hdbayes (version 0.2.0)

glm.logml.map: Log marginal likelihood of a GLM under meta-analytic predictive (MAP) prior

Description

Uses Markov chain Monte Carlo (MCMC) and bridge sampling to estimate the logarithm of the marginal likelihood of a GLM under the meta-analytic predictive (MAP) prior. The MAP prior is equivalent to the prior induced by the Bayesian hierarchical model (BHM).

The arguments related to MCMC sampling are utilized to draw samples from the MAP prior. These samples are then used to compute the logarithm of the normalizing constant of the BHM using only historical data sets.

Usage

glm.logml.map(
  post.samples,
  bridge.args = NULL,
  iter_warmup = 1000,
  iter_sampling = 1000,
  chains = 4,
  ...
)

Value

The function returns a list with the following objects

model

"glm_bhm"

logml

the estimated logarithm of the marginal likelihood of the meta-analytic predictive (MAP) prior

bs

an object of class bridge or bridge_list containing the output from using bridgesampling::bridge_sampler() to compute the logarithm of the normalizing constant of the Bayesian hierarchical model (BHM) using all data sets

bs.hist

an object of class bridge or bridge_list containing the output from using bridgesampling::bridge_sampler() to compute the logarithm of the normalizing constant of the BHM using historical data sets

min_ess_bulk

the minimum estimated bulk effective sample size of the MCMC sampling

max_Rhat

the maximum Rhat

Arguments

post.samples

output from glm.bhm() giving posterior samples of a GLM under the Bayesian hierarchical model (BHM), with an attribute called 'data' which includes the list of variables specified in the data block of the Stan program.

bridge.args

a list giving arguments (other than samples, log_posterior, data, lb, and ub) to pass onto bridgesampling::bridge_sampler().

iter_warmup

number of warmup iterations to run per chain. Defaults to 1000. See the argument iter_warmup in sample() method in cmdstanr package.

iter_sampling

number of post-warmup iterations to run per chain. Defaults to 1000. See the argument iter_sampling in sample() method in cmdstanr package.

chains

number of Markov chains to run. Defaults to 4. See the argument chains in sample() method in cmdstanr package.

...

arguments passed to sample() method in cmdstanr package (e.g., seed, refresh, init).

References

Gronau, Q. F., Singmann, H., and Wagenmakers, E.-J. (2020). bridgesampling: An r package for estimating normalizing constants. Journal of Statistical Software, 92(10).

Examples

if (instantiate::stan_cmdstan_exists()) {
  data(actg019)
  data(actg036)
  ## take subset for speed purposes
  actg019 = actg019[1:100, ]
  actg036 = actg036[1:50, ]
  formula = outcome ~ scale(age) + race + treatment + scale(cd4)
  family = binomial('logit')
  data_list = list(currdata = actg019, histdata = actg036)
  d.bhm = glm.bhm(
    formula = formula,
    family = family,
    data.list = data_list,
    chains = 1, iter_warmup = 500, iter_sampling = 1000
  )
  glm.logml.map(
    post.samples = d.bhm,
    bridge.args = list(silent = TRUE),
    chains = 1, iter_warmup = 1000, iter_sampling = 2000
  )
}