Understanding network influence and its determinants are key challenges in political science and network analysis. Traditional latent variable models position actors within a social space based on network dependencies but often do not elucidate the underlying factors driving these interactions. To overcome this limitation, we propose the Social Influence Regression (SIR) model, an extension of vector autoregression tailored for relational data that incorporates exogenous covariates into the estimation of influence patterns. The SIR model captures influence dynamics via a pair of $n \times n$ matrices that quantify how the actions of one actor affect the future actions of another. This framework not only provides a statistical mechanism for explaining actor influence based on observable traits but also improves computational efficiency through an iterative block coordinate descent method. We showcase the SIR model's capabilities by applying it to monthly conflict events between countries, using data from the Integrated Crisis Early Warning System (ICEWS). Our findings demonstrate the SIR model's ability to elucidate complex influence patterns within networks by linking them to specific covariates. This paper's main contributions are: (1) introducing a model that explains third-order dependencies through exogenous covariates and (2) offering an efficient estimation approach that scales effectively with large, complex networks.

翻译：理解网络影响力及其决定因素是政治学与网络分析领域的核心挑战。传统潜变量模型基于网络依赖关系将行动者置于社会空间中，但往往未能阐明驱动这些交互的潜在因素。为克服这一局限性，我们提出社会影响力回归模型，该模型是针对关系数据定制的向量自回归扩展，将外生协变量纳入影响力模式的估计中。SIR模型通过一对$n \times n$矩阵捕捉影响力动态，这些矩阵量化了一个行动者的行为如何影响另一个行动者的未来行为。该框架不仅提供了基于可观测特征解释行动者影响力的统计机制，还通过迭代块坐标下降法提升了计算效率。我们通过将其应用于国家间月度冲突事件（使用综合危机早期预警系统的数据）来展示SIR模型的能力。研究结果表明，SIR模型能够通过将复杂影响力模式与特定协变量相关联，阐明网络内的这些模式。本文的主要贡献在于：（1）提出通过外生协变量解释三阶依赖关系的模型；（2）提供可有效扩展至大型复杂网络的高效估计方法。