Mutual Influence Regression Model

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