Overcoming near-degeneracy in the autologistic actor attribute model

TL;DR

This paper addresses the near-degeneracy problem in autologistic actor attribute models (ALAAMs) by introducing geometrically weighted statistics, enabling reliable modeling of larger networks where simple models fail.

Contribution

The paper introduces geometrically weighted ALAAM statistics to prevent near-degeneracy in larger networks, expanding the applicability of ALAAMs.

Findings

Simple ALAAMs face near-degeneracy in large networks.

Geometrically weighted ALAAM statistics mitigate near-degeneracy.

Models with these statistics can be reliably estimated for larger networks.

Abstract

The autologistic actor attribute model, or ALAAM, is the social influence counterpart of the better-known exponential-family random graph model (ERGM) for social selection. Extensive experience with ERGMs has shown that the problem of near-degeneracy which often occurs with simple models can be overcome by using "geometrically weighted" or "alternating" statistics. In the much more limited empirical applications of ALAAMs to date, the problem of near-degeneracy, although theoretically expected, appears to have been less of an issue. In this work I present a comprehensive survey of ALAAM applications, showing that this model has to date only been used with relatively small networks, in which near-degeneracy does not appear to be a problem. I show near-degeneracy does occur in simple ALAAM models of larger empirical networks, define some geometrically weighted ALAAM statistics analogous to those for ERGM, and demonstrate that models with these statistics do not suffer from near-degeneracy and hence can be estimated where they could not be with the simple statistics.