Statistical tools for regional data analysis using GIS

ABSTRACT

A GIS provides a powerful collection of tools for the management, visualization and analysis of spatial data. These tools can be even more powerful when they are integrated with statistical methods for spatial data analysis and many GIS users are requesting this integration. The Geostatistical Analyst extension to ArcGIS was developed to integrate statistical methods with GIS tools for mapping and modeling spatially continuous data such as temperature or pollution. However, many GIS applications involve data that are aggregated over geographic regions and the analysis of this type of spatial data poses additional challenges. In this paper, we illustrate several different analytical goals that commonly arise in applications based on regional data. Many of these require a measure of local spatial dependence and this is commonly based on Moran's I index of spatial association. However, as we describe in this paper, other measures that more explicitly take into account the aggregated nature of the data may be preferred. Using county-level crime data in California we show how many different statistical methods for regional data analysis can be implemented within a GIS to provide a powerful set of interactive, analytical tools uniquely suited to the goals of regional analysis.

REFERENCES

• 1: Assunccao, R. M. and Reis, E. A. 1999. A new proposal to adjust Moran's I for population density, Statistics in Medicine, 18: 2147--2162.
• 2: Anselin, L. 1995. Local indicators of spatial association--LISA, Geographical Analysis, 27: 93--116.
• 3: Bailey, T. C. and Gatrell, A. C. 1995. Interactive Spatial Data Analysis. Essex: Addison Wesley Longman Limited.
• 4: Cliff, A. D. and Ord, J. K. 1981. Spatial Processes: Models and Applications, London: Pion Limited.
• 5: Assunccao, R. M. and Reis, E. A. 1999. A new proposal to adjust Moran's I for population density, Statistics in Medicine, 18: 2147--2162.
• 6: Gotway, C. A. and Young, L. J. 2002. Combining incompatible spatial data. Journal of the American Statistical Association, 97: 632--648.
• 7: Krivoruchko K. and Gribov A. 2002. Geostatistical Interpolation in The Presence of Barriers. GeoENV IV - Geostatistics for Environmental Applications, Kluwer Academic Publishers, 2003.
• 8: Moran, P. A. P. 1950. Notes on continuous stochastic phenomena, Biometrika, 37:17--23.
• 9: Oden, N. 1995. Adjusting Moran's I for population density, Statistics in Medicine,14: 17--26.
• 10: Tango, T. 1990. An index for cancer clustering, Environmental Health Perspectives, 87: 157--162.
• 11: Tango, T. 1995. A class of tests for detecting 'general' and 'focused' clustering of rare diseases, Statistics in Medicine, 14: 2323--2334.
• 12: Turnbull, B. W., Iwano, E. J., Burnett, W. S., Howe, H. L., and Clark, L. C. 1990. Monitoring for clusters of disease: Application to leukemia incidence in upstate New York. American Journal of Epidemiology, supplement 132: S136--S143.
• 13: Walter, S. D., 1992. The analysis of regional patterns in health data I: Distributional considerations, American Journal of Epidemiology, 136: 730--741.
• 14: Wartenberg, D. 1985. Multivariate spatial correlation: A method for exploratory geographical analysis. Geographical Analysis, 17: 263--283.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Algorithm design and analysis

General Terms:
Algorithms, Design, Theory