Stochastic Actor Oriented Model with Random Effects

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.