Skip to main content
SpringerLink
Log in

Hidden negative spatial autocorrelation

  • Original Article
  • Published:
Journal of Geographical Systems Aims and scope Submit manuscript

Abstract

Mostly lip service treatments of negative spatial autocorrelation (NSA) appear in the literature, although spatial scientists confront it in practice. NSA was detected serendipitously in recalcitrant empirical analyses containing a sizeable amount of global positive spatial autocorrelation (PSA) unaccounted for by standard spatial statistical models, and labeled hidden because conventional spatial statistical tools detected only PSA while giving absolutely not hint of NSA existing. The meaning of this phenomenon is explored empirically, with findings including: a better understanding of NSA, spatial filter model construction guidelines, effective illustrations of NSA, and how hidden NSA furnishes a diagnostic for model misspecification.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Notes

  1. The island municipios of Culebra and Vieques are not included because they are physically separated from the main island of Puerto Rico. The year 1970 was selected because the municipio of Florida was founded in 1971 by subdividing Barceloneta, but its founding is not based upon a pueblo. Cataño and Bayamon were merged because they often are combined in governmental statistical reporting, as have been, historically, Loíza (which has an ill-defined pueblo) and Canóvanas.

  2. The transformation for the ratio calculated with Thiessen polygons: based upon municipality centroids is LN(ratio-0.20); and, based upon town locations is 1/(ratio + 1.03)2.81.

  3. A shift to analyses based upon local statistics, which often include some negative spatial associations, is another reason for spatial scientists to acquire a better understanding of negative spatial autocorrelation.

References

  • Anselin L (1988) Spatial econometrics. Kluwer, Dordrecht

    Google Scholar 

  • Anselin L (1995) Local indicators of spatial association: LISA. Geogr Anal 27:93–115

    Article  Google Scholar 

  • Bartlett M (1975) The statistical analysis of spatial pattern. Chapman and Hall, London

    Google Scholar 

  • Baumont C, Ertur C, le Gallo J (2004) Spatial analysis of employment and population density: the case of the agglomeration of Dijon 1999. Geogr Anal 36:146–176

    Article  Google Scholar 

  • Besag J (1974) Spatial interaction and the statistical analysis of lattice systems. J R Stat Soc 36B:192–225

    Google Scholar 

  • Cliff A, Ord J (1981) Spatial processes. Pion, London

    Google Scholar 

  • Cressie N (1991) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Dacey M (1966) A county seat model for the areal pattern of an urban system. Geogr Rev 56:527–542

    Article  Google Scholar 

  • Diniz-Filho J, Bini L, Hawkins B (2003) Spatial autocorrelation and red herrings in geographical ecology. Glob Ecol Biogeogr 12:53–64

    Article  Google Scholar 

  • Getis A (1990) Screening for spatial dependence in regression analysis. Pap Reg Sci Assoc 69:69–81

    Article  Google Scholar 

  • Getis A (1995) Spatial filtering in a regression framework: experiments on regional inequality, government expenditures, and urban crime. In: Anselin L, Florax R (eds) New directions in spatial econometrics. Springer, Berlin Heidelberg New York, pp 172–188

    Google Scholar 

  • Glavanakov S., White D, Caraco T, Lapenis A, Robinson G, Szymanski B, Maniatty W (2001) Lyme disease in New York State: spatial pattern at a regional scale. Am J Trop Med Hyg 65:538–545

    Google Scholar 

  • Goodchild M (1986) Spatial autocorrelation (CATMOG 47). GeoBooks, Norwich

  • Gray W, Shadbegian R (2004) The environmental performance of polluting plants: a spatial econometric approach. Presented to the Association of Environmental and Resource Economics workshop, Madison, WI, June 17, 2003

  • Griffith D (2000) A linear regression solution to the spatial autocorrelation problem. J Geogr Syst 2:141–156

    Article  Google Scholar 

  • Griffith D (2003) Spatial autocorrelation and spatial filtering: gaining understanding through theory and scientific visualization. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Griffith D (2005) Effective geographic sample size in the presence of spatial autocorrelation. Ann Assoc Am Geogr 95:740–760

    Article  Google Scholar 

  • Griffith D, Csillag F (1993) Exploring relationships between semi-variogram and spatial autoregressive models. Pap Reg Sci 72:283–296

    Article  Google Scholar 

  • Griffith D, Wong D, Whitfield T (2003) Exploring relationships between the global and regional measures of spatial autocorrelation. J Reg Sci 43:683–710

    Article  Google Scholar 

  • Haining R (1990) Spatial data analysis in the social and environmental sciences. Cambridge University Press, Cambridge

    Google Scholar 

  • Irwin E, Geoghegan J (2001) Theory, data, methods: developing spatially-explicit economic models of land use change. Agric Ecosyst Environ 85:7–24

    Article  Google Scholar 

  • Le Gallo J, Ertur C (2003) Exploratory spatial data analysis of the distribution of regional per capita GDP in Europe, 1980–1995. Pap Reg Sci 82:175–201

    Article  Google Scholar 

  • Odoi A, Martin S, Michel P, Holt J, Middleton D, Wilson J (2003) Geographical and temporal distribution of human giardiasis in Ontario Canada. International J Health Geogr 2: article 5 (http://www.ij-healthgeographics.com/content/2/1/5)

  • Montgomery R, Chazdon R (2001) Forest structure, canopy architecture, and light transmittance in old-growth and second-growth tropical rain forests. Ecology 82:2707–2718

    Article  Google Scholar 

  • Roberts S, Hall G, Calamai P (2000) Analysing forest fragmentation using spatial autocorrelation, graphs and GIS. Int J Geogr Inf Sci 14:85–204

    Article  Google Scholar 

  • Smith T (2001) Aggregation bias in maximum likelihood estimation of spatial autoregressive processes. Paper presented to the North American Regional Science Association, Charleston, 15–17, 2001 November

  • Stirboeck C (2002) Explaining the level of relative investment specialisation: a spatial econometric analysis of EU regions. Discussion Paper No. 02-49, Centre for European Economic Research (ZEW), Mannheim, Germany

  • Tiefelsdorf M (2000) Modelling spatial processes: the identification and analysis of spatial relationships in regression residuals by means of Moran’s I. Springer, Berlin Heidelberg New York

  • Tiefelsdorf M, Griffith D (2006) Semi-parametric filtering of spatial autocorrelation: the eigenvector approach, Environ Plan A (forthcoming)

  • Wu T, Mather D, Dutilleul P (1998) Application of geostatistical and neighbor analyses to data from plant breeding trials. Crop Sci 38:1545–1553

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ashbel Smith Professor, School of Economic, Political and Policy Sciences, University of Texas at Dallas, P.O. Box 830688, Richardson, TX, 75083-0688, USA

    Daniel A. Griffith

Authors
  1. Daniel A. Griffith
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel A. Griffith.

Additional information

Contents of this manuscript benefited greatly from discussions with Giuseppe Arbia, and from suggestions by an anonymous referee. This research was completed while the author was a Visiting Researcher at the Max Planck Institute for Demographic Research, Rostock, Germany.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Griffith, D.A. Hidden negative spatial autocorrelation. J Geograph Syst 8, 335–355 (2006). https://doi.org/10.1007/s10109-006-0034-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10109-006-0034-9

Keywords

JEL Classification

Search

Navigation