Random Effects Models for Digraph Panel Data

Digraph panel data, corresponding to a given set of nodes and the directed graphs (digraphs) on the set of nodes which are observed at two or more discrete time points, are collected in the social sciences and other fields. Conventional models of digraph panel data assume that the data are discrete outcomes of a continuous-time Markov process on the set of possible digraphs defined on the set of nodes. Such models make the implicit assumption that all relevant knowledge with respect to nodes is observed in the form of covariates and correctly incorporated in the model, which may not be satisfied in applications. The present paper proposes Markov models which allow for unobserved heterogeneity across nodes by introducing random variables with unobserved outcomes, called random effects. To estimate parameters, maximum likelihood and Bayesian methods are proposed—using Markov chain Monte Carlo—and illustrated by an application to longitudinal social network data.