R: Posterior of power prior (PP) with fixed a

glm.pp {hdbayes}

R Documentation

Posterior of power prior (PP) with fixed `a_0`

Description

Sample from the posterior distribution of a GLM using the 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,
  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.frame`s. 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`	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.
`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).

Value

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

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
  )
}

[Package hdbayes version 0.0.3 Index]

Posterior of power prior (PP) with fixed a_0