Inferring network properties from fixed-choice design with strong and weak ties

Studies of networked systems typically begin by obtaining information about the network structure. In many settings it is impractical or impossible to directly observe the network, and sampling is used. Sampling the structure of offline social networks is especially costly and time-consuming. Respondents are asked to name close friends and acquaintances (strong and weak ties). However, because a person may have a large number of acquaintances, surveys use a fixed-choice design where respondents are asked to name a small, fixed number of their weak ties. Surprisingly, studies based on fixed-choice designs then directly use the network derived from the responses without correcting for the bias introduced by fixed-choice sampling. In this paper we demonstrate how to account for fixed-choice sampling when inferring network characteristics. Our approach is based on the generalized method of moments. We verify the accuracy of our results via simulation and discuss immediate applications and consequences of our work to existing results.