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Spatial uncertainty in cluster detection

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Abstract

Advances in GIS are increasingly focused on providing more sophisticated spatial analytical capabilities. Much of this work assumes no attribute and positional uncertainties in data. While there has been considerable research devoted to enhanced data creation techniques and metadata associated with error and uncertainty, little has been done to characterize or better understand error/uncertainty impacts in spatial analysis. This paper explores issues associated with the detection and significance of clusters under known positional uncertainty. Multiple equally likely data instances in which positional certainty is not assumed are assessed for existence of clusters. Results suggest that identified patterns can vary significantly when there is error or uncertainty in spatial data.

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References

  1. Knox, E. (2002). An epidemic pattern of murder. Journal of Public Health, 24(1), 34–37.

    Article  Google Scholar 

  2. Johnson, S. D., & Bowers, K. (2004). The stability of space–time clusters of burglary. British Journal of Criminology, 44, 55–65.

    Article  Google Scholar 

  3. Grubesic, T. H., & Mack, E. (2008). Spatio-temporal interaction of urban crime. Journal of Quantitative Criminology, 24(3), 285–306.

    Article  Google Scholar 

  4. Wu, X., & Grubesic, T. H. (2010). Identifying irregularly shaped crime hot-spots using a multiobjective evolutionary algorithm. Journal of Geographical Systems, 12(4), 409–433.

    Article  Google Scholar 

  5. Johnson, S. D. (2010). A brief history of the analysis of crime concentration. European Journal of Applied Mathematics, 21(4–5), 349–370.

    Article  Google Scholar 

  6. Marshall, R. (1991). A review of methods for the statistical analysis of spatial patterns of disease. Journal of the Royal Statistical Society, Series A (Statistics in Society), 154(3), 421–441.

    Article  Google Scholar 

  7. Jacquez, G. M. (1996). A k nearest neighbour test for space–time interaction. Statistics in Medicine, 15, 1935–1949.

    Article  Google Scholar 

  8. Petridou, E., Revinthi, K., Alexander, F., Haidas, S., Koliouskas, D., Kosmidis, H., et al. (1996). Space–time clustering of childhood leukemia in Greece: Evidence supporting a viral etiology. British Journal of Cancer, 73, 1278–1283.

    Article  Google Scholar 

  9. Kulldorff, M. (1998). Statistical methods for spatial epidemiology: Tests for randomness. In A. Gatrell & M. Löytönen (Eds.), GIS and health, 49–62. London: Taylor & Francis.

    Google Scholar 

  10. Jacquez, G. M., & Waller, L. (2000). The effect of uncertain locations on disease cluster statistics. In H. Mowrer & R. Congalton (Eds.), Quantifying spatial uncertainty in natural resources: Theory and applications for GIS and remote sensing (pp. 53–64). Boca Raton: CRC Press.

    Google Scholar 

  11. Ward, M. P., & Carpenter, T. E. (2000). Techniques for analysis of disease clustering in space and in time in veterinary epidemiology. Preventative Veterinary Medicine, 45(3–4), 257–284.

    Article  Google Scholar 

  12. McNally, R. J., & Colver, A. F. (2008). Space–time clustering analyses of occurrence of cerebral palsy in Northern England for births 1991 to 2003. Annals of Epidemiology, 18, 108–112.

    Article  Google Scholar 

  13. Meliker, J. (2009). Approaches for reconstructing exposures accounting for human mobility and space–time variability in environmental contaminants. Epidemiology, 20(6), S242.

    Article  Google Scholar 

  14. Rogerson, P., & Yamada, I. (2009). Statistical detection and surveillance of geographic clusters. Boca Raton, FL: Chapman & Hall/CRC.

    Google Scholar 

  15. Tango, T. (2010). Statistical methods for disease clustering. New York: Springer.

    Book  Google Scholar 

  16. Grubesic, T. H., Wei, R., & Murray, A. T. (2014). Spatial clustering overview and comparison: Accuracy, sensitivity, and computational expense. Annals of the Association of American Geographers, 104(6), 1134–1156.

    Article  Google Scholar 

  17. Messner, S. F., Anselin, L., Baller, R. D., & Hawkins, D. F. (1999). The spatial patterning of county homicide rates: An application of exploratory spatial data analysis. Journal of Quantitative Criminology, 15(4), 423–450.

    Article  Google Scholar 

  18. Harries, K. (1999). Mapping crime: Principles and practice. Washington DC: US Department of Justice.

    Google Scholar 

  19. Murray, A. T., McGuffog, I., Western, J. S., & Mullins, P. (2001). Exploratory spatial data analysis techniques for examining urban crime. British Journal of Criminology, 41, 309–329.

    Article  Google Scholar 

  20. Grubesic, T. H. (2006). On the application of fuzzy clustering for crime hot spot detection. Journal of Quantitative Criminology, 22(1), 77–105.

    Article  Google Scholar 

  21. Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27(2), 209–220.

    Google Scholar 

  22. Kulldorff, M. (1997). A spatial scan statistic. Communication in Statistics, 26(6), 1481–1496.

    Article  Google Scholar 

  23. Burra, T., Jerrett, M., Burnett, R. T., & Anderson, M. (2002). Conceptual and practical issues in the detection of local disease clusters: A study of mortality in Hamilton, Ontario. The Canadian Geographer, 46(2), 160–171.

    Article  Google Scholar 

  24. Jacquez, G. M. (2004). Current practices in the spatial analysis of cancer: Flies in the ointment. International Journal of Health Geographics, 3(1), 22.

    Article  Google Scholar 

  25. Olson, K., Grannis, S., & Mandl, K. (2006). Privacy protection versus cluster detection in spatial epidemiology. American Journal of Public Health, 96(11), 2002–2008.

    Article  Google Scholar 

  26. Rushton, G., Armstrong, M. P., Gittler, J., Greene, B. R., Pavlik, C. E., West, M. M., et al. (2006). Geocoding in cancer research: A review. American Journal of Preventive Medicine, 30(2S), S16–S24.

    Article  Google Scholar 

  27. McNally, R. J. (2010). Clustering studies for identifying the role of environmental factors in aetiology of human cancers. In D. Roy & M. T. Dorak (Eds.), Environmental factors, genes, and the development of human cancers (pp. 97–114). New York: Springer.

    Chapter  Google Scholar 

  28. Meliker, J., & Sloan, C. (2011). Spatio-temporal epidemiology: Principles and opportunities. Spatial and Spatio-temporal Epidemiology, 2(1), 1–9.

    Article  Google Scholar 

  29. Getis, A., Morrison, A. C., Gray, K., & Scott, T. W. (2003). Characteristics of the spatial pattern of the dengue vector, Aedes aegypti, in Iquitos, Peru. The American Journal of Tropical Medicine and Hygiene, 69(5), 494–505.

    Google Scholar 

  30. Abad-Franch, F., Monteiro, F. A., Jaramillo, N., Gurgel-Gonçalves, R., Dias, F. B. S., & Diotaiuti, L. (2009). Ecology, evolution, and the long-term surveillance of vector-borne Chagas disease: A multi-scale appraisal of the tribe Rhodniini (Triatominae). Acta Tropica, 110(2), 159–177.

    Article  Google Scholar 

  31. Murray, A. T., & Estivill-Castro, V. (1998). Cluster discovery techniques for exploratory spatial data analysis. International Journal of Geographical Information Science, 12, 431–443.

    Article  Google Scholar 

  32. Aldstadt, J. (2010). Spatial clustering. In M. Fischer & A. Getis (Eds.), Handbook of applied spatial analysis (pp. 279–300). Berlin: Springer.

    Chapter  Google Scholar 

  33. Alexander, F. (1992). Space–time clustering of childhood acute lymphoblastic leukemia: Indirect evidence for a transmissible agent. British Journal of Cancer, 65, 589–592.

    Article  Google Scholar 

  34. Murray, A. T., Grubesic, T. H., Rey, S., & Anselin, L. (2012). Spatial data uncertainty and cluster detection. In GIScience 2012 conference proceedings (Columbus, Ohio).

  35. Murray, A. T., & Grubesic, T. H. (2013). Exploring spatial patterns of crime using non-hierarchical cluster analysis. In M. Leitner (Ed.), Crime modeling and mapping using geospatial technologies (pp. 105–124). New York: Springer.

    Chapter  Google Scholar 

  36. Goodchild, M. F., & Gopal, S. (1989). The accuracy of spatial databases. Boca Raton, FL: CRC Press.

    Google Scholar 

  37. Heuvalink, G. (1993). Error propagation in quantitative spatial modeling: Applications in geographical information systems. Amsterdam: Koninklijk Nederlands Aardrijkskundig Genootschap.

    Google Scholar 

  38. Kiiveri, H. T. (1997). Assessing, representing and transmitting positional uncertainty in maps. International Journal of Geographical Information Systems, 11, 33–52.

    Article  Google Scholar 

  39. Morris, A. (2003). A framework for modeling uncertainty in spatial databases. Transactions in GIS, 7(1), 83–101.

    Article  Google Scholar 

  40. Wand, M. P., & Jones, M. C. (1995). Kernel smoothing. Boca Raton, FL: CRC Press.

    Book  Google Scholar 

  41. Zimmerman, D. L., Fang, X., Mazumdar, S., & Rushton, G. (2007). Modeling the probability distribution of positional errors incurred by residential address geocoding. International Journal of Health Geographics. doi:10.1186/1476-072X-6-1.

    Google Scholar 

  42. Zandbergen, P. A., & Hart, T. C. (2009). Geocoding accuracy considerations in determining residency restrictions for sex offenders. Criminal Justice Policy Review, 20(1), 62–90.

    Article  Google Scholar 

  43. Fisher, P., Comber, A., & Wadsworth, R. (2006). Approaches to uncertainty in spatial data. In R. Devillers & R. Jeansoulin (Eds.). Fundamentals of spatial data quality (pp. 43–59). New York: Wiley.

    Chapter  Google Scholar 

  44. Hunter, G. J., & Goodchild, M. F. (1995). A new model for handling vector data uncertainty in geographic information systems. Journal of the Urban and Regional Information Systems Association, 8, 51–57.

    Google Scholar 

  45. Goodchild, M. F. (1998). Uncertainty: The Achilles heel of GIS? GeoInfo Systems, 8, 50–52.

    Google Scholar 

  46. Malizia, N. (2013). The effect of data inaccuracy on tests of space–time interaction. Transactions in GIS, 17(3), 426–451.

    Article  Google Scholar 

  47. Murray, A. T., Wei, R., & Grubesic, T. H. (2014). An approach for examining alternatives attributable to locational uncertainty. Environment and Planning B, 41, 93–109.

    Article  Google Scholar 

  48. Guptill, S. C., & Morrison, J. L. (1995). Elements of spatial data quality. Oxford: Elsevier Science.

    Google Scholar 

  49. Hunter, G. J., & Beard, K. (1992). Understanding error in spatial databases. Australian Surveyor, 37(2), 108–119.

    Article  Google Scholar 

  50. Ratcliffe, J. H. (2004). Geocoding crime and a first estimate of a minimum acceptable hit rate. International Journal of Geographical Information Science, 18(1), 61–72.

    Article  Google Scholar 

  51. Ward, M. H., Nuckols, J. R., Giglierano, J., Bonner, M. R., Wolter, C., Airola, M., et al. (2005). Positional accuracy of two methods of geocoding. Epidemiology, 16(4), 542–547.

    Article  Google Scholar 

  52. Bonner, M. R., Han, D., Nie, J., Rogerson, P., Vena, J. E., & Freundenheim, J. L. (2006). Positional accuracy of geocoded addresses in epidemiological research. Epidemiology, 45(5), 512–519.

    Google Scholar 

  53. Cayo, M., & Talbot, T. (2003). Positional error in automated geocoding of residential addresses. International Journal of Health Geographies. doi:10.1186/1476-072X-2-10.

    Google Scholar 

  54. Murray, A. T., Grubesic, T. H., Wei, R., & Mack, E. A. (2011). A hybrid geocoding methodology for spatio-temporal data. Transactions in GIS, 15(6), 795–809.

    Article  Google Scholar 

  55. Bolstad, P. V., Gessler, P., & Lillesand, T. M. (1990). Positional uncertainty in manually digitized map data. International Journal of Geographical Information Systems, 4(4), 299–412.

    Article  Google Scholar 

  56. Chrisman, N. R. (1982). A theory of cartographic error and its measurement in digital data bases. In Proceedings of Auto-Carto 5 (pp. 159–168). Bethesda, MD: American Congress on Surveying and Mapping.

  57. Dutton, G. (1992). Handling positional uncertainty in spatial databases. In Proceedings 5th international symposium on spatial data handling (pp. 460–469). University of South Carolina.

  58. Goodchild, M. F., & Hunter, G. J. (1997). A simple positional accuracy measure for linear features. International Journal of Geographical Information Science, 11, 299–306.

    Article  Google Scholar 

  59. Shi, W. Z. (1998). A generic statistical approach for modelling error in geometric features in GIS. International Journal of Geographical Information Science, 12, 131–143.

    Article  Google Scholar 

  60. Leung, Y., & Yan, J. (1998). A locational error model for spatial features. International Journal of Geographical Information Science, 12, 607–620.

    Article  Google Scholar 

  61. Church, R. L., Curtin, K. M., Fohl, P., Funk, C., Goodchild, M. F., Noronha, V. T., et al. (1998). Positional distortion in geographic datasets as a barrier to interpolation. In Technical papers, ACSM annual conference. Bethesda, MD: American Congress on Surveying and Mapping.

  62. Armstrong, M. P., Rushton, G., & Zimmerman, D. L. (1999). Geographically masking health data to preserve confidentiality. Statistics in Medicine, 18(5), 497–525.

    Article  Google Scholar 

  63. Kulldorff, M. (2010). SaTScan user guide. Retrieved from http://www.satscan.org.

  64. Murray, A. T., Grubesic, T. H., & Wei, R. (2014). Spatially significant cluster detection. Spatial Statistics, 10, 103–116.

    Article  Google Scholar 

  65. Jacquez, G. M. (2008). Spatial cluster analysis. In A. S. Fotheringham & J. P. Wilson (Eds.), The handbook of geographic information science (pp. 395–416). Malden, MA: Blackwell Publishing.

    Google Scholar 

  66. Murray, A. T. (2003). Site placement uncertainty in location analysis. Computers, Environment and Urban Systems, 27, 205–221.

    Article  Google Scholar 

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Kleinschmidt, S., Murray, A.T., Rey, S.J. et al. Spatial uncertainty in cluster detection. Spat. Inf. Res. 24, 181–189 (2016). https://doi.org/10.1007/s41324-016-0019-9

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  • DOI: https://doi.org/10.1007/s41324-016-0019-9

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