rhierLinearModel(bayesm) | R Documentation |
rhierLinearModel
implements a Gibbs Sampler for hierarchical linear models.
rhierLinearModel(Data, Prior, Mcmc)
Data |
list(regdata,Z) |
Prior |
list(Deltabar,A,nu.e,ssq,nu,V) |
Mcmc |
list(R,keep) |
Model: length(regdata) regression equations.
y_i = X_ibeta_i + epsilon_i. epsilon_i ~ N(0,tau_i). nvar X vars in each equation.
Priors:
tau_i ~ nu.e*ssq_i/chisq(nu.e). tau_i is the variance of epsilon_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) | V_beta ~ N(vec(Deltabar),Vbeta (x) A^-1).
V_beta ~ IW(nu,V) or V_beta^-1 ~ W(nu,V^-1).
Delta, Deltabar are nz x nvar. A is nz x nz. Vbeta is nvar x nvar.
Note: if you don't have any z vars, set Z=iota (nreg x 1)
regdata
regdata[[i]]$X
regdata[[i]]$y
Deltabar
A
nu.e
ssq
nu
V
R
keep
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 |
Peter Rossi, Graduate School of Business, University of Chicago, Peter.Rossi@ChicagoGsb.edu.
For further discussion, see Bayesian Statistics and Marketing
by Allenby, McCulloch, and Rossi, Chapter 3.
http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html
## if(nchar(Sys.getenv("LONG_TEST")) != 0) # set env var LONG_TEST to run { 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]]$y)} nu=nvar+3 V=nu*diag(c(rep(1,nvar))) A=diag(c(rep(.01,nz)),ncol=nz) Deltabar=matrix(c(rep(0,nz*nvar)),nrow=nz) R=1000 Data=list(regdata=regdata,Z=Z) Prior=list(Deltabar=Deltabar,A=A,nu.e=nu.e,ssq=ssq,nu=nu,V=V) Mcmc=list(R=R,keep=1) out=rhierLinearModel(Data=Data,Mcmc=Mcmc) cat(" Deltadraws ",fill=TRUE) mat=apply(out$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) }