rmultireg(bayesm)R Documentation

Draw from the Posterior of a Multivariate Regression

Description

rmultireg draws from the posterior of a Multivariate Regression model with a natural conjugate prior.

Usage

rmultireg(Y, X, Bbar, A, nu, V)

Arguments

Y n x m matrix of observations on m dep vars
X n x k matrix of observations on indep vars (supply intercept)
Bbar k x m matrix of prior mean of regression coefficients
A k x k Prior precision matrix
nu d.f. parameter for Sigma
V m x m pdf location parameter for prior on Sigma

Details

Model: Y=XB+U. cov(u_i) = Sigma. B is k x m matrix of coefficients. Sigma is m x m covariance.

Priors: beta|Sigma ~ N(betabar,Sigma (x) A^-1). betabar=vec(Bbar); beta = vec(B)
Sigma ~ IW(nu,V).

Value

A list of the components of a draw from the posterior

B draw of regression coefficient matrix
Sigma draw of Sigma

Warning

This routine is a utility routine that does not check the input arguments for proper dimensions and type.

Author(s)

Peter Rossi, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.

References

For further discussion, see Bayesian Statistics and Marketing by Allenby, McCulloch, and Rossi.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html

See Also

rmultiregfp,init.rmultiregfp

Examples

##
set.seed(66)
n=200
m=2
X=cbind(rep(1,n),runif(n))
k=ncol(X)
B=matrix(c(1,2,-1,3),ncol=m)
Sigma=matrix(c(1,.5,.5,1),ncol=m); RSigma=chol(Sigma)
Y=X%*%B+matrix(rnorm(m*n),ncol=m)%*%RSigma

betabar=rep(0,k*m);Bbar=matrix(betabar,ncol=m)
A=diag(rep(.01,k))
nu=3; V=nu*diag(m)

R=1000
betadraw=matrix(double(R*k*m),ncol=k*m)
Sigmadraw=matrix(double(R*m*m),ncol=m*m)
for (rep in 1:R) 
   {out=rmultireg(Y,X,Bbar,A,nu,V);betadraw[rep,]=out$B
    Sigmadraw[rep,]=out$Sigma}

cat(" Betadraws ",fill=TRUE)
mat=apply(betadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(as.vector(B),mat); rownames(mat)[1]="beta"
print(mat)
cat(" Sigma draws",fill=TRUE)
mat=apply(Sigmadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(as.vector(Sigma),mat); rownames(mat)[1]="Sigma"
print(mat)

[Package bayesm version 0.0 Index]