Fit an exchangeable hierarchical model using a non-centered parameterization

When fitting an EXNEX model with p_exch close to 1, there can be convergence issues due to the funnel-like geometry that arises when \(\tau\) is close to zero. For the special case of p_exch = 1, this function fits the model using a non-centered parameterization, which can fix the convergence issues. See the Stan user guide for more information.

Usage

fit_exch(
  n,
  r,
  mu_prior_mean = -1.73,
  mu_prior_sd = 2.616,
  tau_prior_mean = 0,
  tau_prior_sd = 1,
  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

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.

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

See also

fit_exnex()

Examples

if (FALSE) {
# Example data from Table 1 of Neuenschwander et al.
fit_exch(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(),
         adapt_delta = 0.99)
}