rbprobitGibbs {bayesm} R Documentation

## 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)

### Arguments

 Data list(y, X) Prior list(betabar, A) Mcmc list(R, keep, nprint)

### 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)

### Value

A list containing:

 betadraw R/keep x k matrix of betadraws

### Author(s)

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

### References

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

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)}


[Package bayesm version 3.1-6 Index]