Geographically and temporally weighted Poisson regression for count data

doi:10.11947/j.AGCS.2025.20240502

Abstract

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

CLC Number:

P208

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	—