bayesm (version 3.0-2)

rmultireg: 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

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.

Details

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

Priors: \(\beta\) given \(\Sigma\) \(\sim\) \(N(betabar,\Sigma (x) A^{-1})\). \(betabar=vec(Bbar)\); \(\beta = vec(B)\) \(\Sigma\) \(\sim\) IW(nu,V).

References

For further discussion, see Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch, Chapter 2. http://www.perossi.org/home/bsm-1

Examples

##
if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10}

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)

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)