Suesse, Thomas, Marginalized Curved Exponential Random Graph Models, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 23-10, 2010, 32p.
Curved Exponential random graph models (CERGMs) are a popular tool for modeling social networks representing relational data, such as working relations or friend- ships. Additionally to the network itself some exogenous variables are often collected, such as gender, age, etc. CERGMs allow modeling of the effects of such exogenous variables on the joint distribution, but not on the marginal probabilities of observing a relation. In this paper, we consider a modification of CERGMs that uses a CERGM to model the joint distribution of a network, which is then subject to a marginal logistic regression model for the marginal probabilities of observing a relation. Explanatory variables depend on the exogenous variables, such as the difference in age between two nodes. This model approach, termed a marginalized CERGM, is a natural extension of a CERGM that allows a convenient interpretation of parameters in terms of log odds ratios. Several algorithms to obtain ML estimates and solutions to reduce the computational burden are presented. The methods are illustrated using the working relations between 36 partners in a New England law rm.