Mutual Influence Regression Model

TL;DR

This paper introduces the mutual influence regression model (MIR) that links actors' influence matrices to attribute-based similarity matrices, allowing for dynamic, heterogeneous influence structures with robust estimation and model selection methods.

Contribution

The paper develops the MIR model with novel estimation, selection, and testing procedures, extending spatial autoregressive models to handle time variation and endogenous influences.

Findings

The estimator is asymptotically normal without normality assumptions.

An extended BIC criterion effectively selects relevant matrices.

Simulation and real data validate the model's effectiveness.

Abstract

In this article, we propose the mutual influence regression model (MIR) to establish the relationship between the mutual influence matrix of actors and a set of similarity matrices induced by their associated attributes. This model is able to explain the heterogeneous structure of the mutual influence matrix by extending the commonly used spatial autoregressive model while allowing it to change with time. To facilitate making inferences with MIR, we establish parameter estimation, weight matrices selection and model testing. Specifically, we employ the quasi-maximum likelihood estimation method to estimate unknown regression coefficients, and demonstrate that the resulting estimator is asymptotically normal without imposing the normality assumption and while allowing the number of similarity matrices to diverge. In addition, an extended BIC-type criterion is introduced for selecting relevant matrices from the divergent number of similarity matrices. To assess the adequacy of the proposed model, we further propose an influence matrix test and develop a novel approach in order to obtain the limiting distribution of the test. Finally, we extend the model to accommodate endogenous weight matrices, exogenous covariates, and both individual and time fixed effects, to broaden the usefulness of MIR. The simulation studies support our theoretical findings, and a real example is presented to illustrate the usefulness of the proposed MIR model.