Hello,
Is there a way to have a prior predictive distribution with the same output structure as posterior_predict/epred. I was only able to extract the parameters prior, not the output one.
Thanks
Hello,
Is there a way to have a prior predictive distribution with the same output structure as posterior_predict/epred. I was only able to extract the parameters prior, not the output one.
Thanks
Hi,
donâ€™t know if this will help you but in brms
one can always sample with sample_prior="only"
, and thus get a â€śposteriorâ€ť which consists of values sampled only from the priors.
Iâ€™m a bit unsure what you mean by â€śnot the output one.â€ť
Sorry, it was unclear, I meant the prior distribution of the outcome of the model, that is solving the model using the prior values for the parameters, which is what posterior_predict/epred does.
I might misunderstand you but,
run with brms
(notice I only sample from the priors using sample_prior="only"
)
library(rethinking)
data(chimpanzees)
d <- chimpanzees
detach(package:rethinking, unload = T)
library(brms)
rm(chimpanzees)
m <-
brm(data = d, family = binomial,
pulled_left | trials(1) ~ 1 + prosoc_left,
prior = c(prior(normal(0, 10), class = Intercept),
prior(normal(0, 10), class = b)),
sample_prior = "only")
pl <- posterior_linpred(m)
pe <- posterior_epred(m)
pp <- posterior_predict(m)
Each variable now contains 504 rows and 4000 cols. So the model looks like this:
\mathrm{pulled\_left}_i \sim \mathrm{Binomial}(1,p_i)\\ p_i = \mathrm{inv\_logit}(q_i)\\ q_i = \alpha + \beta_p \cdot \mathrm{prosoc\_left}_i \\ \alpha \sim \mathrm{Normal}(0, 10)\\ \beta_p \sim \mathrm{Normal}(0, 10)
then,
pl
has posterior draws of q
pe
has draws of p, i.e., applying the link function, in this case inv_logit()
pp
has draws from \mathrm{Binomial}(1,p), i.e., the data is on the outcome scale (0/1). (Binomial has no dispersion).> table(pp)
pp
0 1
1006469 1009531
See here for the example I use translated by @Solomon from McElreathâ€™s book:
and here where @jonah explains it very nicely:
Thanks! I actually solved too using brms since rstanarm seemingly doesnâ€™t allow this!