bayesm: rsurGibbs – R documentation

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rsurGibbs

Gibbs Sampler for Seemingly Unrelated Regressions (SUR)

Description

rsurGibbs implements a Gibbs Sampler to draw from the posterior of the Seemingly Unrelated Regression (SUR) Model of Zellner.

Usage

rsurGibbs(Data, Prior, Mcmc)

Arguments

`Data`	list(regdata)
`Prior`	list(betabar, A, nu, V)
`Mcmc`	list(R, keep)

Details

Model and Priors

y_i = X_iβ_i + e_i with i=1,…,m for m regressions
(e(k,1), …, e(k,m))' ~ N(0, Σ) with k=1, …, n

Can be written as a stacked model:
y = Xβ + e where y is a nobs*m vector and p = length(beta) = sum(length(beta_i))

Note: must have the same number of observations (n) in each equation but can have a different number of X variables (p_i) for each equation where p = ∑ p_i.

β ~ N(betabar, A^{-1})
Σ ~ IW(nu,V)

Argument Details

Data = list(regdata)

regdata: list of lists, regdata[[i]] = list(y=y_i, X=X_i), where y_i is n x 1 and X_i is n x p_i

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

`betabar:`	p x 1 prior mean (def: 0)
`A:`	p x p prior precision matrix (def: 0.01*I)
`nu:`	d.f. parameter for Inverted Wishart prior (def: m+3)
`V:`	m x m scale parameter for Inverted Wishart prior (def: nu*I)

Mcmc = list(R, keep) [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 x p matrix of betadraws
`Sigmadraw`	R x (mm)* array of Sigma draws

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.
http://www.perossi.org/home/bsm-1

Examples

if(nchar(Sys.getenv("LONG_TEST")) != 0) {R=1000} else {R=10}
set.seed(66)

## simulate data from SUR
beta1 = c(1,2)
beta2 = c(1,-1,-2)
nobs = 100
nreg = 2
iota = c(rep(1, nobs))
X1 = cbind(iota, runif(nobs))
X2 = cbind(iota, runif(nobs), runif(nobs))
Sigma = matrix(c(0.5, 0.2, 0.2, 0.5), ncol=2)
U = chol(Sigma)
E = matrix(rnorm(2*nobs),ncol=2)%*%U
y1 = X1%*%beta1 + E[,1]
y2 = X2%*%beta2 + E[,2]

## run Gibbs Sampler
regdata = NULL
regdata[[1]] = list(y=y1, X=X1)
regdata[[2]] = list(y=y2, X=X2)

out = rsurGibbs(Data=list(regdata=regdata), Mcmc=list(R=R))

cat("Summary of beta draws", fill=TRUE)
summary(out$betadraw, tvalues=c(beta1,beta2))

cat("Summary of Sigmadraws", fill=TRUE)
summary(out$Sigmadraw, tvalues=as.vector(Sigma[upper.tri(Sigma,diag=TRUE)]))

## plotting examples
if(0){plot(out$betadraw, tvalues=c(beta1,beta2))}

bayesm

Bayesian Inference for Marketing/Micro-Econometrics

v3.1-4

GPL (>= 2)

Authors

Peter Rossi <perossichi@gmail.com>

Initial release

2019-10-14