Today

• ESDA
• Spatial Autocorrelation

• Measures

  • Global
  • Local

ESDA

Exploratory

Spatial

Data

Analysis

[Exploratory]

Focus on discovery and assumption-free investigation

[Spatial]

Patterns and processes that put space and geography at the core

[Data Analysis]

Statistical techniques

Questions that ESDA helps...

Answer

• Is the variable I'm looking at concentrated over space? Do similar values tend to locate closeby?
• Can I identify any particular areas where certain values are clustered?

Spatial Autocorrelation

Spatial Autocorrelation

-Statistical representation of Tobler's law

-Spatial counterpart of traditional correlation

Degree to which similar values are located in similar locations

Examples

Positive SA: income, poverty, vegetation, temperature...

Negative SA: supermarkets, police stations, fire stations, hospitals...

Scales

Global Spatial Autocorr.

Global Spatial Autocorr.

"Clustering"

Overall trend where the distribution of values follows a particular pattern over space

[Positive] Similar values close to each other (high-high, low-low)

[Negative] Similar values far from each other (high-low)

How to measure it???

Moran Plot

• Graphical device that displays a variable on the horizontal axis against its spatial lag on the vertical one
• Variable and spatial weights matrix are preferably standardized
• Asssessment of the overall association between a variable in a given location and in its neighborhood

[Interactive Demo]

Moran's I

Formal test of global spatial autocorrelation

Statistically identify the presence of clustering in a variable

Slope of the Moran plot

Inference based on how likely it is to obtain a map like observed from a purely random pattern

Local Spatial Autocorr.

Local Spatial Autocorr.

"Clusters"

Pockets of spatial instability

Portions of a map where values are correlated in a particularly strong and specific way

[High-High] Positive sp. autocorr. of high values (hotspots)

[Low-Low] Positive sp. autocorr. of low values (coldspots)

[High-Low] Negative sp. autocorr. (spatial outliers)

[Low-High] Negative sp. autocorr. (spatial outliers)

How to measure it???

LISAs

Local Indicators of Spatial Association

Statistical tests for spatial cluster detection  →  Statistical significance

Compares the observed map with many randomly generated ones to see how likely it is to obtain the observed associations for each location

Recapitulation

ESDA is a family of techniques to explore and spatially interrogate data

Main function: characterize spatial autocorrelation, which can be explored:

• Globally (e.g. Moran Plot, Moran's I)
• Locally (e.g. LISAs)