bayesm (version 3.1-6)

rsurGibbs: Gibbs Sampler for Seemingly Unrelated Regressions (SUR)

Description

rsurGibbs implements a Gibbs Sampler to draw from the posterior of the Seemingly Unrelated Regression (SUR) Model of Zellner.

Usage

rsurGibbs(Data, Prior, Mcmc)

Value

A list containing:

betadraw

\(R x p\) matrix of betadraws

Sigmadraw

\(R x (m*m)\) array of Sigma draws

Arguments

Data

list(regdata)

Prior

list(betabar, A, nu, V)

Mcmc

list(R, keep)

Author

Peter Rossi, Anderson School, UCLA, .

Details

Model and Priors

\(y_i = X_i\beta_i + e_i\) with \(i=1,\ldots,m\) for \(m\) regressions
(\(e(k,1), \ldots, e(k,m)\))' \(\sim\) \(N(0, \Sigma)\) with \(k=1, \ldots, n\)

Can be written as a stacked model:
\(y = X\beta + e\) where \(y\) is a \(nobs*m\) vector and \(p\) = length(beta) = sum(length(beta_i))

Note: must have the same number of observations (\(n\)) in each equation but can have a different number of \(X\) variables (\(p_i\)) for each equation where \(p = \sum p_i\).

\(\beta\) \(\sim\) \(N(betabar, A^{-1})\)
\(\Sigma\) \(\sim\) \(IW(nu,V)\)

Argument Details

Data = list(regdata)

regdata:

list of lists, regdata[[i]] = list(y=y_i, X=X_i), where y_i is \(n x 1\) and X_i is \(n x p_i\)

Prior = list(betabar, A, nu, V) [optional]

betabar:	\(p x 1\) prior mean (def: 0)
A:	\(p x p\) prior precision matrix (def: 0.01*I)
nu:	d.f. parameter for Inverted Wishart prior (def: m+3)
V:	\(m x m\) scale parameter for Inverted Wishart prior (def: nu*I)

Mcmc = list(R, keep) [only R required]

R:	number of MCMC draws
keep:	MCMC thinning parameter -- keep every keepth draw (def: 1)
nprint:	print the estimated time remaining for every nprint'th draw (def: 100, set to 0 for no print)

References

For further discussion, see Chapter 3, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

rmultireg

Examples

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10}
set.seed(66)

## simulate data from SUR
beta1 = c(1,2)
beta2 = c(1,-1,-2)
nobs = 100
nreg = 2
iota = c(rep(1, nobs))
X1 = cbind(iota, runif(nobs))
X2 = cbind(iota, runif(nobs), runif(nobs))
Sigma = matrix(c(0.5, 0.2, 0.2, 0.5), ncol=2)
U = chol(Sigma)
E = matrix(rnorm(2*nobs),ncol=2)%*%U
y1 = X1%*%beta1 + E[,1]
y2 = X2%*%beta2 + E[,2]

## run Gibbs Sampler
regdata = NULL
regdata[[1]] = list(y=y1, X=X1)
regdata[[2]] = list(y=y2, X=X2)

out = rsurGibbs(Data=list(regdata=regdata), Mcmc=list(R=R))

cat("Summary of beta draws", fill=TRUE)
summary(out$betadraw, tvalues=c(beta1,beta2))

cat("Summary of Sigmadraws", fill=TRUE)
summary(out$Sigmadraw, tvalues=as.vector(Sigma[upper.tri(Sigma,diag=TRUE)]))

## plotting examples
if(0){plot(out$betadraw, tvalues=c(beta1,beta2))}