Global Measures (last time)



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tarix08.04.2018
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Global Measures (last time)

  • Global Measures (last time)

    • A single value which applies to the entire data set
      • The same pattern or process occurs over the entire geographic area
      • An average for the entire area
  • Local Measures (this time)

    • A value calculated for each observation unit
      • Different patterns or processes may occur in different parts of the region
      • A unique number for each location


We will look at local versions of Moran’s I, Geary’s C, and the Getis-Ord G statistic

  • We will look at local versions of Moran’s I, Geary’s C, and the Getis-Ord G statistic

  • Moran’s I is most commonly used, and the local version is often called Anselin’s LISA, or just LISA



    • The statistic is calculated for each areal unit in the data
    • For each polygon, the index is calculated based on neighboring polygons with which it shares a border


Since a measure is available for each polygon, these can be mapped to indicate how spatial autocorrelation varies over the study region

    • Since a measure is available for each polygon, these can be mapped to indicate how spatial autocorrelation varies over the study region
    • Since each index has an associated test statistic, we can also map which of the polygons has a statistically significant relationship with its neighbors, and show type of relationship


The local Moran statistic for areal unit i is:

  • The local Moran statistic for areal unit i is:

  • where zi is the original variable xi in

  • “standardized form”

  • or it can be in “deviation form”

  • and wij is the spatial weight

  • The summation is across each row i of the spatial weights matrix.

  • An example follows























For illiteracy = .2047

  • For illiteracy = .2047

  • Are provinces really “local”

















Correlation Coefficient is the relationship between two different variables in the same area

  • Correlation Coefficient is the relationship between two different variables in the same area

  • Bivariate LISA is a correlation between two different variables in an area and in nearby areas.



Can view Bivariate LISA as a “local” version of the correlation coefficient

    • Can view Bivariate LISA as a “local” version of the correlation coefficient
    • It shows how the nature & strength of the association between two variables varies over the study region
    • For example, how home values are associated with crime in surrounding areas


Local Indicators of Spatial Autocorrelation

  • Local Indicators of Spatial Autocorrelation

    • Anselin’s LISA
    • Local Getis Ord G
  • Spatial autocorrelation can be calculated for each areal unit

  • Spatial autocorrelation can vary across the region in strength and in type

  • Next time (Friday)

  • Using GeoDA software to explore spatial autocorrelation

  • Next week

  • Spatial regression and modeling



Getis, A. and Ord, J.K. (1992) The analysis of spatial association by use of distance statistics Geographical Analysis, 24(3) 189-206

  • Getis, A. and Ord, J.K. (1992) The analysis of spatial association by use of distance statistics Geographical Analysis, 24(3) 189-206

  • Ord, J.K. and Getis A. (1995) Local Spatial Autocorrelation Statistics: distributional issues and an application Geographical Analysis, 27(4) 286-306

  • Anselin, L. (1995) Local Indicators of Spatial Association-LISA Geographical Analysis 27: 93-115





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