runireg {bayesm} R Documentation

## IID Sampler for Univariate Regression

### Description

runireg implements an iid sampler to draw from the posterior of a univariate regression with a conjugate prior.

### Usage

runireg(Data, Prior, Mcmc)

### Arguments

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

### Details

#### Model and Priors

y = X\beta + e with e \sim N(0, \sigma^2)

\beta \sim N(betabar, \sigma^2*A^{-1})
\sigma^2 \sim (nu*ssq)/\chi^2_{nu}

#### Argument Details

Data = list(y, X)

 y:  n x 1 vector of observations X:  n x k design matrix

Prior = list(betabar, A, nu, ssq) [optional]

 betabar:  k x 1 prior mean (def: 0) A:  k x k prior precision matrix (def: 0.01*I) nu:  d.f. parameter for Inverted Chi-square prior (def: 3) ssq:  scale parameter for Inverted Chi-square prior (def: var(y))

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

 R:  number of draws keep:  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 x k matrix of betadraws sigmasqdraw R x 1 vector of sigma-sq draws

### Author(s)

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

### References

For further discussion, see Chapter 2, Bayesian Statistics and Marketing by Rossi, Allenby, and McCulloch.

runiregGibbs

### Examples

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

n = 200
X = cbind(rep(1,n), runif(n))
beta = c(1,2)
sigsq = 0.25
y = X%*%beta + rnorm(n,sd=sqrt(sigsq))

out = runireg(Data=list(y=y,X=X), Mcmc=list(R=R))

cat("Summary of beta and Sigmasq draws", fill=TRUE)
summary(out$betadraw, tvalues=beta) summary(out$sigmasqdraw, tvalues=sigsq)

## plotting examples