Inward and Outward Network Influence Analysis

TL;DR

This paper introduces the IONI model to measure and classify nodes in a network based on their influence exerted and received, providing a new framework for analyzing nodal heterogeneity with practical estimation and testing methods.

Contribution

The paper proposes a novel IONI model that separately quantifies inward and outward influence, enabling four-quadrant classification of nodes and offering estimation, testing, and model selection techniques.

Findings

Demonstrates the IONI model's effectiveness through simulations.

Shows the model's application in customer segmentation.

Provides asymptotic properties of estimators and model selection criteria.

Abstract

Measuring heterogeneous influence across nodes in a network is critical in network analysis. This paper proposes an Inward and Outward Network Influence (IONI) model to assess nodal heterogeneity. Specifically, we allow for two types of influence parameters; one measures the magnitude of influence that each node exerts on others (outward influence), while we introduce a new parameter to quantify the receptivity of each node to being influenced by others (inward influence). Accordingly, these two types of influence measures naturally classify all nodes into four quadrants (high inward and high outward, low inward and high outward, low inward and low outward, high inward and low outward). To demonstrate our four-quadrant clustering method in practice, we apply the quasi-maximum likelihood approach to estimate the influence parameters, and we show the asymptotic properties of the resulting estimators. In addition, score tests are proposed to examine the homogeneity of the two types of influence parameters. To improve the accuracy of inferences about nodal influences, we introduce a Bayesian information criterion that selects the optimal influence model. The usefulness of the IONI model and the four-quadrant clustering method is illustrated via simulation studies and an empirical example involving customer segmentation.