Simulate mixed predictive replicate datasets: new random-effect levels for a requested block, retaining fitted hyperparameters

For each requested block \(r\) in blocks_to_replicate, retains the posterior draws of \(\tau_r^{(s)}\) and the block's own fitted cross-class correlation \(R_{block[r]}^{(s)}\) (a generated quantity already stored in fitted_model$draws), but draws n_new_levels_per_block ENTIRELY NEW synthetic level effects $$u_{r,\text{new}}^{(s)} \sim MVN(0, \Sigma_r^{(s)})$$ per posterior state, where \(\Sigma_r^{(s)} = \mathrm{diag}(\tau_r^{(s)})\, R_{block[r]}^{(s)}\,\mathrm{diag}(\tau_r^{(s)})\). Every real fitted event is deterministically (seeded) reassigned to one of the n_new_levels_per_block new synthetic levels for each replicated block, so a complete replicate outcome matrix can be generated exactly as in simulate_probit_posterior_predictive. Blocks NOT in blocks_to_replicate use their FITTED posterior random effects (unreplicated_block_behavior = "retain_fitted", default) or cause an error ("error") if any declared block is left unhandled.

Usage

simulate_probit_mixed_predictive(
  fitted_model,
  blocks_to_replicate,
  n_states = 500L,
  seed = 123L,
  n_new_levels_per_block = 1L,
  unreplicated_block_behavior = c("retain_fitted", "error")
)

Arguments

fitted_model

A fitted model object as returned by fit_bayesian_multivariate_probit.

blocks_to_replicate

Character vector; a subset of fitted_model$random_effects_prep$block_names to draw NEW levels for.

n_states

Integer; number of posterior states to use. Default 500.

seed

Integer seed (deterministic).

n_new_levels_per_block

Integer; how many new synthetic levels to draw per replicated block. Default 1.

unreplicated_block_behavior

"retain_fitted" (default) uses fitted posterior random effects for every declared block not in blocks_to_replicate; "error" requires every declared block to be listed in blocks_to_replicate.

Value

An object of class c("amr_mixed_predictive_draws", "amr_ppc_draws") with setup, generate_state, and the other fields shared with simulate_probit_posterior_predictive's return value, plus blocks_to_replicate, unreplicated_blocks, n_new_levels_per_block, unreplicated_block_behavior.

Details

This is NOT standard posterior predictive checking (which conditions on the observed groups' own fitted random effects) – do not conflate the two. blocks_to_replicate is currently exercised for a single block at a time in this package's own tests (the hospital-level use case explicitly scoped by Part 13 of the predictive-checking specification); multi-block replication is implemented generically but not yet covered by synthetic recovery tests.

References

Stan Development Team. "Posterior and Prior Predictive Checks." Stan User's Guide. https://mc-stan.org/docs/stan-users-guide/posterior-predictive-checks.html