Abstract: An interesting problem in social network analysis is whether individuals' behaviors or opinions spread from one to another, which is known as social influence. The degrees of influence describes how far the influence passes through individuals. Here, we explore the degrees of influence in dynamic networks. We build a longitudinal influence model to specify how people's behaviors are influenced by others in a dynamic network. In order to determine the degrees of influence, we propose a sequential hypothesis testing procedure and use generalized estimating equations to account for multiple observations of the same individual across different time points. In addition, we show that the power of our proposed test goes to one as the network size goes to infinity. We illustrate the performance of our proposed method using simulation studies and real-data analyses.

Key words and phrases: Degrees of influence, dynamic network, generalized esti- mating equations, longitudinal analysis, social influence.