Continuous-Time Modeling of Panel Data with Network Structure
In some panel data studies, respondents are nested in social contexts, like classrooms or organizations. The social relations, such as friendship or collaboration, between the individuals in such contexts can be represented by social networks. Like individual outcomes (e.g., behavior or performance), the social relations between individuals are not static. Social networks and individual outcomes change over time and can mutually affect each other. In this chapter, we present a statistical model to study the interdependent dynamics (or coevolution) of network structure and individual outcomes. We assume panel observations of networks and individual attributes to be the discrete-time realizations of an underlying continuous-time process, which is modeled by a stochastic differential equation for the attribute dynamics and a Markov chain model for the network dynamics. We illustrate the proposed method by a study of the coevolution of friendship ties and mathematics grades among 1160 students in 39 classrooms.
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