Fit an EXNEX model with Stan

Usage

fit_exnex(
  n,
  r,
  p_exch,
  mu_prior_mean = -1.73,
  mu_prior_sd = 2.616,
  tau_prior_mean = 0,
  tau_prior_sd = 1,
  nex_prior_mean = -1.73,
  nex_prior_sd = 2.801,
  seed = 123456789,
  chains = 4,
  parallel_chains = 4,
  iter_warmup = 3000,
  iter_sampling = 5000,
  adapt_delta = 0.9,
  ...
)

Arguments

n: An integer vector with the number of observations per strata
r: An integer vector with the number of "successes" per strata
p_exch: A numeric vector specifying the prior probability of exchangeability for each strata
mu_prior_mean: Mean for the normal prior set on mu.
mu_prior_sd: Standard deviation for the normal prior set on mu.
tau_prior_mean: Mean for the normal prior set on tau. Tau has a lower bound of zero so any probability mass below zero will be reallocated. Setting tau_prior_mu = 0 and tau_prior_sd = 1 is equivalent to a standard half-normal distribution.
tau_prior_sd: Standard deviation for the normal prior set on tau. Tau has a lower bound of zero, so setting tau_prior_mu = 0 and tau_prior_sd = 1 is equivalent to a standard half-normal distribution.
nex_prior_mean: Mean for the normal prior set on the non-exchangeable distributions.
nex_prior_sd: Standard deviation for the normal prior set on the non-exchangeable distributions.
seed: Set seed for the random number generated
chains: Number of MCMC chains to run
parallel_chains: Number of cores to use for running chains in parallel
iter_warmup: Number of warmup iterations
iter_sampling: Number of sampling iterations
adapt_delta: Tuning parameter for MCMC sampling
...: Other parameters to be passed into the sample function of cmdstanr

Value

A fitted cmdstanr model

MCMC convergence issues

When p_exch is set close to 1, there can be convergence issues due to the funnel-like geometry that arises when \(\tau\) is close to zero. See the fit_exch() function, which can fix convergence issue using a non-centered parameterization of the model for the special case of p_exch = 1.

Examples

if (FALSE) {
# Example data from Table 1 of Neuenschwander et al.
fit_exnex(r = c(2, 0, 1, 6, 7, 3, 5, 1, 0, 3) |> as.integer(),
          n = c(15, 13, 12, 28, 29, 29, 26, 5, 2, 20) |> as.integer(),
          p_exch = rep(0.5, 10),
          adapt_delta = 0.99)
}