BayesVarSel (version 1.3)

PBvs: Bayesian Variable Selection for linear regression models using parallel computing.

Description

PBvs is a parallelized version of Bvs.

Usage

PBvs(formula, data, prior.betas = "Robust",
     prior.models = "Constant", n.keep, n.nodes = 2)

Arguments

formula

Formula defining the most complex regression model in the analysis (package forces the intercept always to be included). See details.

data

data frame containing the data.

prior.betas

Prior distribution for regression parameters within each model. Possible choices include "Robust", "Liangetal", "gZellner" and "ZellnerSiow" (see details)

prior.models

Prior distribution over the model space. Possible choices are "Constant" and "ScottBerger" (see details)

n.keep

How many of the most probable models are to be kept?

n.nodes

Number of nodes to be used in the computation

Value

• PBvs returns an object of class Bvs with the following elements:
• time
  The internal time consumed in solving the problem
• lm
  The lm class object that results when the model defined by formula is fitted by lm
• variables
  The name of all the potential explanatory variables.
• n
  Number of observations
• p
  Total number of explanatory variables (including the intercept) in the most complex model
• HPMbin
  The binary expression of the Highest Posterior Probability model
• modelsprob
  A data.frame which summaries the n.keep most probable, a posteriori models, and their associated probability.
• inclprob
  A data.frame with the inclusion probabilities of all the variables.
• jointinclprob
  A data.frame with the joint inclusion probabilities of all the variables.
• postprobdim
  Posterior probabilities of the dimension of the true model
• betahat
  The model-averaged estimator of the regression parameters.
• call
  The call to the function
• method
  parallel

Details

This function takes advantage of the library parallel to distribute the models in the model space throughout the number of nodes available. Its intended use is for moderately large model spaces (p>=20).

A detailed description of the arguments can be found in the details section in Bvs.

References

Bayarri, M.J., Berger, J.O., Forte, A. and Garcia-Donato, G. (2012) Criteria for Bayesian Model choice with Application to Variable Selection. The Annals of Statistics. 40: 1550-1557

Liang, F., Paulo, R., Molina, G., Clyde, M. and Berger, J.O. (2008) Mixtures of g-priors for Bayesian Variable Selection. Journal of the American Statistical Association. 103:410-423. Zellner, A. and Siow, A. (1980). Posterior Odds Ratio for Selected Regression Hypotheses. In Bayesian Statistics 1 (J.M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 585-603. Valencia: University Press. Zellner, A. and Siow, A. (1984). Basic Issues in Econometrics. Chicago: University of Chicago Press. Zellner, A. (1986). On Assessing Prior Distributions and Bayesian Regression Analysis with g-prior Distributions. In Bayesian Inference and Decision techniques: Essays in Honor of Bruno de Finetti (A. Zellner, ed.) 389-399. Edward Elgar Publishing Limited.

See Also

plotBvs for different descriptive plots of the results.

GibbsBvs which implements a heuristic approximation to the problem based on Gibbs sampling.

Examples

#Analysis of Crime Data
#load data

data(UScrime)

#Default arguments are Robust prior for the regression parameters
#and constant prior over the model space
#Here we keep the 1000 most probable models a posteriori:
#The computation over the model space is distributed over two
#cores:
crime.Bvs<- PBvs(formula="y~.", data=UScrime, n.keep=1000, 
n.nodes=2)

#A look at the results:
crime.Bvs

summary(crime.Bvs)

#An image plot with the joint inlcusion 
#probabilities:
plotBvs(crime.Bvs, option="joint")