glm.npp {hdbayes}

Posterior of normalized power prior (NPP)

Description

Sample from the posterior distribution of a GLM using the NPP by Duan et al. (2006) doi:10.1002/env.752.

Usage

glm.npp(
  formula,
  family,
  data.list,
  a0.lognc,
  lognc,
  offset.list = NULL,
  beta.mean = NULL,
  beta.sd = NULL,
  disp.mean = NULL,
  disp.sd = NULL,
  a0.shape1 = 1,
  a0.shape2 = 1,
  a0.lower = NULL,
  a0.upper = 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.frames. The first element in the list is the current data, and the rest are the historical data sets.

a0.lognc

a vector giving values of the power prior parameter for which the logarithm of the normalizing constant has been evaluated.

lognc

an S by T matrix where S is the length of a0.lognc, T is the number of historical data sets, and the j-th column, j = 1, ..., T, is a vector giving the logarithm of the normalizing constant (as estimated by glm.npp.lognc() for a0.lognc using the j-th historical data set.

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.

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.

a0.lower

a scalar or a vector whose dimension is equal to the number of historical data sets giving the lower bounds for each element of the a0 vector. If a scalar is provided, a0.lower will be a vector of repeated elements of the given scalar. Defaults to a vector of 0s.

a0.upper

a scalar or a vector whose dimension is equal to the number of historical data sets giving the upper bounds for each element of the a0 vector. If a scalar is provided, same as for a0.lower. Defaults to a vector of 1s.

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

Before using this function, users must estimate the logarithm of the normalizing constant across a range of different values for the power prior parameter (a_0), possibly smoothing techniques over a find grid. The power prior parameters (a_0's) are treated as random with independent beta priors. 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). For normal linear models, the exact normalizing constants for NPP can be computed. See the implementation in lm.npp().

Value

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

References

Duan, Y., Ye, K., and Smith, E. P. (2005). Evaluating water quality using power priors to incorporate historical information. Environmetrics, 17(1), 95–106.

See Also

glm.npp.lognc()

Examples

  if(requireNamespace("parallel")){
    data(actg019)
    data(actg036)
    ## take subset for speed purposes
    actg019 = actg019[1:100, ]
    actg036 = actg036[1:50, ]

    library(parallel)
    ncores    = 2
    data.list = list(data = actg019, histdata = actg036)
    formula   = cd4 ~ treatment + age + race
    family    = poisson()
    a0        = seq(0, 1, length.out = 11)
    if (instantiate::stan_cmdstan_exists()) {
      ## call created function
      ## wrapper to obtain log normalizing constant in parallel package
      logncfun = function(a0, ...){
        hdbayes::glm.npp.lognc(
          formula = formula, family = family, a0 = a0, histdata = data.list[[2]],
          ...
        )
      }

      cl = makeCluster(ncores)
      clusterSetRNGStream(cl, 123)
      clusterExport(cl, varlist = c('formula', 'family', 'data.list'))
      a0.lognc = parLapply(
        cl = cl, X = a0, fun = logncfun, iter_warmup = 500,
        iter_sampling = 1000, chains = 1, refresh = 0
      )
      stopCluster(cl)
      a0.lognc = data.frame( do.call(rbind, a0.lognc) )

      ## sample from normalized power prior
      glm.npp(
        formula = cd4 ~ treatment + age + race,
        family = poisson(),
        data.list = data.list,
        a0.lognc = a0.lognc$a0,
        lognc = matrix(a0.lognc$lognc, ncol = 1),
        chains = 1, iter_warmup = 500, iter_sampling = 1000,
        refresh = 0
      )
    }
  }