Abstract: Owing to the rapid development of social networking sites, the spatial autoregressive (SAR) model plays an important role in social network studies. However, the underlying structure of the SAR model implicitly assumes that all nodes (or actors or users) within the network have the same influential power, measured by the common autocorrelation parameter. Hence, the classical SAR model is unable to identify influential nodes. Therefore, we propose an adaptive SAR model that incorporates a network influence index, which includes the classical SAR model as a special case. Using the proposed model without imposing a specific error distribution, we apply the quasi-maximum likelihood approach to estimate the unknown parameters of the index. Then, we use these parameters to characterize the influential power of each node. We establish the asymptotic properties of the parameter estimates, and present three test statistics that we use to assess the homogeneity of the network influence indices. The usefulness of the adaptive SAR model and its associated network index is illustrated using simulation studies and an empirical investigation of the spillover effects in Chinese mutual fund cash flows.

Key words and phrases: Network influence, quasi-maximum likelihood estimation, spatial autoregressive model, weighted chi-squared test.