Prior predictive distribution as in posterior_predict/epred

Interfaces rstanarm
4

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 McElreath’s book:

and here where @jonah explains it very nicely:

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