Bayesian Analysis of Seemingly Unrelated Regression Models

Implementation of the direct Monte Carlo approach of Zellner and Ando (2010) to sample from posterior of Seemingly Unrelated Regression (SUR) models. In addition, a Gibbs sampler is implemented that allows the user to analyze SUR models using the power prior.

surbayes

The goal of surbayes is to provide tools for Bayesian analysis of the seemingly unrelated regression (SUR) model. In particular, we implement the direct Monte Carlo (DMC) approach of Zellner and Ando (2010). We also implement a Gibbs sampler to sample from a power prior on the SUR model.

Installation

You can install the released version of surbayes from CRAN with:

install.packages("surbayes")

And the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("ethan-alt/surbayes")

Example

This is a basic example which shows you how to sample from the posterior

library(surbayes)
## Taken from bayesm package
M = 10 ## number of samples
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]
X1 = X1[, -1]
X2 = X2[, -1]
data = data.frame(y1, y2, X1, X2)
names(data) = c( paste0( 'y', 1:2 ), paste0('x', 1:(ncol(data) - 2) ))
## run DMC sampler
formula.list = list(y1 ~ x1, y2 ~ x2 + x3)

## Fit models
out_dmc = sur_sample( formula.list, data, M = M )            ## DMC used
#> Direct Monte Carlo sampling used
out_powerprior = sur_sample( formula.list, data, M, data )   ## Gibbs used
#> Gibbs sampling used for power prior model