NEWReduced Rank Multivariate Spatial Autoregressive Model for Large-scale Networks
2026-06-08
In spatial and social network analysis, multivariate spatial autoregressive (MSAR) models are effective tools for analyzing network data with multivariate responses. When the dimension of the response is divergent, however, the number of unknown parameters in an MSAR increases at a rate that is proportional to the square of the dimensionality, which poses significant challenges to the model estimation process. To address this issue, we propose a novel reduced-rank MSAR model by imposing a low-rank structure on the spatial influence matrix of the multivariate responses. The proposed model achieves substantial dimensionality reduction and offers insightful interpretations. To mitigate the high computational cost of the quasi-maximum likelihood estimator (QMLE), we propose a least squares estimator (LSE) for estimating the unknown parameters. Furthermore, we establish the asymptotic nature of the LSE when both the network size and the dimensionality of the responses diverge to infinity. To determine the rank, we propose an information criterion estimator and demonstrate the consistency of its rank selection process. Extensive numerical simulations validate the proposed model and parameter estimates. Finally, a dataset derived from Shouqianba, one of the largest aggregate payment platforms, is analyzed for illustration purposes.
