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Doğrusal Ağlarda Tam Mekânsal Rastgeleliğin Test Edilmesi: Leon County Trafik Kazası Örneği

Year 2022, Volume: 43 Issue: 4, 769 - 776, 27.12.2022

Idris Demirsoy

https://doi.org/10.17776/csj.1120685

Abstract

Nokta süreçlerinin incelenmesi ve uzamsal nokta modellerini içeren verilerin analizi, uzun bir geçmişe ve geniş bir literatüre sahip konumsal istatistikte önemli konulardır. Bunun içinde nispeten yeni bir alt alan, doğrusal ağlar üzerindeki nokta süreçlerinin istatistiksel analizidir, yani uzayda rastgele meydana gelen ancak doğrusal bir ağ üzerinde uzanmak için kısıtlı konumlara sahip olayların süreçleri. Örneğin, trafik kazaları, bir sokak ağı üzerinde yer almakla sınırlandırılmış rastgele konumlarda meydana gelir. Diğer örnekler, nehir ağlarında veya nöron ağlarında meydana gelen olayları içerir. Tüm bu durumlarda ağlar, düzlemde veya üç boyutlu uzayda bir doğru parçaları ağı olarak idealleştirilir. Doğrusal ağlarda nokta süreçlerinin analizi için istatistiksel tekniklerin geliştirilmesi henüz emekleme aşamasındadır. Nokta süreçlerini analiz etmek için birçok standart istatistiksel teknik, doğrusal ağlardan kaynaklanan verilere doğrudan uygulanamaz ve uygun modifikasyon gerektirir. Kuadrat sayılarına veya en yakın komşulara dayalı düzlemdeki nokta süreçleri için Tam Konumsal Rastgelelik Testi (CSR), doğrusal ağlardaki nokta süreçlerine uygulanamaz. Bu makale, Öklid mesafesi yerine ağ ile birlikte en kısa yol mesafesini kullanan doğrusal ağın bir Voronoi mozaiklemesini tanımlar ve ardından bu mozaiklemenin döşemelerindeki olay sayılarına dayalı olarak doğrusal ağlar için bir ki-kare CSR testi geliştirir. Bu test, ABD, Florida, Leon County'deki trafik kazalarına ilişkin verilere uygulandı.

Keywords

Mekansal İstatistik Nokta Modeli Tam Mekansal Rastgelelik Doğrusal Ağ Spatial statistics Point pattern Complete spatial randomness Linear network.

References

  • [1] Moller J., Waagepetersen R. P., Statistical Inference and Simulation for Spatial Point Processes, Chapman and Hall/CRC, (2004).
  • [2] Illian J., Penttinen A., Stoyan H., Stoyan D., Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley & Sons, (2008).
  • [3] Diggle P. J., Besag J., Gleaves J. T., Statistical Analysis of Spatial Point Patterns by Means of Distance Methods, Biometrics, (1976) 659-667.
  • [4] Ripley Brian D., Tests of ‘randomness' for Spatial Point Patterns, Journal of the Royal Statistical Society: Series B (Methodological), 41(3) (1979) 368-374.
  • [5] Assuncao R., Testing Spatial Randomness by Means of Angles, Biometrics, (1994) 531-537.
  • [6] Perry J. N., Spatial Analysis by Distance Indices, Journal of Animal Ecology, (1995) 303-314.
  • [7] Chang X., Test of Complete Spatial Randomness on Networks, Master Thesis, University of Minnesota, (2016).
  • [8] Okabe A., Sugihara K., Spatial Analysis Along Networks: Statistical and Computational Methods, John Wiley & Sons, (2012).
  • [9] Ang Q. W., Baddeley A., and Nair G., Geometrically Corrected Second Order Analysis of Events on A Linear Network, With Applications to Ecology And Criminology, Scandinavian Journal of Statistics, 39(4) (2012) 591–617.
  • [10] Moradi M. M., Cronie O., Rubak E., Lachieze-Rey R., Mateu J., and Baddeley A., Resample-Smoothing of Voronoi Intensity Estimators, Statistics and Computing, 29(5) (2019) 995-1010.
  • [11] McSwiggan G., Baddeley A., and Nair G., Kernel Density Estimation on A Linear Network, Scandinavian Journal of Statistics, 44(2) (2017) 324–345.
  • [12] Lu Y., and Chen X., On the False Alarm of Planar K-Function When Analyzing Urban Crime Distributed Along Streets, Social Science Research, 36(2) (2007) 611–632.
  • [13] Kent J., Leitner M., and Curtis A., Evaluating the Usefulness of Functional Distance Measures When Calibrating Journey-To-Crime Distance Decay Functions, Computers, Environment and Urban Systems, 30(2) (2006) 181–200.
  • [14] Cressie N., Statistics for Spatial Data, Terra Nova, (1992).
  • [15] Diggle P. J., Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Chapman and Hall/CRC, (2013).
  • [16] Bailey T. C., and Gatrell A. C., Interactive Spatial Data Analysis, Volume 413, Longman Scientific & Technical Essex, (1995).
  • [17] Shiode S., Analysis of a Distribution of Point Events Using the Network-Based Quadrat Method, Geographical Analysis, 40(4) (2008) 380–400.
  • [18] Okabe A., Boots B., Sugihara K., and Chiu S. N., Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Series in Probability and Statistics. John Wiley and Sons, Inc., 2nd ed., (2000).
  • [19] Chiu S., Spatial Point Pattern Analysis by Using Voronoi Diagrams and Delaunay Tessellations–A Comparative Study. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 45(3) (2003) 367–376.
  • [20] Demirsoy I., Estimating the Intensity of Point Processes on Linear Networks, PhD thesis, Florida State University, 2020.
  • [21] R Core Team. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, (2020).
  • [22] Esri Redlands. ArcGIS Desktop: Release 10, Environmental Systems Research Institute, CA (2011).
  • [23] Baddeley Adrian, and Rolf Turner, Spatstat: An R Package for Analyzing Spatial Point Patterns, Journal of Statistical Software, 12 (2005) 1-42.

Testing Complete Spatial Randomness on Linear Networks: Leon County Traffic Accident Example

Year 2022, Volume: 43 Issue: 4, 769 - 776, 27.12.2022

Idris Demirsoy

https://doi.org/10.17776/csj.1120685

Abstract

A relatively new sub-area within this is the statistical analysis of point processes on linear networks, that is, processes of events occurring randomly in space but with locations constrained to lie on a linear network. For example, traffic accidents occur at random locations constrained to lie on a network of streets. In this case, the network is idealized as a network of line segments in the plane or three-dimensional space. The development of statistical techniques for the analysis of point processes on linear networks is still in its infancy. Many standard statistical techniques for analyzing point processes cannot be directly applied to data arising from linear networks and require suitable modification. Test of Complete Spatial Randomness (CSR) for point processes on the plane based on quadrat counts or nearest neighbors cannot be applied to point processes on linear networks. This paper defines a Voronoi tessellation of the linear network which uses the shortest path distance along the network instead of Euclidean distance, and then develops a chi-square test of CSR for linear networks based on the event counts in the tiles of this tessellation. This test is applied to data on traffic accidents in Leon County, Florida, USA.

Keywords

Spatial statistics Point pattern Complete spatial randomness Linear network.

References

  • [1] Moller J., Waagepetersen R. P., Statistical Inference and Simulation for Spatial Point Processes, Chapman and Hall/CRC, (2004).
  • [2] Illian J., Penttinen A., Stoyan H., Stoyan D., Statistical Analysis and Modelling of Spatial Point Patterns, John Wiley & Sons, (2008).
  • [3] Diggle P. J., Besag J., Gleaves J. T., Statistical Analysis of Spatial Point Patterns by Means of Distance Methods, Biometrics, (1976) 659-667.
  • [4] Ripley Brian D., Tests of ‘randomness' for Spatial Point Patterns, Journal of the Royal Statistical Society: Series B (Methodological), 41(3) (1979) 368-374.
  • [5] Assuncao R., Testing Spatial Randomness by Means of Angles, Biometrics, (1994) 531-537.
  • [6] Perry J. N., Spatial Analysis by Distance Indices, Journal of Animal Ecology, (1995) 303-314.
  • [7] Chang X., Test of Complete Spatial Randomness on Networks, Master Thesis, University of Minnesota, (2016).
  • [8] Okabe A., Sugihara K., Spatial Analysis Along Networks: Statistical and Computational Methods, John Wiley & Sons, (2012).
  • [9] Ang Q. W., Baddeley A., and Nair G., Geometrically Corrected Second Order Analysis of Events on A Linear Network, With Applications to Ecology And Criminology, Scandinavian Journal of Statistics, 39(4) (2012) 591–617.
  • [10] Moradi M. M., Cronie O., Rubak E., Lachieze-Rey R., Mateu J., and Baddeley A., Resample-Smoothing of Voronoi Intensity Estimators, Statistics and Computing, 29(5) (2019) 995-1010.
  • [11] McSwiggan G., Baddeley A., and Nair G., Kernel Density Estimation on A Linear Network, Scandinavian Journal of Statistics, 44(2) (2017) 324–345.
  • [12] Lu Y., and Chen X., On the False Alarm of Planar K-Function When Analyzing Urban Crime Distributed Along Streets, Social Science Research, 36(2) (2007) 611–632.
  • [13] Kent J., Leitner M., and Curtis A., Evaluating the Usefulness of Functional Distance Measures When Calibrating Journey-To-Crime Distance Decay Functions, Computers, Environment and Urban Systems, 30(2) (2006) 181–200.
  • [14] Cressie N., Statistics for Spatial Data, Terra Nova, (1992).
  • [15] Diggle P. J., Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Chapman and Hall/CRC, (2013).
  • [16] Bailey T. C., and Gatrell A. C., Interactive Spatial Data Analysis, Volume 413, Longman Scientific & Technical Essex, (1995).
  • [17] Shiode S., Analysis of a Distribution of Point Events Using the Network-Based Quadrat Method, Geographical Analysis, 40(4) (2008) 380–400.
  • [18] Okabe A., Boots B., Sugihara K., and Chiu S. N., Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, Series in Probability and Statistics. John Wiley and Sons, Inc., 2nd ed., (2000).
  • [19] Chiu S., Spatial Point Pattern Analysis by Using Voronoi Diagrams and Delaunay Tessellations–A Comparative Study. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 45(3) (2003) 367–376.
  • [20] Demirsoy I., Estimating the Intensity of Point Processes on Linear Networks, PhD thesis, Florida State University, 2020.
  • [21] R Core Team. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, (2020).
  • [22] Esri Redlands. ArcGIS Desktop: Release 10, Environmental Systems Research Institute, CA (2011).
  • [23] Baddeley Adrian, and Rolf Turner, Spatstat: An R Package for Analyzing Spatial Point Patterns, Journal of Statistical Software, 12 (2005) 1-42.
There are 23 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Idris Demirsoy 0000-0002-3321-4748

Publication Date December 27, 2022
Submission Date May 24, 2022
Acceptance Date September 1, 2022
Published in Issue Year 2022Volume: 43 Issue: 4

Cite

APA Demirsoy, I. (2022). Testing Complete Spatial Randomness on Linear Networks: Leon County Traffic Accident Example. Cumhuriyet Science Journal, 43(4), 769-776. https://doi.org/10.17776/csj.1120685
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