Ripley’s K函数方法修正与估计方法比较

葛莹; 刘尉; 李勇

doi:10.13203/j.whugis20210451

Ripley’s K函数方法修正与估计方法比较

doi: 10.13203/j.whugis20210451

葛莹¹,
刘尉²,
李勇¹

1. 河海大学地球科学与工程学院, 江苏南京, 210098;
2. 河海大学理学院, 江苏南京, 210098

基金项目:

国家自然科学基金项目(41071347)

云南省重大科技专项计划项目(202002AE090010)。

详细信息

作者简介:
葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

中图分类号: P2-0

Algorithm Modification and Estimation Comparison of Ripley’s K-function

1. School of Earth Sciences and Engineering, Hohai University, Nanjing 210098;
2. College of Science, Hohai University, Nanjing 210098

Funds:

The National Natural Science Foundation of China (41071347)

the Major Project of Science and Technology of Yunnan Province (202002AE090010).

摘要: 深入研究空间点格局分析方法，探讨Ripley’s K函数应用问题，梳理其边界效应改正的定义，综合考虑随机模拟动态性、参数定义合意性、边界改正算法可靠性，以判定各类边界改正算法的相对优劣。研究发现，蒙特卡洛模拟对空间点格局分析产生一定影响；受困于动态性难题，基于商业软件的空间点格局分析结论随着算法运行而改变，具有一定的不确定性；基于GIS技术的边界改正算法更具优势，它把矩形研究区一般性要求，推广至任意多边形，使Ripley’s K函数估计更稳健。
- 空间点格局分析 /
- Ripley’s K函数 /
- 蒙特卡洛模拟 /
- 边界效应改正 /
- GIS技术 /
- 柑橘植株营养 /
- 云南省新平县
Abstract: The Ripley’s K-function has widely been applied for many fields such as ecology, criminology, and geography. Because of the mathematical confusion of spatial point processes, the corresponding papers contain many errors in measuring the distributions of spatial objects. This paper contributes to an improved understanding for the application for Ripley’s K-function. The focus is first on the estimation methods of spatial point pattern analysis based on Ripley’s K-function. The formula of Ripley’s K-function is corrected, then various definitions of edge effect correction methods applied for the K-function analysis are detailed compared. The relative merits of various algorithm methods are identified by considering the dynamicity of random point pattern, the definition desirability of parameters, and estimation reliability of edge correction methods. The modified algorithms have been employed for the point pattern analysis of the fruit plants in Xinping County, Yunnan Province. The results show: the number of Monte Carlo simulations has a great influence over the analysis of the observed point patterns. Trapped in the dynamicity problems, significance tests of observed patterns are changed that is responsible for changes in Ripley’s K-function measures with uncertainty as ArcGIS software package running. There are advantages of modified algorithms of edge effect correction, the rectangle of study areas is generally extended to complex shape that is robust enough.
- spatial point pattern analysis /
- Ripley’s K-function /
- Monte Carlo simulations /
- edge effect correction /
- GIS functionality /
- citrus plant nutrition /
- Xinping County of Yunnan Province

[1]	Besag J. Discussion of Dr Ripley’s Paper [J]. Journal of the Royal Statistical Society: Series B. 1977, 39: 193-195
[2]	Ripley B D. Tests of ‘Randomness’ for Spatial Point Patterns[J]. Journal of the Royal Statistical Society: Series B (Methodological), 1979, 41(3): 368-374
[3]	Getis A. Interaction Modeling Using Second-Order Analysis[J]. Environment and Planning A: Economy and Space, 1984, 16(2): 173-183
[4]	McIntire E J B, Fajardo A. Beyond Description: The Active and Effective Way to Infer Processes from Spatial Patterns[J]. Ecology, 2009, 90(1): 46-56
[5]	Sweeney S H, Feser E J. Plant Size and Clustering of Manufacturing Activity[J]. Geographical Analysis, 2010, 30(1): 45-64
[6]	Marcon E, Puech F. Evaluating the Geographic Concentration of Industries Using DistanceBased Methods[J]. Journal of Economic Geography, 2003, 3(4): 409-428
[7]	Barff R A. Industrial Clustering and the Organization of Production: A Point Pattern Analysis of Manufacturing in Cincinnati, Ohio[J]. Annals of the Association of American Geographers, 1987, 77(1): 89-103
[8]	Arbia G, Espa G, Quah D. A Class of Spatial Econometric Methods in the Empirical Analysis of Clusters of Firms in the Space[J]. Empirical Economics, 2008, 34(1): 81-103
[9]	Ge Y, Pu Y X, Sun M D. Alternative Measure of Border Effects across Regions: Ripley's K-Function Method[J]. Papers in Regional Science, 2021, 100(1): 287-302
[10]	Perry G L W, Miller B P, Enright N J. A Comparison of Methods for the Statistical Analysis of Spatial Point Patterns in Plant Ecology[J]. Plant Ecology, 2006, 187(1): 59-82
[11]	Law R, Illian J, Burslem D F R P, et al. Ecological Information from Spatial Patterns of Plants: Insights from Point Process Theory[J]. Journal of Ecology, 2009, 97(4): 616-628
[12]	Gottwald T R, Sun X A, Riley T, et al. Geo-Referenced Spatiotemporal Analysis of the Urban Citrus Canker Epidemic in Florida[J]. Phytopathology, 2002, 92(4): 361-377
[13]	Polonsky J A, Martínez-Pino I, Nackers F, et al. Descriptive Epidemiology of Typhoid Fever during an Epidemic in Harare, Zimbabwe, 2012[J]. PLoS One, 2014, 9(12): e114702
[14]	Yamada I, Rogerson P. An Empirical Comparison of Edge Effect Correction Methods Applied to K -Function Analysis[J]. Geographical Analysis, 2003, 35(2): 97-109
[15]	Ripley B D. The Second-Order Analysis of Stationary Point Processes[J]. Journal of Applied Probability, 1976, 13(2): 255-266
[16]	Ripley B D. Modelling Spatial Patterns[J]. Journal of the Royal Statistical Society: Series B (Methodological), 1977, 39(2): 172-192
[17]	Ripley B D. The analysis of geographical maps[M]// Exploratory and explanatory statistical analysis of spatial data. Dordrecht: Springer, 1979: 53-72
[18]	Ripley B D. Spatial Statistics [M]. New York: Willey, 1981
[19]	Diggle P J. Statistical Methods for Spatial Point Patterns in Ecology [J]. Spatial and Temporal Analysis in Ecology, 1979, 95-150
[20]	Besag J, Diggle P J. Simple Monte Carlo Tests for Spatial Pattern[J]. Applied Statistics, 1977, 26(3): 327
[21]	Getis A. second-Order Analysis of Point Patterns: The Case of Chicago as a multi-Center Urban Region[J]. The Professional Geographer, 1983, 35(1): 73-80
[22]	Cliff A D, Ord J K. Spatial Processes – Models and Applications [M]. London: Pion, 1981
[23]	Hope A C A. A Simplified Monte Carlo Significance Test Procedure[J]. Journal of the Royal Statistical Society: Series B (Methodological), 1968, 30(3): 582-598
[24]	Ripley B D, Silverman B W. Quick Tests for Spatial Interaction[J]. Biometrika, 1978, 65(3): 641-642
[25]	Diggle P J. Statistical Analysis of Spatial Point Patterns [M]. London: Academic Press, 1983
[26]	Haase P. Spatial Pattern Analysis in Ecology Based on Ripley's K-Function: Introduction and Methods of Edge Correction[J]. Journal of Vegetation Science, 1995, 6(4): 575-582
[27]	Griffith D A. The Boundary Value Problem in Spatial Statistical Analysis[J]. Journal of Regional Science, 1983, 23(3): 377-387
[28]	Diggle P J. Statistical Analysis of Spatial Point Patterns (2nd ed) [M]. London, UK: Arnold, 2003
[29]	Wiegand T, Moloney K A. Rings, Circles, and Null-Models for Point Pattern Analysis in Ecology[J]. Oikos, 2004, 104(2): 209-229
[30]	Upton G, Fingleton B. Spatial Data Analysis by Example. Volume 1: Point Pattern and Quantitative Data [M]. New York, NY: J. Wiley & Sons, 1985
[31]	Sterner R W, Ribic C A, Schatz G E. Testing for Life Historical Changes in Spatial Patterns of Four Tropical Tree Species[J]. The Journal of Ecology, 1986, 74(3): 621
[32]	Szwagrzyk J, Czerwczak M. Spatial Patterns of Trees in Natural Forests of East-Central Europe[J]. Journal of Vegetation Science, 1993, 4(4): 469-476
[33]	Getis A, Franklin J. Second-Order Neighborhood Analysis of Mapped Point Patterns[M]// Perspectives on Spatial Data Analysis. Berlin, Heidelberg: Springer, 2010: 93-100
[34]	Goreaud F, Pélissier R. On Explicit Formulas of Edge Effect Correction for Ripley's K - Function[J]. Journal of Vegetation Science, 1999, 10(3): 433-438
[35]	Ge Y, Sun M D, Pu Y X. Geographic Information System-Based Edge Effect Correction for Ripley's K -Function under Irregular Boundaries[J]. Geographical Research, 2019, 57(4): 436-447
[36]	Anselin L. Local Indicators of Spatial Association-LISA[J]. Geographical Analysis, 2010, 27(2): 93-115

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Ripley’s K函数方法修正与估计方法比较

doi: 10.13203/j.whugis20210451

作者简介:
葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

Algorithm Modification and Estimation Comparison of Ripley’s K-function

计量

Ripley’s K函数方法修正与估计方法比较

doi: 10.13203/j.whugis20210451

1. 河海大学地球科学与工程学院, 江苏南京, 210098;

2. 河海大学理学院, 江苏南京, 210098

作者简介:
葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

English Abstract

Algorithm Modification and Estimation Comparison of Ripley’s K-function

1. School of Earth Sciences and Engineering, Hohai University, Nanjing 210098;

2. College of Science, Hohai University, Nanjing 210098

全文HTML

目录

留言板

Ripley’s K函数方法修正与估计方法比较

doi: 10.13203/j.whugis20210451

作者简介: 葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

Algorithm Modification and Estimation Comparison of Ripley’s K-function

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出版历程

Ripley’s K函数方法修正与估计方法比较

doi: 10.13203/j.whugis20210451

1. 河海大学地球科学与工程学院, 江苏 南京, 210098; 2. 河海大学理学院, 江苏 南京, 210098

作者简介: 葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

English Abstract

Algorithm Modification and Estimation Comparison of Ripley’s K-function

1. School of Earth Sciences and Engineering, Hohai University, Nanjing 210098; 2. College of Science, Hohai University, Nanjing 210098

全文HTML

目录

作者简介:
葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

1. 河海大学地球科学与工程学院, 江苏南京, 210098;

2. 河海大学理学院, 江苏南京, 210098

作者简介:
葛莹,博士,教授,主要从事空间数据分析研究。Email:geying@hhu.edu.cn

1. School of Earth Sciences and Engineering, Hohai University, Nanjing 210098;

2. College of Science, Hohai University, Nanjing 210098