面向计数数据的时空地理加权泊松回归模型

doi:10.11947/j.AGCS.2025.20240502

测绘学报 ›› 2025, Vol. 54 ›› Issue (11): 2026-2039.doi: 10.11947/j.AGCS.2025.20240502

• 地图学与地理信息 • 上一篇

面向计数数据的时空地理加权泊松回归模型

吴超¹^,²^,³(), 梁咏翔¹, 岳瀚⁴, 崔远政⁵^,⁶, 黄波⁷()

^1.南京邮电大学物联网学院，江苏　南京　210023
^2.南京师范大学地理科学学院，江苏　南京　210023
^3.虚拟地理环境教育部重点实验室（南京师范大学），江苏　南京　210023
^4.广州大学地理科学与遥感学院公共安全地理信息分析中心，广东　广州　510006
^5.中国科学院南京地理与湖泊研究所，江苏　南京　211135
^6.湖泊与流域水安全全国重点实验室，江苏　南京　211135
^7.香港大学地理系，香港　999077

收稿日期:2024-12-10 修回日期:2025-09-23 发布日期:2025-12-15
通讯作者: 黄波 E-mail:chaowu@njupt.edu.cn;bohuang@hku.hk
作者简介:吴超（1992—），女，博士，副教授，研究方向为时空数据分析与建模。E-mail：chaowu@njupt.edu.cn
基金资助:
国家自然科学基金(42571485);国家重点研发计划(2022YFB3903700)

Geographically and temporally weighted Poisson regression for count data

Chao WU¹^,²^,³(), Yongxiang LIANG¹, Han YUE⁴, Yuanzheng CUI⁵^,⁶, Bo HUANG⁷()

^1.School of Internet of Things, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
^2.School of Geography, Nanjing Normal University, Nanjing 210023, China
^3.Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China
^4.Center of GeoInformatics for Public Security, School of Geography and Remote Sensing, Guangzhou University, Guangzhou 510006, China
^5.Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 211135, China
^6.State Key Laboratory of Lake and Watershed Science for Water Security, Nanjing 211135, China
^7.Department of Geography, The University of Hong Kong, Hong Kong 999077, China

Received:2024-12-10 Revised:2025-09-23 Published:2025-12-15
Contact: Bo HUANG E-mail:chaowu@njupt.edu.cn;bohuang@hku.hk
About author:WU Chao (1992—), female, PhD, associate professor, majors in spatio-temporal data analysis and modeling.　E-mail: chaowu@njupt.edu.cn
Supported by:
The National Natural Science Foundation of China(42571485);The National Key Research and Development Program of China(2022YFB3903700)

摘要/Abstract

摘要：

时空地理加权回归模型（GTWR）作为局部时空统计的核心方法，能够精准且灵活地捕捉数据中的时空异质性。然而，针对诸如犯罪数、病例数和交通事故数等具有非连续性和非正态性特征的计数数据时，传统的基于高斯分布的GTWR模型常面临预测不准确和模型设定不恰当等挑战。因此，本文将泊松回归方法融入GTWR模型框架，提出时空地理加权泊松回归模型（GTWPR），以适用于计数数据的建模和分析，并详细阐述基于局部似然估计的GTWPR模型拟合方法。为验证GTWPR模型的优越性，本文设计了3组模拟试验，结果显示GTWPR模型的拟合精度分别达到0.941、0.794和0.965，表明GTWPR模型在处理计数数据时能够有效刻画时空异质性，显著提升模型结果的准确性。最后，本文基于ZG市格网尺度下财产犯罪数据及其影响机制开展实证分析。结果表明，与地理加权泊松回归模型（GWPR）相比，GTWPR模型的拟合精度显著提升，该结果不仅验证了GTWPR模型在处理计数数据与时空异质性特征方面的显著优势，也体现了其解决实际问题的能力。综上，本文提出的GTWPR模型为犯罪学、公共卫生和交通安全等领域的计数数据应用提供了有力的统计工具，有助于揭示复杂时空数据中蕴含的深层次规律和机制。

关键词: 时空异质性, 计数数据, 泊松回归, 财产犯罪

Abstract:

Geographically and temporally weighted regression model (GTWR) serves as the core method for local spatio-temporal statistics, accurately and flexibly capturing spatio-temporal heterogeneity. However, the traditional Gaussian-based GTWR model encounters issues of inaccurate prediction and improper model setting when dealing with discontinuous and non-normal counting data, including the number of crimes, illnesses and traffic accidents. Therefore, the present study introduces the geographically and temporally weighted Poisson regression model (GTWPR) for modeling and analyzing count data, which integrates the Poisson regression method into the GTWR model framework. A detailed description of the GTWPR fitting method, based on local likelihood estimation, is provided. To validate the superiority of the GTWPR model, three simulation experiments were designed. The results show that the fitting accuracy of the GTWPR model reached 0.941, 0.794, and 0.965, respectively, which fully demonstrates that the GTWPR model effectively captures spatio-temporal heterogeneity and significantly improves the accuracy of modeling results for count data. Finally, an empirical analysis was conducted using property crime data and its influencing factors at the grid level in ZG city. The results indicate that, compared with the geographically weighted Poisson regression model (GWPR), the GTWPR model significantly improved the fitting accuracy. This outcome not only verifies the notable advantages of GTWPR in handling count data and spatio-temporal heterogeneity but also highlights its capability to address practical problems. In summary, the GTWPR model proposed in this study provides solid statistical support for applications of count data in fields such as criminology, public health, and traffic safety, and helps to uncover deeper patterns and mechanisms embedded in complex spatio-temporal data.

Key words: spatio-temporal heterogeneity, count data, Poisson regression, property crime

中图分类号:

P208

吴超, 梁咏翔, 岳瀚, 崔远政, 黄波. 面向计数数据的时空地理加权泊松回归模型[J]. 测绘学报, 2025, 54(11): 2026-2039.

Chao WU, Yongxiang LIANG, Han YUE, Yuanzheng CUI, Bo HUANG. Geographically and temporally weighted Poisson regression for count data[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(11): 2026-2039.

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模拟数据	R²			AICc			RMSE
模拟数据	PRM	GWPR	GTWPR	PRM	GWPR	GTWPR	PRM	GWPR	GTWPR
第1组	0.079	0.510	0.941	16 724.266	11 332.035	9 141.148	24.225	3.811	1.212
第2组	0.438	0.740	0.794	12 523.050	9 504.782	8 682.780	8.633	2.108	1.457
第3组	0.434	0.923	0.965	17 251.177	12 683.593	11 000.641	14.708	8.770	5.924

模拟数据	空间带宽		时间带宽
模拟数据	GWPR	GTWPR	GWPR	GTWPR
第1组	1.981	1.228	—	8.220
第2组	1.654	2.264	—	8.698
第3组	1.151	1.222	—	7.092

模拟数据	GWPR			GTWPR
模拟数据	的RMSE	的RMSE	的RMSE	的RMSE	的RMSE	的RMSE
第1组	1.326	1.707	0.777	0.084	1.115	0.018
第2组	0.365	0.469	1.273	0.728	0.111	0.617
第3组	2.125	2.096	4.549	1.599	1.412	2.914

变量	最大值	平均值	标准差
犯罪数量	388	9.205	19.518
酒吧数量	101	0.729	3.692
超市数量	36	2.106	4.091
便利店数量	37	1.558	3.927
公交站数量	47	2.661	4.677
地铁站数量	20	0.313	1.297
手机用户数量	119 094	6 506.450	11 217.486

模型	R²	RMSE	AICc	空间带宽	时间带宽
GTWPR	0.696	482.520	126 833.058	38.005	1.995
GWPR	0.597	484.635	137 274.457	40.004	—

面向计数数据的时空地理加权泊松回归模型

Geographically and temporally weighted Poisson regression for count data

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