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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

• •    

基于系数平均的混合地理加权回归模型的估计及其系数类型辨识

梅长林,   成佳媛,   续秋霞   

  1. 西安工程大学理学院，西安 710048
  • 收稿日期:2022-07-04 接受日期:2022-11-18 发布日期:2025-06-15
  • 基金资助:
    国家自然科学基金(11871056; 12271420).

Coefficient-average-based Estimation of Mixed Geographically Weighted Regression Models with the Identification of the Coefficient Types

MEI Changlin,  CHENG Jiayuan,  XU Qiuxia   

  1. School of Science, Xi'an Polytechnic University, Xi'an 710048
  • Received:2022-07-04 Accepted:2022-11-18 Published:2025-06-15
  • Supported by:
    The National Natural Science Foundation of China (11871056; 12271420).

摘要：

混合地理加权回归模型假定部分回归系数是常数，其余回归系数随空间位置变化，是综合探索自变量对因变量影响的空间变化特征的有力工具。以回归系数的局部线性地理加权估计为基础，提出了基于系数平均的混合地理加权回归模型的估计方法及其常值系数的Bootstrap检验方法。进一步将估计和检验方法推广到多类型系数混合地理加权回归模型的估计及其系数类型的辨识。模拟实验表明所提出的估计方法与现有的二步估计相比对空间变系数具有更高的估计精度，有关检验方法对辨识特殊类型系数具有满意的检验功效。最后，通过实例分析说明了所提估计和检验方法的具体应用。

关键词: 地理加权回归, 混合地理加权回归模型, 假设检验, Bootstrap方法

Abstract:

Mixed geographically weighted regression (MGWR) models, assuming that some regression coefficients are constant and the others are spatially varying, have been a powerful tool for comprehensively exploring spatial variation characteristics of impact of the exploratory variables on the response variable. Based on the local-linear geographically weighted regression estimators of the coefficients, we propose in this paper a coefficient-average-based estimation method for the MGWR models, on which a bootstrap test is formulated to identify constant coefficients in the models. In addition, the estimation and test methods are extended to the estimation of the multi-type MGWR models and the identification of special types of the coefficients. The simulation studies show that, compared with the existing two-step estimation of the MGWR models, the proposed estimation method can yield more accurate estimators for the spatially varying coefficients and the test method is of valid size and satisfactory power. A real-life example is finally given to demonstrate the applicability of the proposed estimation and test methods.

Key words: geographically weighted regression, mixed geographically weighted regression model, hypothesis testing, Bootstrap method

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