BayesVarSel (version 1.7.0)

BMAcoeff: Bayesian Model Averaged estimations of regression coefficients

Description

Samples of the model averaged objective posterior distribution of regression coefficients

Usage

BMAcoeff(x, n.sim=10000, method="svd")

Arguments

x

An object of class Bvs

n.sim

Number of simulations to be produced

method

Text specifying the matrix decomposition used to determine the matrix root of 'sigma' when simulating from the multivariate t distribution. Possible methods are eigenvalue decomposition ('"eigen"', default), singular value decomposition ('"svd"'), and Cholesky decomposition ('"chol"'). See the help of command rmvnorm in package mvtnorm for more details

Value

returns an object of class bma.coeffs which is a matrix with n.sim rows with the simulations. Each column of the matrix corresponds to a regression coefficient in the full model.

Details

The distribution that is sampled from is the discrete mixture of the (objective) posterior distributions of the regression coefficients with weights proportional to the posterior probabilities of each model. That is, from

$ sum_M f(\beta | data, M) Pr(M | data)$

The models used in the mixture above are the retained best models (see the argument n.keep in Bvs) if x was generated with Bvs and the sampled models with the associated frequencies if x was generated with GibbsBvs. The formula for the objective posterior distribution within each model $f(\beta | data, M)$ is taken from Bernardo and Smith (1994) page 442.

Note: The above mixture is potentially highly multimodal and this command ends with a multiple plot with the densities of the different regression coefficients to show the user this peculiarity. Hence which summaries should be used to describe this distribution is a delicate issue and standard functions like the mean and variance are not recommendable.

See Also

See histBMA for a histogram-like representation of the columns in the object. See Bvs, PBvs and GibbsBvs for creating objects of the class Bvs. See rmvnorm for details about argument method.

Examples

## Not run: 
# 	
# #Analysis of Crime Data
# #load data
# data(UScrime)
# 
# crime.Bvs<- Bvs(formula="y~.", data=UScrime, n.keep=1000)
# crime.Bvs.BMA<- BMAcoeff(crime.Bvs, n.sim=10000)
# #the best 1000 models are used in the mixture
# 
# #We could force all  possible models to be included in the mixture
# crime.Bvs.all<- Bvs(formula="y~.", data=UScrime, n.keep=2^15)
# crime.Bvs.BMA<- BMAcoeff(crime.Bvs.all, n.sim=10000)
# #(much slower as this implies ordering many more models...)
# 
# #With the Gibbs algorithms:
# data(Ozone35)
# 
# Oz35.GibbsBvs<- GibbsBvs(formula="y~.", data=Ozone35, prior.betas="gZellner",
# prior.models="Constant", n.iter=10000, init.model="Full", n.burnin=100, 
# time.test = FALSE)
# Oz35.GibbsBvs.BMA<- BMAcoeff(Oz35.GibbsBvs, n.sim=10000)
# 
# 
# ## End(Not run)