bayesm (version 3.1-6)

rordprobitGibbs: Gibbs Sampler for Ordered Probit

Description

rordprobitGibbs implements a Gibbs Sampler for the ordered probit model with a RW Metropolis step for the cut-offs.

Usage

rordprobitGibbs(Data, Prior, Mcmc)

Value

A list containing:

betadraw

\(R/keep x p\) matrix of betadraws

cutdraw

\(R/keep x (k-1)\) matrix of cutdraws

dstardraw

\(R/keep x (k-2)\) matrix of dstardraws

accept

acceptance rate of Metropolis draws for cut-offs

Arguments

Data

list(y, X, k)

Prior

list(betabar, A, dstarbar, Ad)

Mcmc

list(R, keep, nprint, s)

Author

Peter Rossi, Anderson School, UCLA, .

Details

Model and Priors

\(z = X\beta + e\) with \(e\) \(\sim\) \(N(0, I)\)
\(y = k\) if c[k] \(\le z <\) c[k+1] with \(k = 1,\ldots,K\)
cutoffs = {c[1], \(\ldots\), c[k+1]}

\(\beta\) \(\sim\) \(N(betabar, A^{-1})\)
\(dstar\) \(\sim\) \(N(dstarbar, Ad^{-1})\)

Be careful in assessing prior parameter Ad: 0.1 is too small for many applications.

Argument Details

Data = list(y, X, k)

y:	\(n x 1\) vector of observations, (\(1, \ldots, k\))
X:	\(n x p\) Design Matrix
k:	the largest possible value of y

Prior = list(betabar, A, dstarbar, Ad) [optional]

betabar:	\(p x 1\) prior mean (def: 0)
A:	\(p x p\) prior precision matrix (def: 0.01*I)
dstarbar:	\(ndstar x 1\) prior mean, where \(ndstar=k-2\) (def: 0)
Ad:	\(ndstar x ndstar\) prior precision matrix (def: I)

Mcmc = list(R, keep, nprint, s) [only R required]

R:	number of MCMC draws
keep:	MCMC thinning parameter -- keep every keepth draw (def: 1)
nprint:	print the estimated time remaining for every nprint'th draw (def: 100, set to 0 for no print)
s:	scaling parameter for RW Metropolis (def: 2.93/sqrt(p))

References

Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

rbprobitGibbs

Examples

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=2000} else {R=10}
set.seed(66)

## simulate data for ordered probit model

simordprobit=function(X, betas, cutoff){
  z = X%*%betas + rnorm(nobs)   
  y = cut(z, br = cutoff, right=TRUE, include.lowest = TRUE, labels = FALSE)  
  return(list(y = y, X = X, k=(length(cutoff)-1), betas= betas, cutoff=cutoff ))
}

nobs = 300 
X = cbind(rep(1,nobs),runif(nobs, min=0, max=5),runif(nobs,min=0, max=5))
k = 5
betas = c(0.5, 1, -0.5)       
cutoff = c(-100, 0, 1.0, 1.8, 3.2, 100)
simout = simordprobit(X, betas, cutoff) 
  
Data=list(X=simout$X, y=simout$y, k=k)

## set Mcmc for ordered probit model
   
Mcmc = list(R=R)   
out = rordprobitGibbs(Data=Data, Mcmc=Mcmc)

cat(" ", fill=TRUE)
cat("acceptance rate= ", accept=out$accept, fill=TRUE)
 
## outputs of betadraw and cut-off draws
  
cat(" Summary of betadraws", fill=TRUE)
summary(out$betadraw, tvalues=betas)
cat(" Summary of cut-off draws", fill=TRUE) 
summary(out$cutdraw, tvalues=cutoff[2:k])

## plotting examples
if(0){plot(out$cutdraw)}