Understanding User Relationships in a Social Network: A Dyadic Interaction Modelling Approach

Individuals who are connected to each other in a network are more likely to exhibit similar behaviours. This implies that the formation of a dyadic link could be inferred from common factors shared by two nodes. In this study, we propose a varying coefficient dyadic interaction model with a random effect to understand user relationships in social networks. Specifically, we assume that the generation of a dyadic link is driven by an observed common factor. Owing to the existence of heterogeneity, we assume that the influence of the common factor is a linear combination of several moderate variables. Obtaining a maximum likelihood estimator in this situation is infeasible. To address this issue, we propose a pseudo‐maximum likelihood estimator, which is feasible and can substantially alleviate the computational cost. Although the proposed estimator is not as accurate as a maximum likelihood estimator, it can be used when heterogeneity exists or the sample size is extremely large. We then conduct numerical studies to assess the finite sample performance of the proposed method. Finally, to empirically examine the usefulness and practicality of the proposed method, we apply the model to two different real‐world datasets. The empirical results demonstrate the influence of common factors on dyadic link generation.