Weakly informative priors for Shifted LogNormal

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!

Grusha.

Hi Grusha!

We’Re trying not to make threads overly long, so I moved your post to a new one. Also this usually helps to get more eyes on your problem. As I said in the other thread I am not at all an expert on the Shifted LogNormal. Also I find it hard to give substantial meaning to its parameters.

My suggestion would be to do prior predictive checks and play around with the parameters a bit. I your second paragraph you laid out the reasoning perfectly and I’d suggest you just try these values and see what prior predictive distributions they produce. Check out the sample_prior='only' option in brms.

I hope this helps. Maybe someone else can chime in and share their thoughts.

Cheers!
Max

2 Likes

Hi Max,

Thank you for moving this into a new post!

I plotted the prior predictive distributions (using the sample_prior) for these priors and I think they look mostly reasonable. I wanted to understand the intuitions behind the shifted lognormal distribution a bit more for the future, both because I was curious but also because fitting each prior predictive distribution takes > 6 hours. I will see if anyone else has insights about interpreting the parameters of the Shifted LogNormal, but until then just keep examining the prior predictive distribution of different priors.

Thanks again!

Grusha.