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Chapter 5. Part A: Spatial data exploration. Spatial data exploration. Spatial analysis and data models (Anselin, 2002). Spatial data exploration. Sampling frameworks Pure random sampling Stratified random – by class/strata (proportionate, disproportionate) Randomised within defined grids

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chapter 5

Chapter 5

Part A: Spatial data exploration

www.spatialanalysisonline.com

spatial data exploration
Spatial data exploration
  • Spatial analysis and data models (Anselin, 2002)

www.spatialanalysisonline.com

spatial data exploration1
Spatial data exploration
  • Sampling frameworks
    • Pure random sampling
    • Stratified random – by class/strata (proportionate, disproportionate)
    • Randomised within defined grids
    • Uniform
    • Uniform with randomised offsets
    • Sampling and declustering

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spatial data exploration2
Spatial data exploration
  • Sampling frameworks – point sampling

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spatial data exploration3
Spatial data exploration
  • Sampling frameworks – within zones

Grid generation (hexagonal) - selection of 1 point per cell, random offset from centre

Grid generation - square grid within field boundaries

Selection of 5 random points per zone

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spatial data exploration4
Spatial data exploration

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spatial data exploration5
Spatial data exploration
  • Random points on a network

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spatial data exploration6
Spatial data exploration
  • EDA, ESDA and ESTDA
    • EDA – basic aims (after NIST)
      • maximize insight into a data set
      • uncover underlying structure
      • extract important variables
      • detect outliers and anomalies
      • test underlying assumptions
      • develop parsimonious models
      • determine optimal factor settings

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spatial data exploration7
Spatial data exploration
  • ESDA (see GeoDa and STARS)
    • Extending EDA ideas to the spatial domain (lattice/zone models)
      • Brushing
      • Linking
      • Mapped histograms
      • Outlier mapping
      • Box plots
      • Conditional choropleth plots
      • Rate mapping

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spatial data exploration8
Spatial data exploration
  • ESDA: Brushing & linking

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spatial data exploration9
Spatial data exploration
  • ESDA: Histogram linkage

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spatial data exploration10
Spatial data exploration
  • ESDA: Parallel coordinate plot & star plot

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spatial data exploration11
Spatial data exploration
  • ESDA: Mapped box plots

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spatial data exploration12
Spatial data exploration
  • ESDA: Conditional choropleth mapping

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spatial data exploration13
Spatial data exploration
  • ESDA: Mapped point data

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spatial data exploration14
Spatial data exploration
  • ESDA: Trend analysis (continuous spatial data)

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spatial data exploration15
Spatial data exploration
  • ESDA: Cluster hunting – GAM/K (steps)
  • Read data for the population at risk
  • Identify the MBR containing the data, identify starting circle radius, and degree of overlap
  • Generate a grid covering the MBR
  • For each grid-intersection generate a circle of radius r
  • Retrieve two counts for the population at risk and the variable of interest
  • Apply some “significance” test procedure
  • Keep the result if significant
  • Repeat Steps 5 to 7 until all circles have been processed
  • Increase circle radius by dr and return to Step 3 else go to Step 10
  • Create a smoothed density surface of excess incidence for the significant circles
  • Map this surface and inspect the results

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spatial data exploration16
Spatial data exploration
  • Grid-based statistics
    • Univariate analysis of attribute data (non-spatial metrics)
    • Cross-classification and cross-tab analyses
    • Spatial pattern analysis for grid data (including Landscape metrics)
      • Patch metrics; Class-level metrics; Landscape-level metrics
    • Quadrat analysis
    • Multi-grid regression analysis

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spatial data exploration17
Spatial data exploration
  • Grid-based statistics
    • Landscape metrics
      • Non-spatial
        • Proportional abundance; Richness; Evenness; Diversity
      • Spatial
        • Patch size distribution and density; Patch shape complexity; Core Area; Isolation/Proximity; Contrast; Dispersion; Contagion and Interspersion; Subdivision; Connectivity

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spatial data exploration18
Spatial data exploration
  • Point (event) based statistics
    • Typically analysis of point-pair distances
    • Points vs events
    • Distance metrics: Euclidean, spherical, Lp or network
    • Weighted or unweighted events
    • Events, NOT computed points (e.g. centroids)
    • Classical statistical models vs Monte Carlo and other computational methods

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spatial data exploration19
Spatial data exploration
  • Point (event) based statistics
    • Basic Nearest neighbour (NN) model
      • Input coordinates of all points
      • Compute (symmetric) distances matrix D
      • Sort the distances to identify the 1st, 2nd,...kth nearest values
      • Compute the mean of the observed 1st, 2nd, ...kth nearest values
      • Compare this mean with the expected mean under Complete Spatial Randomness (CSR or Poisson) model

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spatial data exploration20
Spatial data exploration
  • Point (event) based statistics – NN model

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spatial data exploration21
Spatial data exploration
  • Point (event) based statistics – NN model
    • Mean NN distance:
    • Variance:
    • NN Index (Ratio):
    • Z-transform:

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spatial data exploration22
Spatial data exploration
  • Point (event) based statistics
    • Issues
      • Are observations n discrete points?
      • Sample size (esp. for kth order NN, k>1)
      • Model requires density estimation, m
      • Boundary definition problems (density and edge effects) – affects all methods
      • NN reflexivity of point sets
      • Limited use of frequency distribution
      • Validity of Poisson model vs alternative models

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spatial data exploration23
Spatial data exploration
  • Frequency distribution of nearest neighbour distances, i.e.
    • The frequency of NN distances in distance bands, say 0-1km, 1-2kms, etc
    • The cumulative frequency distribution is usually denoted
      • G(d) = #(di < r)/n where di are the NN distances

and n is the number of

measurements, or

      • F(d) = #(di < r)/m where m is the number of random

points used in sampling

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spatial data exploration24
Spatial data exploration
  • Computing G(d) [computing F(d) is similar]
  • Find all the NN distances
  • Rank them and form the cumulative frequency distribution
  • Compare to expected cumulative frequency distribution:
  • Similar in concept to K-S test with quadrat model, but compute the critical values by simulation rather than table lookup

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spatial data exploration25
Spatial data exploration
  • Point (event) based statistics – clustering (ESDA)
    • Is the observed clustering due to natural background variation in the population from which the events arise?
    • Over what spatial scales does clustering occur?
    • Are clusters a reflection of regional variations in underlying variables?
    • Are clusters associated with some feature of interest, such as a refinery, waste disposal site or nuclear plant?
    • Are clusters simply spatial or are they spatio-temporal?

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spatial data exploration26
Spatial data exploration
  • Point (event) based statistics – clustering
    • kth order NN analysis
    • Cumulative distance frequency distribution, G(r)
    • Ripley K (or L) function – single or dual pattern
    • PCP
    • Hot spot and cluster analysis methods

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spatial data exploration27
Spatial data exploration
  • Point (event) based statistics – Ripley K or L
  • Construct a circle, radius d, around each point (event), i
  • Count the number of other events, labelled j, that fall inside this circle
  • Repeat these first two stages for all points i, and then sum the results
  • Increment d by a small fixed amount
  • Repeat the computation, giving values of K(d) for a set of distances, d
  • Adjust to provide ‘normalised measure’ L:

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spatial data exploration28
Spatial data exploration
  • Point (event) based statistics – Ripley K

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spatial data exploration29
Spatial data exploration
  • Point (event) based statistics – comments
    • CSR vs PCP vs other models
    • Data: location, time, attributes, error, duplicates
      • Duplicates: deliberate rounding, data resolution, genuine duplicate locations, agreed surrogate locations, deliberate data modification
    • Multi-approach analysis is beneficial
    • Methods: choice of methods and parameters
    • Other factors: borders, areas, metrics, background variation, temporal variation, non-spatial factors
    • Rare events and small samples
    • Process-pattern vs cause-effect
    • ESDA in most instances

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spatial data exploration30
Spatial data exploration
  • Hot spot and cluster analysis – questions
    • where are the main (most intensive) clusters located?
    • are clusters distinct or do they merge into one another?
    • are clusters associated with some known background variable?
    • is there a common size to clusters or are they variable in size?
    • do clusters themselves cluster into higher order groupings?
    • if comparable data are mapped over time, do the clusters remain stable or do they move and/or disappear?

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spatial data exploration31
Spatial data exploration
  • Hot spot (and cool-spot) analysis
    • Visual inspection of mapped patterns
    • Scale issues
    • Proximal and duplicate points
    • Point representation (size)
    • Background variation/controls (risk adjustment)
    • Weighted or unweighted
    • Hierarchical or non-hierarchical
    • Kernel & K-means methods

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spatial data exploration32
Spatial data exploration
  • Hot spot analysis – Hierarchical NN

Cancer incidence data 1st and 2nd order clusters

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