zsDC: Zellner-Siow g-prior with design covariates

In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.

Description

The Zellner-Siow cauchy g-prior utilizes the inverse crossproduct is to determine the proper scale of the coefficient priors by treating the inverse crossproduct of the model matrix as a covariance matrix for a multivariate normal prior distribution for the coefficients, which is scaled by the parameter "g". The logic is that variables which carry the most information will consequently have a more dispersed prior, while variables that carry less information will have priors more concentrated about zero. While the joint prior is multivariate normal, the implied independent marginal priors are Cauchy distributions. The approach here is to let g be a random variable estimated as part of the model, rather than fixed values of g=N. This avoids several problems associated with fixed-g priors. For more information, see Liang et al. (2008).

In addition, this function allows for a set of covariates that are held constant across all models. For example, you may wish to keep variables such as age and gender constant in order to control for them, so that the selected variables are chosen in light of the effects of age and gender on the outcome variable.



Plugin Pseudo-Variances:

Usage

zsDC(formula, design.formula, data, family = "gaussian",
  log_lik = FALSE, iter = 10000, warmup = 1000, adapt = 5000,
  chains = 4, thin = 1, method = "parallel", cl = makeCluster(2),
  ...)

Arguments

formula	the model formula
design.formula	the formula for the design covariates
data	a data frame
family	one of "gaussian", "binomial", or "poisson".
log_lik	Should the log likelihood be monitored? The default is FALSE.
iter	How many post-warmup samples? Defaults to 10000.
warmup	How many warmup samples? Defaults to 1000.
adapt	How many adaptation steps? Defaults to 2000.
chains	How many chains? Defaults to 4.
thin	Thinning interval. Defaults to 1.
method	Defaults to "parallel". For an alternative parallel option, choose "rjparallel". Otherwise, "rjags" (single core run).
cl	Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores.
...	Other arguments to run.jags.

Value

A run.jags object.

References

Zellner, A. & Siow S. (1980). Posterior odds ratio for selected regression hypotheses. In Bayesian statistics. Proc. 1st int. meeting (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley & A. F. M. Smith), 585–603. University Press, Valencia.

Zellner, A. (1986) On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In P. K. Goel and A. Zellner, editors, Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, 233–243.

Liang, Paulo, Molina, Clyde, & Berger (2008) Mixtures of g Priors for Bayesian Variable Selection, Journal of the American Statistical Association, 103:481, 410-423, DOI: 10.1198/016214507000001337

Examples

zsDC()

abnormally-distributed/Bayezilla documentation built on Oct. 31, 2019, 1:57 a.m.