bayesm (version 3.1-6)

rbprobitGibbs: Gibbs Sampler (Albert and Chib) for Binary Probit

Description

rbprobitGibbs implements the Albert and Chib Gibbs Sampler for the binary probit model.

Usage

rbprobitGibbs(Data, Prior, Mcmc)

Value

A list containing:

betadraw

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

Arguments

Data

list(y, X)

Prior

list(betabar, A)

Mcmc

list(R, keep, nprint)

Author

Peter Rossi, Anderson School, UCLA, .

Details

Model and Priors

\(z = X\beta + e\) with \(e\) \(\sim\) \(N(0, I)\)
\(y = 1\) if \(z > 0\)

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

Argument Details

Data = list(y, X)

y:	\(n x 1\) vector of 0/1 outcomes
X:	\(n x k\) design matrix

Prior = list(betabar, A) [optional]

betabar:	\(k x 1\) prior mean (def: 0)
A:	\(k x k\) prior precision matrix (def: 0.01*I)

Mcmc = list(R, keep, nprint) [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)

References

For further discussion, see Chapter 3, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

See Also

rmnpGibbs

Examples

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

## function to simulate from binary probit including x variable
simbprobit = function(X, beta) {
  y = ifelse((X%*%beta + rnorm(nrow(X)))<0, 0, 1)
  list(X=X, y=y, beta=beta)
}

nobs = 200
X = cbind(rep(1,nobs), runif(nobs), runif(nobs))
beta = c(0,1,-1)
nvar = ncol(X)
simout = simbprobit(X, beta)

Data1 = list(X=simout$X, y=simout$y)
Mcmc1 = list(R=R, keep=1)

out = rbprobitGibbs(Data=Data1, Mcmc=Mcmc1)
summary(out$betadraw, tvalues=beta)

## plotting example
if(0){plot(out$betadraw, tvalues=beta)}