Bergm: Bayesian Exponential Random Graph Models

Bergm provides a comprehensive framework for Bayesian parameter estimation and model selection for exponential random graph models using advanced computational algorithms. It can also supply graphical Bayesian goodness-of-fit procedures that address the issue of model adequacy and missing data imputation.

What’s new

Bergm 6 is a rewrite of the computational core that keeps the Bergm 5 interface (same functions, arguments and returned elements) while making every function faster and more flexible. See NEWS.md for the full list.

Faster. Auxiliary networks are drawn by single calls to ergm’s compiled sampler on pre-built network states; pseudolikelihood-based methods (bergmC, ergmAPL, evidenceCJ, evidencePP) run their MCMC and pseudolikelihood evaluations in compiled code; bgof monitors goodness-of-fit statistics inside the sampler.
More efficient samplers. Burn-in adaptation of the ADS move factor, optional delayed acceptance that skips network simulation for proposals a cheap surrogate already rejects, parallel population updates (cores), and a Newton-type stochastic approximation for the posterior mode in bergmC.
More flexible. Curved terms (gwesp(fixed = FALSE)), one-parameter models, user-defined priors (log.prior), network proposals via ..., reusable pseudolikelihood adjustments (apl =), posterior predictive simulation (simulate()), per-chain output with R-hat, and coef(), vcov(), as.mcmc() methods.

Speed-ups over Bergm 5.0.7

Wall-clock time on a 2-core machine (ergm 4.12.0), average of two runs; “ESS/s gain” compares effective samples per second for the worst-mixing parameter. Full table, settings and validation against Bergm 5 in benchmarks/ (in the source repository).

Function, data, (Bergm 6 option)	Bergm 5	Bergm 6	ESS/s gain
`bergm()`, Florentine	9.4 s	3.6 s	2.7x
`bergm()`, Lazega	45.4 s	31.9 s	1.4x
`bergm()`, Lazega, (delayed acceptance)	45.4 s	18.2 s	1.9x
`bergm()`, Faux Mesa High, (delayed acceptance)	44.2 s	19.1 s	2.7x
`bergmM()`, Florentine with missing nodes	62.2 s	5.4 s	10.0x
`bergmC()`, Florentine	17.9 s	1.0 s	14.8x
`bergmC()`, Lazega	33.1 s	6.0 s	5.1x
`evidencePP()`, Florentine	18.1 s	2.2 s	8.1x
`evidencePP()`, Lazega	77.2 s	13.3 s	5.8x
`bgof()`, Florentine	3.9 s	0.2 s
`bgof()`, Lazega	7.5 s	2.0 s

library(Bergm)
data(florentine)

# Curved ERGM, delayed acceptance (default) and 4 workers
data(lazega)

fit2 <- bergm(lazega ~ edges + nodematch("Office") + gwesp(0.5, fixed = FALSE),
              burn.in = 200, main.iters = 2000, aux.iters = 3000,
              cores = 4, seed = 1)

# Model selection
a1 <- ergmAPL(flomarriage ~ edges + kstar(2))
a2 <- ergmAPL(flomarriage ~ edges + triangle)
evidencePP(flomarriage ~ edges + kstar(2), apl = a1)$log.evidence -
  evidencePP(flomarriage ~ edges + triangle, apl = a2)$log.evidence

# Goodness of fit and posterior predictive networks
bgof(fit, sample.size = 100, aux.iters = 5000)
nets <- simulate(fit, nsim = 10)

How to cite Bergm

Caimo, A., Bouranis, L., Krause, R., and Friel, N. (2022). Statistical Network Analysis with Bergm. Journal of Statistical Software, 104(1), 1–23. doi: https://doi.org/10.18637/jss.v104.i01.