Exponential random graph models (ERGMs) are a popular tool for modeling social
networks representing relational data, such as working relationships or friendships.
Data on exogenous variables relating to participants in the network, such as gender or
age, are also often collected. ERGMs allow modeling of the effects of such exogenous
variables on the joint distribution, specified by the ERGM, but not on the marginal
probabilities of observing a relationship. In this article, we consider an approach to
modeling a network that uses an ERGM for the joint distribution of the network, but
then marginally constrains the fit to agree with a generalized linear model (GLM)
defined in terms of this set of exogenous variables. This type of model, which we refer
to as a marginalized ERGM, is a natural extension of the standard ERGM that allows
a convenient population-averaged interpretation of parameters, for example, in terms
of log odds ratios when the GLM includes a logistic link, as well as fast computation
of marginal probabilities. Several algorithms to obtain maximum likelihood estimates
are presented, with a particular focus on reducing the computational burden. These
methods are illustrated using data on the working relationship between 36 partners in a
New England law firm.