Regression Modeling of the Count Relational Data with Exchangeable Dependencies

TL;DR

This paper introduces a flexible latent multiplicative Poisson model for count relational data with exchangeable dependencies, enabling effective inference of network effects in social science applications.

Contribution

It develops a novel latent Poisson model with exchangeable errors for count relational data, along with a consistent pseudo-likelihood estimator for regression coefficients.

Findings

Model captures various network effects through exchangeable error dependence.

Estimator demonstrates consistency and asymptotic normality.

Application reveals significant network effects in gift exchange behaviors.

Abstract

Relational data characterized by directed edges with count measurements are common in social science. Most existing methods either assume the count edges are derived from continuous random variables or model the edge dependency by parametric distributions. In this paper, we develop a latent multiplicative Poisson model for relational data with count edges. Our approach directly models the edge dependency of count data by the pairwise dependence of latent errors, which are assumed to be weakly exchangeable. This assumption not only covers a variety of common network effects, but also leads to a concise representation of the error covariance. In addition, the identification and inference of the mean structure, as well as the regression coefficients, depend on the errors only through their covariance. Such a formulation provides substantial flexibility for our model. Based on this, we propose a pseudo-likelihood based estimator for the regression coefficients, demonstrating its consistency and asymptotic normality. The newly suggested method is applied to a food-sharing network, revealing interesting network effects in gift exchange behaviors.