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.
翻译:在本条中,我们提出相互影响回归模型(MIR),以建立行为者相互影响矩阵与一组相关属性引发的相似矩阵之间的关系;这一模型能够通过扩展常用的空间自动递减模型来解释相互影响矩阵的不同结构,同时允许该模型随时间变化;为了便利与MIR进行推论,我们建立了参数估计、加权矩阵选择和模型测试;具体地说,我们采用准最大可能性估算方法来估计未知回归系数,并表明由此产生的估计值在不强加正常假设的情况下是绝对正常的,同时允许差异的相似矩阵数量;此外,还采用扩展的BIC型标准,从不同数量相似矩阵中选择相关矩阵;为了评估拟议模型的适足性,我们进一步提出影响矩阵测试,并制定新的方法,以获得测试的有限分布;最后,我们扩大模型,以适应内生重矩阵、外源变量以及个体和时间固定效应,从而扩大MIR的实用性。模拟研究为我们提出的理论结论和模型提供了支持。