Thanks for being helpful, the overall idea is sensible, but the execution is unfortunately incorrect - to have leave-one-participant-out cross validation, you sum the individual log-likelihoods directly. This actually could lead to a more compact code, as you can then have (ignoring generating predictions):
generated quantities {
real log_lik[N];
for(n in 1:N) {
log_lik[n] = binomial_lpmf(y[n,] | trials[n, ], performance[n, ]);
}
}
Some more discussion at:
I think (not 100% sure) that elpd_loo
can be a somewhat meaningful quantity (it is the “expected log predictive density”), but generally I find interpretation without another model to compare to challenging. PPC’s are in my experience much more useful to asses fit of a single model.
Hope that helps!