Posterior predictive replicates

Draw replicated responses from the posterior predictive distribution: the linear predictor is rebuilt per posterior draw (fixed effects, formula random effects, offset, and a posterior-mean SPDE field when present) and pushed through the family's sampling distribution.

Fits carrying posterior draws use them directly (fixed and random effects jointly per draw). The Laplace tier samples the fixed effects from the Gaussian approximation N(coef(fit), vcov(fit)) and holds the random effects at their posterior mode, so its replicates understate the RE posterior uncertainty. At newdata the prediction is population level (random effects at zero), matching predict.tulpa_fit().

Usage

posterior_predict(object, ...)

# S3 method for class 'tulpa_fit'
posterior_predict(
  object,
  newdata = NULL,
  ndraws = NULL,
  n_trials = NULL,
  seed = NULL,
  ...
)

Arguments

object

A tulpa_fit object from tulpa().

...

Passed to methods.

newdata

Optional data frame of covariates to predict at. Population level (fixed effects only); NULL (default) replicates at the training data with random effects and offset included.

ndraws

Number of posterior draws to use. Defaults to all stored draws, or 400 on the draw-free Laplace tier.

n_trials

Binomial / beta-binomial trial counts for the replicates. Defaults to the training trials when newdata is NULL, else 1.

seed

Optional integer seed (RNG state is restored on exit).

Value

A ndraws x n_obs numeric matrix of replicated responses.

See also

pp_check(), which uses these replicates; simulate.tulpa_fit().

Examples

# \donttest{
set.seed(1)
d <- data.frame(y = rpois(100, 4), x = rnorm(100))
fit <- tulpa(y ~ x, data = d, family = "poisson", mode = "laplace")
yrep <- posterior_predict(fit, ndraws = 100)
dim(yrep)  # 100 x 100
# }