Differing posterior predictive checks for logistic binomial model with and without addition-terms

Question

I’m fitting a logistic binomial model where the response variable is the sum of how many times a target picture was looked at during a certain time period out of how many times all pictures were looked at during that period (sum | trials(N) ~ x). This kind of response variable falls under “addition-terms” according to the brms documentation. The model estimates are plausible and the fit is good, but the posterior predictive check isn’t as good as if I fit a regular logistic binomial model to the same data but unaggregated (y ~ x). Below is a dummy example of both models.

My questions are:

• The posterior predictive check of the addition-terms model isn’t actually bad, but is it expected that it would not be as clean as the regular model? And if so, why?
• Out of curiosity, is there any way to do a predictive check with the addition-terms model on the binomial scale rather than predicting "sum"?

# fake data

## long format
(dat_long <- data.frame(
  subj = rep(1:10, each = 100),
  item = rep(1:10, each = 10),
  bin  = rep(1:10, times = 10),
  cond = c(-.5,.5),
  pTarget = rbinom(1000, 1, .6)
))

## aggregated over bins/items
(dat_aggregated <- dat_long %>%
  dplyr::group_by(subj, cond) %>%
  dplyr::summarise(sum = sum(pTarget), N = length(pTarget)))


# model using addition-terms
m_aggregated <- brm(formula = sum | trials(N) ~ cond,
                     family = binomial(),
                     iter = 5000,
                     prior = priors,
                     data =  dat_aggregated)

# regular model
m_long <- brm(formula = pTarget ~ cond,
                   iter = 1000,
                   family = binomial(),
                   prior = priors,
                   data =  dat_long)


# posterior predictive checks
pp_check(m_aggregated)
pp_check(m_long)

The pp_check plots:

pp_check of addition-terms model

pp_check of regular mode