Abstract: The rapid development of social networks has resulted in an increase in the use of the spatial autoregression model with covariates. However, traditional estimation methods, such as the maximum likelihood estimation, are practically infeasible if the network size n is very large. Here, we propose a novel estimation approach, that reduces the computational complexity from O(n³) to O(n). This approach is developed by ignoring the endogeneity issue induced by network dependence. We show that the resulting estimator is consistent and asymptotically normal under certain conditions. Extensive simulation studies are presented to demonstrate its finite-sample performance, and a real social network data set is analyzed for illustration purposes.

Key words and phrases: Maximum likelihood estimator, naive least squares estimator, social network analysis, spatial autoregression model.