Spatial Point Pattern Analysis

  • Roger S. Bivand
  • Edzer Pebesma
  • Virgilio Gómez-Rubio
Chapter
Part of the Use R! book series (USE R, volume 10)

Abstract

The analysis of point patterns appears in many different areas of research. In ecology, for example, the interest may be focused on determining the spatial distribution (and its causes) of a tree species for which the locations have been obtained within a study area. Furthermore, if two or more species have been recorded, it may also be of interest to assess whether these species are equally distributed or competition exists between them. Other factors which force each species to spread in particular areas of the study region may be studied as well. In spatial epidemiology, a common problem is to determine whether the cases of a certain disease are clustered. This can be assessed by comparing the spatial distribution of the cases to the locations of a set of controls taken at random from the population.

Keywords

Stratification Smoke Lawson Berman Stpp 

References

  1. Baddeley, A., Gregori, P., Mateu, J., Stoica, R., and Stoyan, D., editors (2005). Case Studies in Spatial Point Process Modeling. Lecture Notes in Statistics, 185. Springer-Verlag, Berlin.Google Scholar
  2. Baddeley, A., Möller, J., and Waagepetersen, R. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54:329–350.MathSciNetMATHCrossRefGoogle Scholar
  3. Baddeley, A. and Turner, R. (2005). Spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software, 12(6):1–42.Google Scholar
  4. Baddeley, A. J. and Silverman, B. W. (1984). A cautionary example on the use of second-order methods for analysing point patterns. Biometrics, 40: 1089–1093.MathSciNetCrossRefGoogle Scholar
  5. Berman, M. and Diggle, P. J. (1989). Estimating weighted integrals of the second-order intensity of a spatial point process. Journal of the Royal Statistical Society B, 51:81–92.MathSciNetMATHGoogle Scholar
  6. Clark, A. B. and Lawson, A. B. (2004). An evaluation of non-parametric relative risk estimators for disease mapping. Computational Statistics and Data Analysis, 47:63–78.MathSciNetMATHCrossRefGoogle Scholar
  7. Cox, C. R. (1955). Some statistical methods connected with series of events (with discussion). Journal of the Royal Statistical Society, Series B, 17:129–164.MATHGoogle Scholar
  8. Cressie, N. and Wikle, C. (2011). Statistics for Spatio-temporal Data. John Wiley & Sons, New York.MATHGoogle Scholar
  9. Diggle, P. J. (1985). A kernel method for smoothing point process data. Applied Statistics, 34:138–147.MATHCrossRefGoogle Scholar
  10. Diggle, P. J. (1990). A point process modelling approach to raised incidence of a rare phenomenon in the vicinity of a prespecified point. Journal of the Royal Statistical Society, Series A, 153:349–362.Google Scholar
  11. Diggle, P. J. (2000). Overview of statistical methods for disease mapping and its relationship to cluster detection. In Elliott, P., Wakefield, J., Best, N., and Briggs, D., editors, Spatial Epidemiology: Methods and Applications, pages 87–103. Oxford University Press, Oxford.Google Scholar
  12. Diggle, P. J. (2003). Statistical Analysis of Spatial Point Patterns. Arnold, London, second edition.Google Scholar
  13. Diggle, P. J. (2006). Spatio-temporal point processes: Methods and applications. In Finkenstadt, B., Held, L., and Isham, V., editors, Statistical Methods for Spatio-Temporal Systems, pages 1–46. CRC Press, Boca Raton.Google Scholar
  14. Diggle, P. J. and Chetwynd, A. (1991). Second-order analysis of spatial clustering for inhomogeneous populations. Biometrics, 47:1155–1163.CrossRefGoogle Scholar
  15. Diggle, P. J., Elliott, P., Morris, S., and Shaddick, G. (1997). Regression modelling of disease risk in relation to point sources. Journal of the Royal Statistical Society, Series A, 160:491–505.Google Scholar
  16. Diggle, P. J., Gómez-Rubio, V., Brown, P. E., Chetwynd, A., and Gooding, S. (2007). Second-order analysis of inhomogeneous spatial point processes using case-control data. Biometrics, 63:550–557.MathSciNetMATHCrossRefGoogle Scholar
  17. Diggle, P. J., Morris, S., and Wakefield, J. (2000). Point-source modelling using case-control data. Biostatistics, 1:89–105.MATHCrossRefGoogle Scholar
  18. Diggle, P. J. and Rowlingson, B. (1994). A conditional approach to point process modelling of elevated risk. Journal of the Royal Statistical Society, Series A, 157:433–440.Google Scholar
  19. Elliott, P., Wakefield, J., Best, N., and Briggs, D., editors (2000). Spatial Epidemiology. Methods and Applications. Oxford University Press, Oxford.Google Scholar
  20. Gabriel, E. and Diggle, P. J. (2009). Second-order analysis of inhomogeneous spatio-temporal point process data. Statistica Neerlandica, 63(1):43–51.MathSciNetCrossRefGoogle Scholar
  21. Gaetan, C. and Guyon, X. (2010). Spatial Statistics and Modeling. Springer, New York.MATHCrossRefGoogle Scholar
  22. Gatrell, A. C., Bailey, T. C., Diggle, P. J., and Rowlingson, B. S. (1996). Spatial point pattern analysis and its application in geographical epidemiology. Transactions of the Institute of British Geographers, 21:256–274.CrossRefGoogle Scholar
  23. Gelfand, A. E., Diggle, P. J., Guttorp, P., and Fuentes, M., editors (2010). Handbook of Spatial Statistics. Chapman & Hall/CRC Press.Google Scholar
  24. Gerard, D. J. (1969). Competition quotient: a new measure of the competition affecting individual forest trees. Research Bulletin 20, Agricultural Experiment Station, Michigan State University.Google Scholar
  25. Härdle, W., Müller, M., Sperlich, S., and Werwatz, A. (2004). Nonparametric and Semiparametric Models. Springer-Verlag, Berlin.MATHCrossRefGoogle Scholar
  26. Illian, J., Pentinen, A., Stoyan, H., and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, New York.MATHGoogle Scholar
  27. Jarner, M. F., Diggle, P., and Chetwynd, A. G. (2002). Estimation of spatial variation in risk using matched case-control data. Biometrical Journal, 44:936–945.MathSciNetCrossRefGoogle Scholar
  28. Kelsall, J. E. and Diggle, P. J. (1995a). Kernel estimation of relative risk. Bernoulli, 1:3–16.MathSciNetMATHCrossRefGoogle Scholar
  29. Kelsall, J. E. and Diggle, P. J. (1995b). Non-parametric estimation of spatial variation in relative risk. Statistics in Medicine, 14:559–573.CrossRefGoogle Scholar
  30. Kelsall, J. E. and Diggle, P. J. (1998). Spatial variation in risk: a non-parametric binary regression approach. Applied Statistics, 47:559–573.MATHGoogle Scholar
  31. Krivoruchko, K. (2011). Spatial Statistical Data Analysis for GIS Users. ESRI Press, Redlands, CA. DVD.Google Scholar
  32. Möller, J. and Waagepetersen, R. (2003). Statistical Inference and Simulation for Spatial Point Processes. Chapman & Hall/CRC, Boca Raton.CrossRefGoogle Scholar
  33. Numata, M. (1961). Forest vegetation in the vicinity of Choshi. Coastal flora and vegetation at Choshi, Chiba Prefecture IV. Bulletin of Choshi Marine Laboratory, Chiba University, 3:28–48 [in Japanese].Google Scholar
  34. O’Sullivan, D. and Unwin, D. J. (2010). Geographical Information Analysis. Wiley, Hoboken, NJ.CrossRefGoogle Scholar
  35. Prince, M. I., Chetwynd, A., Diggle, P. J., Jarner, M., Metcalf, J. V., and James, O. F. (2001). The geographical distribution of primary biliary cirrhosis in a well-defined cohort. Hepatology, 34:1083–1088.CrossRefGoogle Scholar
  36. Ripley, B. D. (1976). The second order analysis of stationary point processes. Journal of Applied Probability, 13:255–266.MathSciNetMATHCrossRefGoogle Scholar
  37. Ripley, B. D. (1977). Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39:172–212.MathSciNetGoogle Scholar
  38. Rowlingson, B. and Diggle, P. J. (1993). Splancs: spatial point pattern analysis code in S-PLUS TM . Computers and Geosciences, 19:627–655.CrossRefGoogle Scholar
  39. Schabenberger, O. and Gotway, C. A. (2005). Statistical Methods for Spatial Data Analysis. Chapman & Hall/CRC, Boca Raton/London.MATHGoogle Scholar
  40. Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London.MATHGoogle Scholar
  41. Singleton, C. D., Gatrell, A. C., and Briggs, J. (1995). Prevalence of asthma and related factors in primary school children in an industrial part of England. Journal of Epidemiology and Community Health, 49:326–327.CrossRefGoogle Scholar
  42. Strauss, D. J. (1975). A model for clustering. Biometrika, 62:467–475.MathSciNetMATHCrossRefGoogle Scholar
  43. Venables, W. N. and Ripley, B. D. (2002). Modern Applied Statistics with S. Fourth Edition. Springer, New York.CrossRefGoogle Scholar
  44. Waller, L. A. and Gotway, C. A. (2004). Applied Spatial Statistics for Public Health Data. John Wiley & Sons, Hoboken, NJ.MATHCrossRefGoogle Scholar
  45. Wood, S. (2006). Generalized Additive Models: An Introduction with R . Chapman & Hall/CRC, Boca Raton.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Roger S. Bivand
    • 1
  • Edzer Pebesma
    • 2
  • Virgilio Gómez-Rubio
    • 3
  1. 1.Norwegian School of EconomicsBergenNorway
  2. 2.Westfälische Wilhelms-UniversitätMünsterGermany
  3. 3.Department of MathematicsUniversidad de Castilla-La ManchaAlbaceteSpain

Personalised recommendations