A return to biased nets: new specifications and approximate Bayesian Inference*

ABSTRACT

The biased net paradigm was the first general and empirically tractable scheme for parameterizing complex patterns of dependence in networks, expressing deviations from uniform random graph structure in terms of latent “bias events,” whose realizations enhance reciprocity, transitivity, or other structural features. Subsequent developments have introduced local specifications of biased nets, which reduce the need for approximations required in early specifications based on tracing processes. Here, we show that while one such specification leads to inconsistencies, a closely related Markovian specification both evades these difficulties and can be extended to incorporate new types of effects. We introduce the notion of inhibitory bias events, with satiation as an example, which are useful for avoiding degeneracies that can arise from closure bias terms. Although our approach does not lead to a computable likelihood, we provide a strategy for approximate Bayesian inference using random forest prevision. We demonstrate our approach on a network of friendship ties among college students, recapitulating a relationship between the sibling bias and tie strength posited in earlier work by Fararo.

KEYWORDS:

• Approximate Bayesian computation
• biased nets
• prevision
• random graphs
• social networks

Acknowledgments

Paper prepared in memory of the late Thomas Fararo, whom the author thanks for his mentoring and input. The author also thanks John Skvoretz for his helpful discussions. This work was supported under NIH award 1R01GM144964-01.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ Inhibitory and dichotomized events were first implemented in version 2.4 of the sna package, but the former have not previously been described in print.

² I.e., under weak regularity conditions, their prediction surface will converge to the conditional expectation in the limit of sample size.