The stochastic actor oriented model (SAOM) is a method for modelling social interactions and social behaviour over time. It can be used to model network effects using both exogenous covariates and endogenous network configurations, but also the co-evolution of behaviour and social interactions. The estimation method mostly used is the Method of Moments (MoM). The model assumption that all individuals have the same evaluation function, however, is one of its limitations. The aim of this paper is to generalize the MoM estimation method for the SAOM to include random effects, so that the heterogeneity of individuals can be modelled more accurately. The linear evaluation function that models the probability of forming or removing a tie from the network, is decomposed in a fixed part, which is the current evaluation function of the SAOM, and a random part, with parameters that are individual-specific and random. The Robbins-Monro algorithm that is commonly used for MoM estimation in the SAOM, is extended to allow the estimation of the variance of the random parameters. We illustrate how for the model with random out-degree we can estimate the parameter of the random components, and how to test its significance. An application is made to Kapferer's Tailor shop dataset. It is shown that including a random out-degree constitutes a serious alternative to including various transitivity effects.
翻译:SAOM随机有向模型 (Stochastic Actor Oriented Model) 是一种用于建模社会互动和社会行为的方法,可用于使用外生协变量和内生网络配置来模拟网络效应,以及行为和社会互动的共同进化。该模型的估计方法通常使用矩估计法 (Method of Moments,MoM)。然而,该模型假设所有个体具有相同的评估功能,这是其局限之一。本文的目的是将SAOM的MoM估计方法推广到包括随机效应,从而可以更准确地建模个体间的异质性。将线性评估函数分解为固定部分(即SAOM的当前评估函数)和随机部分,其中随机参数是个体特定且随机的。通常用于MoM估计的Robbins-Monro算法被扩展以允许估计随机参数的方差。我们演示了如何估计具有随机出度的模型的随机部分参数,并说明了如何测试其显著性。我们将其应用到Kapferer的裁缝店数据集中。结果表明,包括随机出度是包括各种传递性效应的一个严肃的替代方案。