Session 4: Exploratory Spatial Data Analysis (ESDA)

Session 4: Exploratory Spatial
Data Analysis (ESDA)
Course on Spatial Econometrics with Applications
Profesora: Coro Chasco Yrigoyen
Univeridad Autónoma de Madrid
Lugar: Universidad Politécnica de Barcelona
12-13, 18-20 de junio, 2007
©2007, Coro Chasco Yrigoyen
All Rights Reserved
Course Index
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S1: Introduction to spatial econometrics
S2: Spatial effects, spatial dependence
S3: Spatial autocorrelation tests
S4: Exploratory Spatial Data Analysis (ESDA)
S5: Specification of spatial dependence models
S6: Spatial regression models: OLS estimation and testing
PS1: GeoDa: introduction and ESDA
S7: Spatial dependence models: estimation and testing
S8: Modelling strategies in spatial regression models
PS2: SpaceStat:
SpaceStat: confirmatory spatial data analysis
S9: Specification of spatial heterogeneity models
S10: Spatial heterogeneity models: estimation and testing
PS3: Practical exercise and evaluation
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. CHASCO, C. (2003), “Econometría espacial aplicada a la
predicción-extrapolación de datos microterritoriales”. Comunidad
de Madrid; pp. 28-48.
Session 4
Overview and Goals
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Introduction to ESDA
Spatial distributions plots:
1. Choropleth maps
2. Box-map
3. Cartogram
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Spatial association plots:
1. Moran’s scatterplot
2. LISA maps
3. Bivariate & space-time autocorrelation plots
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Readings
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Session 4
4.1. Introduction to ESDA (I)
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ESDA is a subset of EDA.
EDA is a collection of descriptive
and graphical statistical tools
intended to discover patterns in
data and suggest hypotheses.
EDA allow the user to directly
manipulate various “views” of the
data: histograms, box plots, q-q
plots, dot plots, and scatterplot
matrices.
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Statistica (StatSoft)
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Session 4
4.1. Introduction to ESDA (II)
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Geographic maps: a
way of illustrating
spatial data.
ESDA: the explicit
consideration of the
map as an integrated
“view” of the data in a
dynamic graphics
framework.
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Session 4
. ANSELIN, L. (1998),“Exploratory spatial data analysis in a
geocomputational environment”. Conference in
GeoComputation’98, Bristol (UK), pp. 17-19.
4.1. Introduction to ESDA (III)
ESDA techniques:
1. Describe and visualize
spatial distributions.
2. Linking & brushing:
allows the selection of
locations in different
views or screens.
3. Identify atypical
locations or spatial
outliers.
4. Discover patterns of
spatial association,
clusters or hot spots.
5. Suggest spatial regimes
or other forms of spatial
heterogeneity.
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Geostatistical data: point data as a
sample of an underlying continuous
distribution
Lattice data: discrete spatial locations
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2
Session 4
4.2. Spatial distributions plots
4.2.1. Choropleth maps
4.2.2. Box-map
4.2.3. Cartogram
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4.2. Spatial distributions plots
4.2.1. Choropleth maps
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QUANTILE MAPS
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4.2. Spatial distributions plots
4.2.1. Choropleth maps (II)
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Session 4
Session 4
PERCENTILE MAP
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4.2. Spatial distributions plots
Session 4
4.2.1. Choropleth maps (III)
STANDARD
DEVIATION
MAP
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4.2. Spatial distributions plots
Session 4
4.2.2. Box-map
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4.2. Spatial distributions plots
Session 4
4.2.3. Cartogram
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4
Session 4
4.3. Spatial association plots
4.3.1. Moran’s scatterplot
4.3.2. LISA maps
4.3.3. Bivariate & space-time
autocorrelation plots.
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Session 4
4.3. Spatial association plots
4.3.1. Moran’s scatterplot
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Visualizes I as the slope of the regression line in a
scatterplot with Wz on Y-axis and z on X-axis.
. ANSELIN, L. & S. BAO (1997),
“Exploratory Spatial Data Analysis”. In
“Recent developments in spatial analysis”
(Eds. Fischer y Getis), Springer-Verlag,
Berlín; pp. 35-59.
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Session 4
4.3. Spatial association plots
4.3.1. Moran’s scatterplot (II)
Moran scatterplot map
IV
I
(-)
(+)
II
III
(+)
(-)
Moran scatterplot
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5
Session 4
4.3. Spatial association plots
4.3.1. Moran’s scatterplot (II)
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4.3. Spatial association
plots
Session 4
4.3.1. LISA maps
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Local spatial autocorrelation statistics are
useful to identify hot spots:
Spatial concentration of high/low values or
Spatial outliers
Local autocorrelation is always present in
global spatial autocorrelation, but it can
also exist in the absence of it.
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Session 4
4.3. Spatial association plots
4.3.1. LISA maps (II)
Non-significant Moran’s I
over the whole area of the
Spanish provinces
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4.3. Spatial association plotsSession 4
4.3.1. LISA maps (III)
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. LÓPEZ, F. & C. CHASCO (2004), “Space-time lags: Specification
strategy in spatial regression models ”. REAL 04-T17,
Session 4
http://www2.uiuc.edu/unit/real/d-paper/real04-t-17.pdf .
4.3.3. Bivariate & space-time plots (II)
Multivariate
spatial
correlation
Bivariate
Moran spatial
autocorrelation
Wartenberg, 1985
Moran
space-time
autocorrelation
Anselin et al., 2002
mkl = zk′W s zl
I kl =
zk = [Yk − µk ]/ σ k
z k′Wzl
z ′z k
Our proposal
I t − k ,t =
zt′− kWzt
zt′− k zt − k
zt = [Yt − µ t ] / σ t
z l = [Yl − µ l ] / σ l
z t − k = [Yt − k − µ t − k ] / σ t − k
Ws is a doubly standardized W
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Session 4
4.3.3. Bivariate & space-time plots
(III)
It-k,t: Moran space-time autocorrelation coefficient
Moran’s I value coincides with the slope
Employment rate (E) of the regression line of Wzt on zt-k
p-value=0.001
p-value=0.427
Wzt
Zt-k
t=2002
k=4
W:contiguity matrix (0-1)
Population (P)
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4.3.3. Bivariate & spacetime plots (IV)
Session 4
Bivariate LISA
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Session 4
4.4. Readings
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2
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Session 4
4.4. Readings (II)
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4
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Session 4
4.4. Readings (III)
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