Zhao Jing, Pu Yue
Army Logistics Academy, Chong Qing, China.
Beijing Police College, Bei Jing, China.
PLoS One. 2025 Jul 1;20(7):e0327316. doi: 10.1371/journal.pone.0327316. eCollection 2025.
Spatial Autoregressive (SAR) models are widely used to analyze interactions among regions. However, the traditional model assumes a constant spatial autocorrelation coefficient, which fails to effectively capture spatial heterogeneity. To address this issue, we propose proposes a novel Spatial Single-Index Varying Coefficient Autoregressive (SSIVCAR) model. By introducing a single-index varying coefficient function, this model allows the spatial correlation strength to dynamically change with the characteristics of spatial units, thereby more accurately capturing spatial dependence relationships. To estimate the model parameters, we combine spline methods with two-stage least squares, and we assess the model's performance under finite sample conditions under Monte Carlo simulations. The simulation results show that the proposed model performs significantly better in capturing spatial heterogeneity and improving estimation accuracy. Finally, the model is applied to analyze the impact of digital economy development on environmental quality, and find that it has significant heterogeneous effects across different regions. This study provides a new framework for analyzing complex spatial dependence structures and offers valuable insights for regional governance policies.
空间自回归（SAR）模型被广泛用于分析区域间的相互作用。然而，传统模型假定空间自相关系数是恒定的，这无法有效捕捉空间异质性。为解决这一问题，我们提出了一种新颖的空间单指标变系数自回归（SSIVCAR）模型。通过引入单指标变系数函数，该模型允许空间相关强度随空间单元的特征动态变化，从而更准确地捕捉空间依赖关系。为估计模型参数，我们将样条方法与两阶段最小二乘法相结合，并在蒙特卡罗模拟下评估模型在有限样本条件下的性能。模拟结果表明，所提出的模型在捕捉空间异质性和提高估计精度方面表现显著更好。最后，该模型被应用于分析数字经济发展对环境质量的影响，并发现其在不同区域具有显著的异质性效应。本研究为分析复杂的空间依赖结构提供了一个新框架，并为区域治理政策提供了有价值的见解。
