hdbayes (version 0.2.0)

glm.pp: Posterior of power prior (PP) with fixed \(a_0\)

Description

Sample from the posterior distribution of a GLM using the power prior (PP) by Ibrahim and Chen (2000) doi:10.1214/ss/1009212673.

Usage

glm.pp(
  formula,
  family,
  data.list,
  a0.vals,
  offset.list = NULL,
  beta.mean = NULL,
  beta.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.

a0.vals

a scalar between 0 and 1 or a vector whose dimension is equal to the number of historical data sets giving the (fixed) power prior parameter for each historical data set. Each element of vector should be between 0 and 1. If a scalar is provided, same as for beta.mean.

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.

beta.mean

a scalar or a vector whose dimension is equal to the number of regression coefficients giving the mean parameters for the initial prior on regression coefficients. 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. If a scalar is provided, same as for beta.mean. Defaults to a vector of 10s.

disp.mean

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

disp.sd

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

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 power prior parameters (\(a_0\)'s) are treated as fixed. The initial priors on the regression coefficients are independent normal priors. The current and historical data sets are assumed to have a common dispersion parameter with a half-normal prior (if applicable).

References

Chen, M.-H. and Ibrahim, J. G. (2000). Power prior distributions for Regression Models. Statistical Science, 15(1).

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.pp(
    formula = cd4 ~ treatment + age + race,
    family = poisson('log'),
    data.list = data_list,
    a0.vals = 0.5,
    chains = 1, iter_warmup = 500, iter_sampling = 1000
  )
}