glm.napp {hdbayes}

Posterior of normalized asymptotic power prior (NAPP)

Description

Sample from the posterior distribution of a GLM using the NAPP by Ibrahim et al. (2015) doi:10.1002/sim.6728.

Usage

glm.napp(
  formula,
  family,
  data.list,
  offset.list = NULL,
  a0.shape1 = 1,
  a0.shape2 = 1,
  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.

data.list

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

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.

a0.shape1

first shape parameter for the i.i.d. beta prior on a0 vector. When a0.shape1 == 1 and a0.shape2 == 1, a uniform prior is used.

a0.shape2

second shape parameter for the i.i.d. beta prior on a0 vector. When a0.shape1 == 1 and a0.shape2 == 1, a uniform prior is used.

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 NAPP assumes that the regression coefficients and logarithm of the dispersion parameter are a multivariate normal distribution with mean equal to the maximum likelihood estimate of the historical data and covariance matrix equal to a_0^{-1} multiplied by the inverse Fisher information matrix of the historical data, where a_0 is the power prior parameter (treated as random).

Value

The function returns an object of class draws_df giving posterior samples.

References

Ibrahim, J. G., Chen, M., Gwon, Y., and Chen, F. (2015). The power prior: Theory and applications. Statistics in Medicine, 34(28), 3724–3749.

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