Sometimes we know the shape parameter, e.g. when we look at the sampling distribution for the variance (of a normal r.v.) from a study.

My first attempt at doing this didn’t work, but I got this to work with distributional regression using ` bf( precision ~ 1 + (1|study) + offset(log(known_shape)), shape ~ 0 + offset(log(known_shape))`

, where as far as I can tell no actual model is fit for shape and it’s just being treated as a constant (as per the Stan code I inspected). However, it looks like the offset for the shape is being ignored when I use the `predict`

method.

Have I made some obvious mistake or is there an easier way to do this?

```
library(tidyverse)
library(brms)
varests = tibble(vest = c(1, 1.2, 1.1, 0.7),
n = c(50, 48, 100, 10),
study=factor(1:4)) %>%
mutate(precision = 1/vest,
nu = n-1,
tvest = 1/(vest*nu/2))
# Note for estimated variances, we have
# vest * nu /2 ~ Gamma(shape = nu/2, rate = 1/sigma^2)
# So, to model variances across studies, we want to model something like
# expected -log(variance) = 1 + (1|study)
# or (because there's no negative-log-link function):
# expected log(precision) = 1 + (1|study)
# and fix shape = nu/2.
# Try 1: This does not work, apparently a constant prior defined in terms of
# a variable is not possible like this.
brmfit1 = brm(tvest ~ 1 + (1|study),
data = varests,
family=Gamma(link="log"),
prior=prior(normal(0,2),class="Intercept") +
prior(constant(nu/2),class="shape"),
backend="cmdstanr"
)
# Try 2: this samples and by looking at the Stan code via stancode(brmfit2)
# it seems to do what I want.
brmfit2 = brm(bf( precision ~ 1 + (1|study) + offset(log(nu/2)),
shape ~ 0 + offset(log(nu/2)) ),
data = varests,
family=brmsfamily(family="Gamma", link="log", link_shape="log"),
prior=prior(normal(0,2),class="Intercept"),
backend="cmdstanr",
control = list(adapt_delta=0.99))
# However, the predictions I get, here seem wrong:
predict(brmfit2, newdata=tibble(nu=100, study=1L))
# Gets me about 2.2 (as median)
predict(brmfit2, newdata=tibble(nu=10, study=1L))
# Gets me about 0.22 (as median)
# This seems to be off by exactly what you'd expect when the offset in the shape
# parameter is ommitted.
```

- Operating System: Windows 10
- brms Version: 2.16.1