glm.npp.lognc {hdbayes}

Estimate the logarithm of the normalizing constant for normalized power prior (NPP) for one data set

Description

Uses Markov chain Monte Carlo (MCMC) and bridge sampling to estimate the logarithm of the normalizing constant for the NPP for a fixed value of the power prior parameter a_0 \in (0, 1) for one data set. The initial priors are independent normal priors on the regression coefficients and a half-normal prior on the dispersion parameter (if applicable).

Usage

glm.npp.lognc(
  formula,
  family,
  histdata,
  a0,
  offset0 = NULL,
  beta.mean = NULL,
  beta.sd = NULL,
  disp.mean = NULL,
  disp.sd = NULL,
  bridge.args = NULL,
  iter_warmup = 1000,
  iter_sampling = 1000,
  chains = 4,
  ...
)

Arguments

formula

a two-sided formula giving the relationship between the response variable and covariates.

family

an object of class family. See ?stats::family.

histdata

a data.frame giving the historical data.

a0

the power prior parameter (a scalar between 0 and 1).

offset0

vector whose dimension is equal to the rows of the historical data set giving an offset for the historical data. Defaults to a vector of 0s.

beta.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the mean parameters for the normal initial prior on regression coefficients given the dispersion parameter. If a scalar is provided, beta.mean will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.

beta.sd

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sd parameters for the initial prior on regression coefficients. The sd used is sqrt(dispersion) * beta.sd. If a scalar is provided, same as for beta.mean. Defaults to a vector of 10s.

disp.mean

mean parameter for the half-normal prior on dispersion parameter. Defaults to 0.

disp.sd

sd parameter for the half-normal prior on dispersion parameter. Defaults to 10.

bridge.args

a list giving arguments (other than samples, log_posterior, data, lb, 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).

Value

The function returns a vector giving the value of a0, the estimated logarithm of the normalizing constant, the minimum estimated bulk effective sample size of the MCMC sampling, and the maximum Rhat.

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(actg036)
  ## take subset for speed purposes
  actg036 = actg036[1:50, ]
  glm.npp.lognc(
    cd4 ~ treatment + age + race,
    family = poisson(), histdata = actg036, a0 = 0.5,
    chains = 1, iter_warmup = 500, iter_sampling = 5000
  )
}