Geographic Data Science - Lecture VI

Exploring Space in Data

Dani Arribas-Bel

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?

Ask

  • What is behind this pattern? What could be generating the process?
  • Why do we observe certain clusters over space?

Spatial Autocorrelation

Everything is related to everything else, but near things are more related than distant things

Waldo Tobler (1970)

Spatial Autocorrelation

-Statistical representation of Tobler's law

-Spatial counterpart of traditional correlation

Degree to which similar values are located in similar locations

Two flavors:

  • Positive: similar values  →  similar location (closeby)
  • Negative: similar values  →  disimilar location (further apart)

Examples

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

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

Scales

[Global]

Clustering: do values tend to be close to other (dis)similar values?

[Local]

Clusters: are there any specific parts of a map with an extraordinary concentration of (dis)similar values?

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

IMD Choropleth IMD Moran Plot

[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

Choropleth LISA Map

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)

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Geographic Data Science'16 - Lecture 6 by Dani Arribas-Bel is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.