GeographicData Science -

Lecture VIExploring Space in Data

Dani Arribas-Bel

TodayESDASpatial AutocorrelationMeasures

GlobalLocal

ESDA

Exploratory

Spatial

Data

Analysis

[Exploratory]

Focus on discovery and assumption-free investigation

[Spatial]

Patterns and processes that put space and geography at thecore

[Data Analysis]

Statistical techniques

Questions that ESDA helps...

AnswerIs the variable I'm looking at concentrated over space? Dosimilar values tend to locate closeby?Can I identify any particular areas where certain values areclustered?

Questions that ESDA helps...

AnswerIs the variable I'm looking at concentrated over space? Dosimilar values tend to locate closeby?Can I identify any particular areas where certain values areclustered?

AskWhat is behind this pattern? What could be generating theprocess?Why do we observe certain clusters over space?

Spatial Autocorrelation

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

Waldo Tobler (1970)

Spatial Autocorrelation-Statistical representation of Tobler's law

-Spatial counterpart of traditional correlation

Spatial Autocorrelation-Statistical representation of Tobler's law

-Spatial counterpart of traditional correlation

Degree to which similar values are located in similarlocations

Spatial Autocorrelation-Statistical representation of Tobler's law

-Spatial counterpart of traditional correlation

Degree to which similar values are located in similarlocations

Two flavors:Positive: similar values  →  similar location (closeby)Negative: similar values  →  disimilar location (furtherapart)

ExamplesPositive SA:

Negative SA:

ExamplesPositive SA: income,

Negative SA:

ExamplesPositive SA: income, poverty,

Negative SA:

ExamplesPositive SA: income, poverty, vegetation,

Negative SA:

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

Negative SA:

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

Negative SA: supermarkets,

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

Negative SA: supermarkets, police stations,

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

Negative SA: supermarkets, police stations, fire stations,

ExamplesPositive 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)similarvalues?

Scales[Global]

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

[Local]

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

Global Spatial Autocorr.

Global Spatial Autocorr."Clustering"

Overall trend where the distribution of values follows a particularpattern over space

Global Spatial Autocorr."Clustering"

Overall trend where the distribution of values follows a particularpattern over space

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

Global Spatial Autocorr."Clustering"

Overall trend where the distribution of values follows a particularpattern over space

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

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

Global Spatial Autocorr."Clustering"

Overall trend where the distribution of values follows a particularpattern 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 PlotGraphical device that displays a variable on thehorizontal axis against its spatial lag on the vertical oneVariable and spatial weights matrix are preferablystandardizedAsssessment of the overall association between a variablein a given location and in its neighborhood

[Interactive Demo]

Moran's IFormal 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 likeobserved from a purely random pattern

Moran's IFormal 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 likeobserved from a purely random pattern

I =N

∑ i∑ jwij

( )( )∑ i∑ jwij Zi Zj(∑ i Zi)2

Local Spatial Autocorr.

Local Spatial Autocorr."Clusters"

Pockets of spatial instability

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

Local Spatial Autocorr."Clusters"

Pockets of spatial instability

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

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

Local Spatial Autocorr."Clusters"

Pockets of spatial instability

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

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

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

Local Spatial Autocorr."Clusters"

Pockets of spatial instability

Portions of a map where values are correlated in aparticularly 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)

Local Spatial Autocorr."Clusters"

Pockets of spatial instability

Portions of a map where values are correlated in aparticularly 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)

Local Spatial Autocorr."Clusters"

Pockets of spatial instability

Portions of a map where values are correlated in aparticularly 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???

LISAsLocal Indicators of Spatial Association

Statistical tests for spatial cluster detection  →  Statisticalsignificance

Compares the observed map with many randomlygenerated ones to see how likely it is to obtain the observedassociations for each location

LISAsLocal Indicators of Spatial Association

Statistical tests for spatial cluster detection  →  Statisticalsignificance

Compares the observed map with many randomlygenerated ones to see how likely it is to obtain the observedassociations for each location

= ; =IiZim2 ∑

jWijZj m2

∑ i Z2iN

RecapitulationESDA is a family of techniques to explore and spatiallyinterrogate data

Main function: characterize spatial autocorrelation, whichcan be explored:

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

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