rhierLinearModel {bayesm}R Documentation

Gibbs Sampler for Hierarchical Linear Model

Description

rhierLinearModel implements a Gibbs Sampler for hierarchical linear models.

Usage

rhierLinearModel(Data, Prior, Mcmc)

Arguments

Data list(regdata,Z) (Z optional).
Prior list(Deltabar,A,nu.e,ssq,nu,V) (optional).
Mcmc list(R,keep) (R required).

Details

Model: length(regdata) regression equations.
y_i = X_ibeta_i + e_i. e_i ~ N(0,tau_i). nvar X vars in each equation.

Priors:
tau_i ~ nu.e*ssq_i/chi^2_{nu.e}. tau_i is the variance of e_i.
beta_i ~ N(ZDelta[i,],V_{beta}).
Note: ZDelta is the matrix Z * Delta; [i,] refers to ith row of this product.

vec(Delta) given V_{beta} ~ N(vec(Deltabar),V_{beta} (x) A^{-1}).
V_{beta} ~ IW(nu,V).
Delta, Deltabar are nz x nvar. A is nz x nz. V_{beta} is nvar x nvar.

Note: if you don't have any z vars, set Z=iota (nreg x 1).

List arguments contain:

Value

a list containing

betadraw nreg x nvar x R/keep array of individual regression coef draws
taudraw R/keep x nreg array of error variance draws
Deltadraw R/keep x nz x nvar array of Deltadraws
Vbetadraw R/keep x nvar*nvar array of Vbeta draws

Author(s)

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 3.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html

Examples

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

nreg=100; nobs=100; nvar=3
Vbeta=matrix(c(1,.5,0,.5,2,.7,0,.7,1),ncol=3)
Z=cbind(c(rep(1,nreg)),3*runif(nreg)); Z[,2]=Z[,2]-mean(Z[,2])
nz=ncol(Z)
Delta=matrix(c(1,-1,2,0,1,0),ncol=2)
Delta=t(Delta) # first row of Delta is means of betas
Beta=matrix(rnorm(nreg*nvar),nrow=nreg)%*%chol(Vbeta)+Z%*%Delta
tau=.1
iota=c(rep(1,nobs))
regdata=NULL
for (reg in 1:nreg) { X=cbind(iota,matrix(runif(nobs*(nvar-1)),ncol=(nvar-1)))
        y=X%*%Beta[reg,]+sqrt(tau)*rnorm(nobs); regdata[[reg]]=list(y=y,X=X) }

nu.e=3
ssq=NULL
for(reg in 1:nreg) {ssq[reg]=var(regdata[[reg]]$y)}
nu=nvar+3
V=nu*diag(c(rep(1,nvar)))
A=diag(c(rep(.01,nz)),ncol=nz)
Deltabar=matrix(c(rep(0,nz*nvar)),nrow=nz)

Data=list(regdata=regdata,Z=Z)
Prior=list(Deltabar=Deltabar,A=A,nu.e=nu.e,ssq=ssq,nu=nu,V=V)
Mcmc=list(R=R,keep=1)
out=rhierLinearModel(Data=Data,Mcmc=Mcmc)

cat(" Deltadraws ",fill=TRUE)
mat=apply(out$Deltadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(as.vector(Delta),mat); rownames(mat)[1]="delta"; print(mat)
cat(" Vbetadraws ",fill=TRUE)
mat=apply(out$Vbetadraw,2,quantile,probs=c(.01,.05,.5,.95,.99))
mat=rbind(as.vector(Vbeta),mat); rownames(mat)[1]="Vbeta"; print(mat)


[Package bayesm version 2.0-8 Index]