bergmM {Bergm}

Parameter estimation for Bayesian ERGMs under missing data

Description

Function to fit Bayesian exponential random graphs models under missing data using the approximate exchange algorithm.

Usage

bergmM(
  formula,
  burn.in = 100,
  main.iters = 1000,
  aux.iters = 1000,
  prior.mean = NULL,
  prior.sigma = NULL,
  nchains = NULL,
  gamma = 0.5,
  V.proposal = 0.0025,
  seed = NULL,
  startVals = NULL,
  offset.coef = NULL,
  nImp = NULL,
  missingUpdate = NULL,
  ...
)

Arguments

formula

formula; an ergm formula object, of the form <network> ~ <model terms> where <network> is a network object and <model terms> are ergm-terms.

burn.in

count; number of burn-in iterations for every chain of the population.

main.iters

count; number of iterations for every chain of the population.

aux.iters

count; number of auxiliary iterations used for network simulation.

prior.mean

vector; mean vector of the multivariate Normal prior. By default set to a vector of 0's.

prior.sigma

square matrix; variance/covariance matrix for the multivariate Normal prior. By default set to a diagonal matrix with every diagonal entry equal to 100.

nchains

count; number of chains of the population MCMC. By default set to twice the model dimension (number of model terms).

gamma

scalar; parallel adaptive direction sampling move factor.

V.proposal

count; diagonal entry for the multivariate Normal proposal. By default set to 0.0025.

seed

count; random number seed for the Bergm estimation.

startVals

vector; optional starting values for the parameter estimation.

offset.coef

vector; A vector of coefficients for the offset terms.

nImp

count; number of imputed networks to be returned. If null, no imputed network will be returned.

missingUpdate

count; number of tie updates in each imputation step. By default equal to number of missing ties. Smaller numbers increase speed. Larger numbers lead to better sampling.

...

additional arguments, to be passed to lower-level functions.

References

Caimo, A. and Friel, N. (2011), "Bayesian Inference for Exponential Random Graph Models," Social Networks, 33(1), 41-55. https://arxiv.org/abs/1007.5192

Caimo, A. and Friel, N. (2014), "Bergm: Bayesian Exponential Random Graphs in R," Journal of Statistical Software, 61(2), 1-25. https://www.jstatsoft.org/v61/i02

Koskinen, J.H., Robins, G.L., Pattison, P.E. (2010), "Analysing exponential random graph (p-star) models with missing data using Bayesian data augmentation," Statistical Methodology 7(3), 366-384.

Krause, R.W., Huisman, M., Steglich, C., Snijders, T.A. (2020), "Missing data in cross-sectional networks-An extensive comparison of missing data treatment methods", Social Networks 62: 99-112.

Examples

## Not run: 
# Load the florentine marriage network
data(florentine)

# Create missing data
set.seed(14021994)
n <- dim(flomarriage[, ])[1]
missNode <- sample(1:n, 1)
flomarriage[missNode, ] <- NA
flomarriage[, missNode] <- NA

# Posterior parameter estimation:
m.flo <- bergmM(flomarriage ~ edges + kstar(2),
                burn.in    = 50,
                aux.iters  = 500,
                main.iters = 1000,
                gamma      = 1.2,
                nImp       = 5)

# Posterior summaries:
summary(m.flo)

## End(Not run)