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：随机行动者导向模型(SAOM)是一种对随时间变化的社会互动与行为进行建模的方法。该模型既可利用外生协变量和内生网络构型来建模动态互动的驱动因素，也可用于行为与社会互动的协同演化分析。在标准实现中，该模型假设所有个体具有相同的互动评价函数——这种同质性假设是其主要局限之一。本文旨在将SAOM的推断框架扩展至包含随机效应，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撤销概率的线性评价函数，分解为同质性固定部分与个体特异性的随机部分，并扩展Robbins-Monro算法以估计随机参数的方差。该方法适用于一般随机效应设定。我们通过随机出度模型展示该方法的实现，并给出随机分量的参数估计、显著性检验及模型评估。将该方法应用于Kapferer裁缝店案例研究，结果表明随机出度结构可作为包含传递性及高阶依赖效应的严肃替代方案。