Bayesian Analysis of the Network Autocorrelation Model

The network autocorrelation model (NAM) can be used for studying the degree of social influence regarding an outcome variable based on one or more known networks. The degree of social influence is quantified via the network autocorrelation parameters. In case of a single network, the Bayesian methods of Dittrich, Leenders, and Mulder (2017) and Dittrich, Leenders, and Mulder (2019) are implemented using a normal, flat, or independence Jeffreys prior for the network autocorrelation. In the case of multiple networks, the Bayesian methods of Dittrich, Leenders, and Mulder (2020) are implemented using a multivariate normal prior for the network autocorrelation parameters. Flat priors are implemented for estimating the coefficients. For Bayesian testing of equality and order-constrained hypotheses, the default Bayes factor of Gu, Mulder, and Hoijtink, (2018) is used with the posterior mean and posterior covariance matrix of the NAM parameters based on flat priors as input.

BANAM: Bayesian Analysis of the Network Autocorrelation Model

R package for Bayesian Analysis of the Network Autocorrelation Model. The methodology is based on:

Dittrich, D., Leenders, R.Th.A.J., & Mulder, J. (2017). Bayesian estimation of the network autocorrelation model. Social Network, 48, 213–236. doi:10.1016/j.socnet.2016.09.002

Dittrich, D., Leenders, R.Th.A.J., & Mulder, J. (2019). Network autocorrelation modeling: A Bayes factor approach for testing (multiple) precise and interval hypotheses. Sociological Methods & Research, 48, 642-676. doi:10.1177/0049124117729712

Dittrich, D., Leenders, R.Th.A.J., & Mulder, J. (2020). Network Autocorrelation Modeling: Bayesian Techniques for Estimating and Testing Multiple Network Autocorrelations. Sociological Methodology, 50, 168–214. doi:10.1177/0081175020913899

Licensed under the GNU General Public License version 2 (June, 1991)

Installation

You can install BANAM from github with:

# install.packages("devtools")
devtools::install_github("jomulder/BANAM")

Basic example

library("BANAM")
library("sna")
library("BFpack")

# Generate data
set.seed(3)
n <- 50
d1 <- .1
Wadj1 <- sna::rgraph(n, tprob=d1, mode="graph")
W1 <- sna::make.stochastic(Wadj1, mode="row")
d2 <- .3
Wadj2 <- sna::rgraph(n, tprob=d2, mode="graph")
W2 <- sna::make.stochastic(Wadj2, mode="row")
# set rho, beta, sigma2, and generate y
rho1 <- 0
rho2 <- .4
K <- 3
beta <- rnorm(K)
sigma2 <- 1
X <- matrix(c(rep(1, n), rnorm(n*(K-1))), nrow=n, ncol=K)
y <- c(solve(diag(n) - rho1*W1 - rho2*W2)%*%(X%*%beta + rnorm(n)))

# Bayesian estimation of a NAM with a single weight matrix
best1 <- banam(y,X,W1)
print(best1)

# Bayesian estimation of a NAM with two weight matrices
best2 <- banam(y,X,W=list(W1,W2))
print(best2)

# Bayesian hypothesis testing of equality/order constraints on network
# autocorrelation parameters
BFbest2 <- BF(best2,hypothesis="rho1>rho2>0; rho1=rho2>0; rho1=rho2=0")
print(BFbest2)