Thank you both for this useful thread! I am also trying to specify weakly informative priors for a lognormal distribution (modeling reading times). Unlike Anthony, I am not interested in testing the effect of condition on the ndt parameter. I only want to treat it as a by-participant random intercepts for of sorts as mentioned in this post. Max, I just want to clarify that I understood your comment here and shifted lognormal distributions in general correctly. Let us say that I thought the RT distribution had its mean around 400 ms and most of the probability mass was assigned to values lower than 2000 ms (as is assumed here). Lets us also say I thought that the shift parameter for most participants was ~150 ms and was unlikely to be greater than 500 ms. I am trying to figure out what priors I should be specifying for the intercept of the model and the ndt intercept.
I know with a lognormal distribution where shift = 0, I would want to specify a prior for the intercept like Normal(6, 0.5). As a first guess, since I expect the shift to be around 150 ms, I was thinking the prior for the ndt parameter should be Normal(1.6, 0.2) because exp(exp(1.6)) = 141.6. Is this correct? And if I am specifying the ndt parameter as 1.6, then would I just be subtracting this amount from my estimate for the intercept? So instead of Normal(6,0.5), would I have Normal(4.4, 0.5)? Or am I misunderstanding this?
In case it is helpful, here is my model:
bf(rt ~ sentence_type*group + (1 + sentence_type | ID | participant) + (1 + sentence_type*group | item), ndt ~ (1 | ID | participant)), family = shifted_lognormal()
Thanks in advance!