Numerical integration error against the number of integration points

Ported from multinma::plot_integration_error() (Phillippo et al. 2020). Aggregate arms are fitted by integrating the individual-level model over the study's covariate distribution with Sobol' quasi-Monte-Carlo points. The integration error at N points is the estimate using the first N points minus the estimate using all of them; the typical convergence rate of QMC integration, 1/N, is drawn for reference. If the error has not settled well inside the 1/N envelope by n_int, refit with more integration points.

Usage

plot_integration_error(
  x,
  ...,
  int_thin = NULL,
  ndraws = 200L,
  show_expected_rate = TRUE
)

Arguments

x: A cmlnmr() fit.
...: Unused.
int_thin: Report the error every int_thin points. Default is n_int / 8, rounded up.
ndraws: Number of posterior draws to summarize over. Default 200.
show_expected_rate: Draw the 1/N convergence envelope? Default TRUE.

Value

A ggplot object.

Details

cpaic does not save cumulative integration points inside Stan, so the integrated aggregate-arm quantity is reconstructed here from the posterior draws and the (deterministic) Sobol' point set. This is exact, not an approximation, but it is not free: subsample the posterior with ndraws on a large fit.

Not available for family = "survival", where the aggregate contribution is a log_sum_exp over integration points of the likelihood rather than an integrated mean outcome; multinma declines this plot for survival models too. Nor for a Gaussian model fitted with all-normal margins, which is exact at the covariate means and uses a single integration point.

Examples