Hi Mircea,

the short answer is: You should use the Stan Forum which has an own brms hashtag, which probably will motivate Paul Bürkner to answer directly ;) (https://discourse.mc-stan.org)

Longer answer, .. accuracy is distributed binomial, which also makes the truncation superfluous. "family=binomial()" .

For instance to use a binomial model with % data then the dependent variable of the model can be defined as the number of successes given a total amount of observations/trials:

(success | trials(success + failure) ~ predictors...)

You find vignettes for how to use the model (and to define priors) appropriately on Pauls vignette repository here: https://cran.r-project.org/web/packages/brms/vignettes/

Now the complicated part is ... What priors should one use in a logistic (/binomial) model. There is no simple answer, because of the logit transform of every model term. For example

1/(1+exp(1)) predicts 26.6%

1/(1+exp(1+1)) predicts 12%

compare this to:

1/(1+exp(0)) predicts 50%

1/(1+exp(0+1)) predicts 26.6%

In words, if there is more than one predictor, and the first one contributes to the explained variance like about +1 estimate on average, then "an additional" + 1, by a second predictor "on top" has not the same consequence on the % in the data. This is the first reason why the definition of (theory driven) priors is (almost ?) impossible in complex binomial models.

A second problem is, that usually the model 're-codes' the predictors into some kind of contrasts (e.g. effect coding or dummy coding), these types of recoding (from a logistic model view) may be called "geometric transformation" (although being mathematically equivalent, because this transformation gives the model properties that will lead to nice convergence. Without this, these models would look like Rasch models (or Item Response Theory models; which do not converge that nicely, because intercept and slope are estimated independently but then multiplied...). As a consequence of this coding (or I should say, as a consequence of the nature of logistic models), main effects and interactions of categorical and continuous predictors in the same model (e.g., two groups with repeated observations over time within groups) are not independent (the size of the intercept depends on the size of the slope). I can elaborate on that if necessary, but for now it, the message again is just. No meaningful priors possible.

However, as a rule of thump: I would suggest, wide priors do not make sense in any case, because the larger the effect the less identifiably it is (because its variance should become larger as well, on the log scale).

Difficult topic in any case :), so I would always circumvent calculating Bayes factors here, but use the model as measurement model (checking whether the 95% posteriors include zero).

Best, René

This may or may not be helpful!

Most people use MCMC in a non-Bayesian way and use default (non informative) priors as even this brings useful improvement in the resultant estimates (the posterior).

In the MCMC chapter in the following I discuss and illustrate fairly gently and from a practical perspective , the role of the priors, the use of defaults, and then how a sensitivity analysis can be done by tightening one of the priors round a theorized estimate.

Book Developing multilevel models for analysing contextuality, he...

Hope this does help.

René Schlegelmilch thanks for the (detailed) answer! I was planning on asking on that forum, but wanted to see if on RG, which is more research/theory-driven, some peers would have more specific "i already had this issue, here was the solution i found" approach.

From my reading of things, and the useful comment by Kelvyn Jones (thank you!), it seems that the sensible approach is to let brms "sort itself out" and then use PPC or other methods to see if the priors and posteriors make sense given my vague expectations (e.g., most answers should pool around 50%, and effects should be less than d = .5).

My question was motivated by the post of Vehtari on the value of using at least weakly informative priors (especially with smaller samples). https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations

And if my goal is to switch over to using R and bayesian for all my future research, to have a better understanding of what I am doing beyond simply writing in a paper "i used the default settings, as I don't know any better".