The stochastic actor oriented model (SAOM) is a method for modelling social interactions and social behaviour over time. It can be used to model drivers of dynamic interactions using both exogenous covariates and endogenous network configurations, but also the co-evolution of behaviour and social interactions. In its standard implementations, it assumes that all individual have the same interaction evaluation function. This lack of heterogeneity is one of its limitations. The aim of this paper is to extend the inference framework for the SAOM to include random effects, so that the heterogeneity of individuals can be modeled more accurately. We decompose the linear evaluation function that models the probability of forming or removing a tie from the network, in a homogeneous fixed part and a random, individual-specific part. We extend the Robbins-Monro algorithm to the estimation of the variance of the random parameters. Our method is applicable for the general random effect formulations. We illustrate the method with a random out-degree model and show the parameter estimation of the random components, significance tests and model evaluation. We apply the method to the Kapferer's Tailor shop study. It is shown that a random out-degree constitutes a serious alternative to including transitivity and higher-order dependency effects.

翻译：随机行为者导向模型（Stochastic Actor Oriented Model, SAOM）是一种对社交互动及其随时间演变行为进行建模的方法。它既能利用外生协变量和内生网络结构模拟动态互动的驱动因素，也能刻画行为与社交互动的协同演化过程。在标准实现中，该模型假设所有个体具有相同的互动评估函数，这种同质性假设是其局限性之一。本文旨在扩展SAOM的推断框架以纳入随机效应，从而更精确地刻画个体异质性。我们将用于建模网络中关系建立或断裂概率的线性评估函数分解为同质性固定部分与个体特异性随机部分，并将Robbins-Monro算法扩展至随机参数方差估计。该方法适用于一般形式的随机效应设定。通过随机出度模型进行实证分析，我们展示了随机成分的参数估计、显著性检验及模型评估，并将该方法应用于Kapferer裁缝店研究案例。结果表明，随机出度效应可作为包含传递性及高阶依赖效应的有效替代方案。