| rivGibbs(bayesm) | R Documentation |
rivGibbs is a Gibbs Sampler for a linear structural equation with an arbitrary number of instruments.
rivGibbs(Data, Prior, Mcmc)
Data |
list(z,w,x,y) |
Prior |
list(md,Ad,mbg,Abg,nu,V) this is an optional parm |
Mcmc |
list(R,keep) |
Model:
x=z'delta + e1.
y=beta*x + w'gamma + e2.
e1,e2 ~ N(0,Sigma).
Priors:
delta ~ N(md,Ad^-1). vec(beta,gamma) ~ N(mbg,Abg^-1)
Sigma ~ IW(nu,V)
zyxwmdAdmbgAbgnuVRkeepa 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 |
##
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$R = 500
Mcmc$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)