  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.
