Thank you! This is very helpful. I have two more clarification questions to make sure I understand how the lognormal distribution works. Lets say I have the following formula where X_1 is a continuous predictor and specify a lognormal data distribution:
RT = Beta_0 + Beta_1*X_1 + error
In this case, if Beta_1 = 0.1 according to the MAP estimate, we can interpret that with 1 unit increase in X_1, there is a a 0.1 increase in log(RT) or a 1.1 ms increase in RTs right? Also if my (weak) prior beliefs were that X_1 leads to a an increase between 0.5 ms and 10 ms, I would specify a prior like norm(1.4, 0.4) right?
Another alternative would have been to have the following formula instead and specify a lognormal data distribution.
log(RT) = Beta_0 + Beta_1*X_1 + error
In this case, if Beta_1 = 0.1, we would have a similar interpretation as earlier. However, the model assumptions are different, because in this case we are assuming that the predictors are multiplicative on the raw scale right? So is the only difference between using a lognormal distribution and modeling log(RTs) whether or not the predictors and the error term are additive/ multiplicative? Or are there other factors I need to keep in mind? (I have always modeled log(RTs) in LMER models and this is the first time I am shifting to Bayesian models with other data distributions, so I just want to be doubly sure)