Hi! I am fitting a brms model using the brms lognormal family with reaction times in milliseconds as the outcome.
The documentation states that the links are identity for the mean and log for sigma, but:
When I get the default priors the default for the intercept is student_t(3, 6.6, 2.5) which to me looks like it’s in logs.
When I print the summary, it says Links: mu = identity; sigma = identity.
Can anybody shed light? :)
Do you have any predictors in your model?
The parameters of a Lognormal distribution does not correspond to its central moments (e.g. mean and variance/standard deviation). I recommend the Wikipedia article for further reading.
sjp
August 5, 2024, 10:07pm
4
Yeah, I think it’s because the Stan lpdf parameterizes it on the log scale? 16.1 Lognormal Distribution | Stan Functions Reference
This is also relevant:
opened 08:05AM - 21 Jun 18 UTC
closed 07:58AM - 22 Jun 18 UTC
bug
Hi again, I might have stumbled upon another issue, related to the default prior… s for lognormal models.
As an example, take this very simple model:
```
set.seed(32443)
n1 <- 200
d <- data.frame(y = rlnorm(n1, 7, 2))
make_stancode(y ~ 1,
family = lognormal,
data = d)
```
The prior for mu and sigma seems to be based on the observed data scale? But I believe that Stan's lognormal_lpdf parameterize mu and sigma on the log scale? Hence the default priors are pretty extreme with e.g. location 1171 and scale 1656, for parameters on a log scale.
```
target += student_t_lpdf(temp_Intercept | 3, 1171, 1656);
target += student_t_lpdf(sigma | 3, 0, 1656) ...
```
It seems like this also happens to group-level effects, and for hurdle_lognormal models.
Thank you, that seems to be relevant indeed.
I will open an issue on GitHub because it seems to be a discrepancy in documentation, rather a general question. :)
Thanks all!