rmultireg {bayesm}

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 with cov(u_i) = \Sigma
B is k x m matrix of coefficients; \Sigma is m x m covariance matrix.

Priors:
\beta | \Sigma \sim N(betabar, \Sigma(x) A^{-1})
betabar = vec(Bbar); \beta = vec(B)
\Sigma \sim 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, Anderson School, UCLA, [e-mail].

References

For further discussion, see Chapter 2, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

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, 0.5, 0.5, 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(0.01,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(0.01, 0.05, 0.5, 0.95, 0.99))
mat = rbind(as.vector(B),mat)
rownames(mat)[1] = "beta"
print(mat)

cat(" Sigma draws", fill=TRUE)
mat = apply(Sigmadraw, 2 ,quantile, probs=c(0.01, 0.05, 0.5, 0.95, 0.99))
mat = rbind(as.vector(Sigma),mat); rownames(mat)[1]="Sigma"
print(mat)