hdbayes (version 0.2.0)

glm.bhm: Posterior of Bayesian hierarchical model (BHM)

Description

Sample from the posterior distribution of a GLM using the Bayesian hierarchical model (BHM).

Usage

glm.bhm(
  formula,
  family,
  data.list,
  offset.list = NULL,
  meta.mean.mean = NULL,
  meta.mean.sd = NULL,
  meta.sd.mean = NULL,
  meta.sd.sd = NULL,
  disp.mean = NULL,
  disp.sd = NULL,
  get.loglik = FALSE,
  iter_warmup = 1000,
  iter_sampling = 1000,
  chains = 4,
  ...
)

Value

The function returns an object of class draws_df containing posterior samples. The object has two attributes:

data

a list of variables specified in the data block of the Stan program

model

a character string indicating the model name

Arguments

formula

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

family

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

data.list

a list of data.frames. The first element in the list is the current data, and the rest are the historical data sets.

offset.list

a list of vectors giving the offsets for each data. The length of offset.list is equal to the length of data.list. The length of each element of offset.list is equal to the number of rows in the corresponding element of data.list. Defaults to a list of vectors of 0s.

meta.mean.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the means for the normal hyperpriors on the mean hyperparameters of regression coefficients. If a scalar is provided, meta.mean.mean will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.

meta.mean.sd

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sds for the normal hyperpriors on the mean hyperparameters of regression coefficients. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 10s.

meta.sd.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the means for the half-normal hyperpriors on the sd hyperparameters of regression coefficients. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 0s.

meta.sd.sd

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the sds for the half-normal hyperpriors on the sd hyperparameters of regression coefficients. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 1s.

disp.mean

a scalar or a vector whose dimension is equal to the number of data sets (including the current data) giving the location parameters for the half-normal priors on the dispersion parameters. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 0s.

disp.sd

a scalar or a vector whose dimension is equal to the number of data sets (including the current data) giving the scale parameters for the half-normal priors on the dispersion parameters. If a scalar is provided, same as for meta.mean.mean. Defaults to a vector of 10s.

get.loglik

whether to generate log-likelihood matrix. Defaults to FALSE.

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).

Details

The Bayesian hierarchical model (BHM) assumes that the regression coefficients for the historical and current data are different, but are correlated through a common distribution, whose hyperparameters (i.e., mean and standard deviation (sd) (the covariance matrix is assumed to have a diagonal structure)) are treated as random. The number of regression coefficients for the current data is assumed to be the same as that for the historical data.

The hyperpriors on the mean and the sd hyperparameters are independent normal and independent half-normal distributions, respectively. The priors on the dispersion parameters (if applicable) for the current and historical data sets are independent half-normal distributions.

Examples

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