Inference in a probit model for affiliation networks

作者：Wang, Qian; Zhao, Chen; Luo, Jing^*

来源：COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2022, 51(21): 7528-7546.

DOI：10.1080/03610926.2021.1873381

• Affiliation networks
• asymptotic normality
• consistency
• the probit model
• moment estimators

Affiliation network is a two-mode social network composed of two different groups of nodes (a group of actors and a group of social events) and the edge between nodes to represent the affiliation relationship between actors and social events. Although a number of statistical models are proposed to analyze affiliation networks, the probit distribution to model the degree heterogeneity of the affiliation networks are still unknown or have not been properly explored. In this paper, we use the probit distribution to model the degree heterogeneity of the affiliation networks and establish the uniform consistency and the asymptotic normality of the moment estimator when the number of actors and events both go to infinity. Simulation studies and a real data example demonstrate our theoretical results.