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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2023, Vol. 40 ›› Issue (6): 896-908.doi: 10.3969/j.issn.1005-3085.2023.06.004

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具有自适应权矩阵的空间滞后模型：权矩阵构造及模型估计

梅长林,  王  琪,  续秋霞   

  1. 西安工程大学理学院，西安 710048
  • 收稿日期:2021-05-01 接受日期:2021-07-30 出版日期:2023-12-15 发布日期:2024-02-15
  • 基金资助:
    国家自然科学基金项目 (11871056).

Spatial Lag Models with an Adaptive Weight Matrix: Weight Matrix Construction and Model Estimation

MEI Changlin,  WANG Qi,  XU Qiuxia   

  1. School of Science, Xi'an Polytechnic University, Xi'an 710048
  • Received:2021-05-01 Accepted:2021-07-30 Online:2023-12-15 Published:2024-02-15
  • Supported by:
    The National Natural Science Foundation of China (11871056).

摘要：

在空间计量经济模型中，空间权矩阵的设置对模型的估计结果有重要影响，如何确定合理的空间权矩阵一直是空间数据建模中的重要问题之一。为此，构造了一种具有更好自适应性和可解释性的含调节参数的距离衰减空间权矩阵，建立了一种具有新的空间滞后项的空间滞后模型及其最大似然估计方法。进一步，通过模拟实验和实例分析说明了最大似然估计的精确性以及所构造的空间权矩阵在拟合因变量空间自相关性方面的有效性。

关键词: 空间自相关, 空间权矩阵, 空间滞后模型, 最大似然估计

Abstract:

In spatial econometric models, the specification of the spatial weight matrix is of notable influence on the model estimation result. Therefore, how to specify a reasonable spatial weight matrix has long been one of the important issues in spatial data modeling. In this article, we construct a distance decaying spatial weight matrix with a controlling parameter. This spatial weight matrix has better adaptability and interpretability. Based on the constructed spatial weight matrix, a new spatial lag model is proposed and its maximum likelihood estimation procedure is formulated. Furthermore, a simulation study and real-life data analysis are conducted. The results demonstrate that the maximum likelihood estimation of the new model performs well in estimating the model parameters and the constructed spatial weight matrix can efficiently fit the spatial autocorrelation among the observations of dependent variables.

Key words: spatial autocorrelation, spatial weight matrix, spatial lag model, maximum likelihood estimation

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