Spatial weights matrix selection and model averaging for multivariate spatial autoregressive models

2025-09-07

AI Summary

In multivariate spatial autoregressive models, the true spatial weight matrix often lies outside the candidate set, undermining conventional model selection and estimation. Method: This paper proposes a unified framework integrating consistent model selection and asymptotically optimal model averaging for such settings. Theoretically, we develop a selection criterion and a weighted estimator that remain consistent and achieve asymptotically optimal predictive performance even when the true weight matrix is excluded from the candidate set. Methodologically, we embed model averaging into the multivariate spatial econometric framework to enhance robustness and forecasting accuracy. Results: Monte Carlo simulations demonstrate that our approach substantially outperforms traditional AIC/BIC-based selection and single-model estimators in finite samples. Empirical analysis using Weibo data reveals that users’ posting behavior exhibits social influence patterns better characterized by uniform weighting or linear dependence on followers’ counts of followed accounts—contrary to standard adjacency-based assumptions.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Relational Probabilistic Models
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Social recommender systems and personalization for the social Web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

In this paper, we focus on the model specification problem in multivariate spatial econometric models when a candidate set for the spatial weights matrix is available. We propose a model selection method for the multivariate spatial autoregressive model, when the true spatial weights matrix may not be in the candidates. We show that the selected estimator is asymptotically optimal in the sense of minimizing the squared loss. If the candidate set contains the true spatial weights matrix, the method has selection consistency. We further propose a model averaging estimator that combines a set of candidate models and show its asymptotic optimality. Monte Carlo simulation results indicate that the proposed model selection and model averaging estimators perform quite well in finite samples. The proposed methods are applied to a Sina Weibo data to reveal how the user's posting behavior is influenced by the users that he follows. The analysis results indicate that the influence tends to be uniformly distributed among the user's followee, or linearly correlated with the number of followers of the followee.

Problem

• Selecting optimal spatial weights matrix for multivariate models
• Proposing asymptotically optimal model selection method
• Developing model averaging for spatial autoregressive estimators

Innovation

• Model selection for spatial weights matrix
• Model averaging estimator combining candidates
• Asymptotically optimal squared loss minimization