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.

翻译：自Logistic行为者属性模型（ALAAM）是更广为人知的用于社会选择的指数族随机图模型（ERGM）在社会影响方面的对应模型。对ERGM的大量经验研究表明，简单模型常出现的近退化问题可通过使用“几何加权”或“交替”统计量加以克服。在迄今为止极为有限的ALAAM经验应用中，近退化问题虽理论上可预见，但实际出现较少。本文对ALAAM应用进行了全面综述，表明该模型至今仅用于相对较小的网络，其中近退化问题似乎不显著。实证结果表明，在较大经验网络的简单ALAAM模型中确实存在近退化现象；本文定义了与ERGM中类似的若干几何加权ALAAM统计量，并证明采用这些统计量的模型不会出现近退化，从而可在简单统计量无法估计的情况下进行模型估计。