# rbprobitGibbs: Gibbs Sampler (Albert and Chib) for Binary Probit In bayesm: Bayesian Inference for Marketing/Micro-Econometrics

## Description

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

## Usage

 `1` ```rbprobitGibbs(Data, Prior, Mcmc) ```

## Arguments

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

## Details

#### Model and Priors

z = Xβ + e with e ~ N(0, I)
y = 1 if z > 0

β ~ 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 `keep`th 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, [email protected].

## References

For further discussion, see Chapter 3, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.
http://www.perossi.org/home/bsm-1

`rmnpGibbs`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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)} ```

### Example output

```
Starting Gibbs Sampler for Binary Probit Model
with  200  observations
Table of y Values
y
0   1
90 110

Prior Parms:
betabar
[1] 0 0 0
A
[,1] [,2] [,3]
[1,] 0.01 0.00 0.00
[2,] 0.00 0.01 0.00
[3,] 0.00 0.00 0.01

MCMC parms:
R=  10  keep=  1  nprint=  100

MCMC Iteration (est time to end - min)
Total Time Elapsed: 0.00
fewer than 100 draws submitted
```

bayesm documentation built on Dec. 21, 2018, 9:04 a.m.