment added Sextus Empiricus I agree that this should be treated as a mixed effects model and the random effect is the year of the participants. Unfortunately this random effect is nested within the fixed effect and this is a situation like $n=1$. A Bayesian approach might work especially if there is data from literature about what sort of variation to expect. But the information from the experiment/data is very low and one may risk over-interpretation of the results by subjectively selecting priors after having seen the results.
Mar 13 at 19:49 history edited Galen CC BY-SA 4.0
added 22 characters in body
Mar 13 at 19:14 history answered Galen CC BY-SA 4.0