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：自逻辑演员属性模型（ALAAM）是社会选择中更为知名的指数族随机图模型（ERGM）在社会影响方面的对应模型。对ERGM的广泛经验表明，简单模型中常见的近退化问题可以通过使用“几何加权”或“交替”统计量来克服。在迄今为止非常有限的ALAAM实证应用中，尽管理论上预期会出现近退化问题，但实际上这一问题似乎并不突出。本文对ALAAM的应用进行了全面综述，表明该模型迄今仅用于相对较小的网络，在这些网络中近退化并未构成问题。我展示了在较大实证网络的简单ALAAM模型中确实会出现近退化现象，定义了与ERGM类似的几何加权ALAAM统计量，并证明了使用这些统计量的模型不会遭受近退化问题，因此可以在简单统计量无法估计的情况下进行估计。