glm.rmap.bhm.approx {hdbayes}

Posterior of robust meta-analytic predictive prior (RMAP)

Description

Second step for sampling from the posterior distribution of a GLM using the RMAP by Schmidli et al. (2014) doi:10.1111/biom.12242.

Usage

glm.rmap.bhm.approx(samples.bhm, G = NULL, ...)

Arguments

samples.bhm

a matrix of the samples of regression coefficients from the prior induced by the BHM, output from the glm.rmap.bhm() function.

G

an integer vector giving the numbers of mixtures components (in the mixture approximation to the BHM) for which the BIC is to be calculated. Defaults to 1:9. See the argument G in ?mclust::Mclust.

...

arguments passed to mclust::Mclust(). See https://mclust-org.github.io/mclust/reference/Mclust.html.

Details

This function approximates the distribution of the output "beta_pred" from the glm.rmap.bhm() function (i.e., samples from the prior induced by the Bayesian hierarchical model (BHM)) by a mixture of multivariate normal distributions. We use the mclust package by Scrucca et al. (2023) to implement the mixture approximation.

Value

The function returns a list giving the parameters estimated from the optimal (according to BIC) mixture model including the mixing proportions, the estimated mean and covariance matrix for each mixture component. An object of class Mclust from the mclust::Mclust() function is also included.

References

Scrucca, L., Fraley, C., Murphy, T. B., and Raftery, A. E. (2023). Model-Based Clustering, Classification, and Density Estimation Using mclust in R. Chapman and Hall/CRC. ISBN 978-1032234953. https://mclust-org.github.io/book/.

See Also

glm.rmap.bhm() for the first step and glm.rmap() for the final step of implementing RMAP.

Examples

  if (instantiate::stan_cmdstan_exists()) {
    data(actg036) ## historical data
    ## take subset for speed purposes
    actg036 = actg036[1:100, ]
    hist_data_list = list(actg036)
    samples_bhm = glm.rmap.bhm(
      formula = outcome ~ scale(age) + race + treatment + scale(cd4),
      family = binomial('logit'),
      hist.data.list = hist_data_list,
      chains = 1, iter_warmup = 1000, iter_sampling = 2000
    )$beta_pred
    glm.rmap.bhm.approx(
      samples.bhm = samples_bhm,
      G = 1:5, verbose = FALSE
    )
  }