rivGibbs {bayesm}R Documentation

Gibbs Sampler for Linear "IV" Model

Description

rivGibbs is a Gibbs Sampler for a linear structural equation with an arbitrary number of instruments.

Usage

rivGibbs(Data, Prior, Mcmc)

Arguments

Data list(z,w,x,y)
Prior list(md,Ad,mbg,Abg,nu,V) (optional)
Mcmc list(R,keep) (R required)

Details

Model:
x=z'delta + e1.
y=beta*x + w'gamma + e2.
e1,e2 ~ N(0,Sigma).

Note: if intercepts are desired in either equation, include vector of ones in z or w

Priors:
delta ~ N(md,Ad^{-1}). vec(beta,gamma) ~ N(mbg,Abg^{-1})
Sigma ~ IW(nu,V)

List arguments contain:

Value

a list containing:

deltadraw R/keep x dim(delta) array of delta draws
betadraw R/keep x 1 vector of beta draws
gammadraw R/keep x dim(gamma) array of gamma draws
Sigmadraw R/keep x 4 array of Sigma draws

Author(s)

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

References

For further discussion, see Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch, Chapter 5.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html

Examples

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

set.seed(66)
simIV = function(delta,beta,Sigma,n,z,w,gamma) {
eps = matrix(rnorm(2*n),ncol=2) %*% chol(Sigma)
x = z %*% delta + eps[,1]; y = beta*x +  eps[,2] + w%*%gamma
list(x=as.vector(x),y=as.vector(y)) }
n = 200 ; p=1 # number of instruments
z = cbind(rep(1,n),matrix(runif(n*p),ncol=p))
w = matrix(1,n,1)
rho=.8
Sigma = matrix(c(1,rho,rho,1),ncol=2)
delta = c(1,4); beta = .5; gamma = c(1)
simiv = simIV(delta,beta,Sigma,n,z,w,gamma)

Mcmc=list(); Prior=list(); Data = list()
Data$z = z; Data$w=w; Data$x=simiv$x; Data$y=simiv$y
Mcmc$R = R
Mcmc$keep=1
out=rivGibbs(Data=Data,Prior=Prior,Mcmc=Mcmc)

cat(" deltadraws ",fill=TRUE)
mat=apply(out$deltadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(delta,mat); rownames(mat)[1]="delta"; print(mat)
cat(" betadraws ",fill=TRUE)
qout=quantile(out$betadraw,probs=c(.01,.05,.5,.95,.99))
mat=matrix(qout,ncol=1)
mat=rbind(beta,mat); rownames(mat)=c("beta",names(qout)); print(mat)
cat(" Sigma draws",fill=TRUE)
mat=apply(out$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 2.0-8 Index]