Asymptotic Analysis of Generalized Logistic Affiliation Network Models with Node Attributes

Affiliation networks, with their bipartite structure and non-binary features, pose unique challenges due to their complex relationships and diverse node attributes. These challenges differ from those in symmetric one-mode networks. To address them, we propose a generalized logistic affiliation network model. Despite the structural asymmetry, the model incorporates node attributes and includes parameters for actor activeness, event popularity, and symmetric patterns in actor–event interactions. We study the theoretical properties of this model under an asymptotic framework, where the number of actors and events grows to infinity. Using maximum likelihood estimation, we show that the estimators for degree heterogeneity and node homophily converge to multivariate normal distributions under mild conditions. To validate the model and our theory, we conduct experiments on both simulated data and a movie-rating dataset.