Grouped spatial autoregressive model

With the development of the internet, network data with replications can be collected at different time points. The spatial autoregressive panel (SARP) model is a useful tool for analyzing such network data. However, in the traditional SARP model, all individuals are assumed to be homogeneous in their network autocorrelation coefficients, while in practice, correlations could differ for the nodes in different groups. Here, a grouped spatial autoregressive (GSAR) model based on the SARP model is proposed to permit network autocorrelation heterogeneity among individuals, while analyzing network data with independent replications across different time points and strong spatial effects. Each individual in the network belongs to a latent specific group, which is characterized by a set of parameters. Two estimation methods are studied: two-step naive least-squares estimator, and two-step conditional least-squares estimator. Furthermore, their corresponding asymptotic properties and technical conditions are investigated. To demonstrate the performance of the proposed GSAR model and its corresponding estimation methods, numerical analysis was performed on simulated and real data.