bayesm (version 3.0-2)

rhierBinLogit: MCMC Algorithm for Hierarchical Binary Logit

Description

rhierBinLogit implements an MCMC algorithm for hierarchical binary logits with a normal heterogeneity distribution. This is a hybrid sampler with a RW Metropolis step for unit-level logit parameters.

rhierBinLogit is designed for use on choice-based conjoint data with partial profiles. The Design matrix is based on differences of characteristics between two alternatives. See Appendix A of Bayesian Statistics and Marketing for details.

Usage

rhierBinLogit(Data, Prior, Mcmc)

Arguments

Data

list(lgtdata,Z) (note: Z is optional)

Prior

list(Deltabar,ADelta,nu,V) (note: all are optional)

Mcmc

list(sbeta,R,keep) (note: all but R are optional)

Value

a list containing:

Deltadraw

R/keep x nz*nvar matrix of draws of Delta

betadraw

nlgt x nvar x R/keep array of draws of betas

Vbetadraw

R/keep x nvar*nvar matrix of draws of Vbeta

llike

R/keep vector of log-like values

reject

R/keep vector of reject rates over nlgt units

Details

Model: \(y_{hi} = 1\) with \(\Pr=exp(x_{hi}'\beta_h)/(1+exp(x_{hi}'\beta_h)\). \(\beta_h\) is nvar x 1. h=1,…,length(lgtdata) units or "respondents" for survey data.

\(\beta_h\)= ZDelta[h,] + \(u_h\). Note: here ZDelta refers to Z%*%Delta, ZDelta[h,] is hth row of this product. Delta is an nz x nvar array.

\(u_h\) \(\sim\) \(N(0,V_{beta})\).

Priors: \(delta= vec(Delta)\) \(\sim\) \(N(vec(Deltabar),V_{beta} (x) ADelta^{-1})\) \(V_{beta}\) \(\sim\) \(IW(nu,V)\)

Lists contain:

• lgtdatalist of lists with each cross-section unit MNL data

• lgtdata[[h]]$y \(n_h\) vector of binary outcomes (0,1)

• lgtdata[[h]]$X \(n_h\) by nvar design matrix for hth unit

• Deltabarnz x nvar matrix of prior means (def: 0)

• ADelta prior prec matrix (def: .01I)

• nu d.f. parm for IW prior on norm comp Sigma (def: nvar+3)

• V pds location parm for IW prior on norm comp Sigma (def: nuI)

• sbeta scaling parm for RW Metropolis (def: .2)

• R number of MCMC draws

• keep MCMC thinning parm: keep every keepth draw (def: 1)

References

For further discussion, see Bayesian Statistics and Marketing by Rossi, Allenby and McCulloch, Chapter 5. http://www.perossi.org/home/bsm-1

See Also

rhierMnlRwMixture

Examples

##  
if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=10000} else {R=10}

set.seed(66)
nvar=5                           ## number of coefficients
nlgt=1000                        ## number of cross-sectional units
nobs=10                          ## number of observations per unit
nz=2                             ## number of regressors in mixing distribution

## set hyper-parameters
##     B=ZDelta + U  

Z=matrix(c(rep(1,nlgt),runif(nlgt,min=-1,max=1)),nrow=nlgt,ncol=nz)
Delta=matrix(c(-2,-1,0,1,2,-1,1,-.5,.5,0),nrow=nz,ncol=nvar)
iota=matrix(1,nrow=nvar,ncol=1)
Vbeta=diag(nvar)+.5*iota%*%t(iota)

## simulate data
lgtdata=NULL

for (i in 1:nlgt) 
{ beta=t(Delta)%*%Z[i,]+as.vector(t(chol(Vbeta))%*%rnorm(nvar))
  X=matrix(runif(nobs*nvar),nrow=nobs,ncol=nvar)
  prob=exp(X%*%beta)/(1+exp(X%*%beta)) 
  unif=runif(nobs,0,1)
  y=ifelse(unif<prob,1,0)
  lgtdata[[i]]=list(y=y,X=X,beta=beta)
}

out=rhierBinLogit(Data=list(lgtdata=lgtdata,Z=Z),Mcmc=list(R=R))

cat("Summary of Delta draws",fill=TRUE)
summary(out$Deltadraw,tvalues=as.vector(Delta))
cat("Summary of Vbeta draws",fill=TRUE)
summary(out$Vbetadraw,tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)]))

if(0){
## plotting examples
plot(out$Deltadraw,tvalues=as.vector(Delta))
plot(out$betadraw)
plot(out$Vbetadraw,tvalues=as.vector(Vbeta[upper.tri(Vbeta,diag=TRUE)]))
}