rordprobitGibbs {bayesm}R Documentation

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)

Arguments

Data

list(y, X, k)

Prior

list(betabar, A, dstarbar, Ad)

Mcmc

list(R, keep, nprint, s)

Details

Model and Priors

z = Xβ + e with e ~ N(0, I)
y = k if c[k] ≤ z < c[k+1] with k = 1,…,K
cutoffs = {c[1], , c[k+1]}

β ~ N(betabar, A^{-1})
dstar ~ 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, …, 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))

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

Note

set c[1] = -100 and c[k+1] = 100. c[2] is set to 0 for identification.

The relationship between cut-offs and dstar is:
c[3] = exp(dstar[1]),
c[4] = c[3] + exp(dstar[2]), ...,
c[k] = c[k-1] + exp(dstar[k-2])

Author(s)

Peter Rossi, Anderson School, UCLA, perossichi@gmail.com.

References

Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch
http://www.perossi.org/home/bsm-1

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)}

[Package bayesm version 3.1-4 Index]