Ch 5 Practical Point Pattern Analysis

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Ch 5Practical Point Pattern Analysis

• Spatial Stats Data Analysis
• by Magdaléna Dohnalová

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Problems of pure Spatial Statistical Analysis

• Null Hypothesis Is that IRP/CSR?
• Insufficient description
• First-order influence
• Process-Pattern Matching
• Either it does or it doesnt
• Global technique

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In fact, what we need to know is..

• Where the pattern deviates from expectations
• gtgtgt CLUSTER DETECTION
• Where are the Clusters?

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Case StudySellafield Leukemia Study, UK

• Children leukemia deaths clustered around nuclear
  plant
• Proved that THERE WAS a cluster, but missing
  evidence of linking cause
• Apparent clusters occur naturally in many
  diseases
• The actual number in cluster was very low
• Similar clusters have been found around
  nonnuclear plants

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Cluster analysis of Point Patterns

• Problem with small clusters
• Distance Rings
• Rates of occurrence
• Distance form the plant
• Geographical Analysis Machine (GAM)
• Automated cluster detector for point patterns

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GAMhow the heck?_at_!!_at_

• Two dimensional grid
• Series of different circles
• various size and density
• Number of events within each circle
• Exceeds threshold? (Monte Carlo simulation of
  expected pattern)
• If YES, draw circle on the map
• END RESULT map of significant circles

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Pattern of Circles used by GAM
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About Cluster Detectors

• More recent genetic algorithms (intelligent)
• Map Explorer (MAPEX) Space Time Attribute
  Creature (STAC)
• Data Availability
• When aggregate data -gt MAUP
• Variation in Background Rate
• Assume uniform geography
• Overlapping of significant circles
• not independent
• Setting variable threshold!!!
• Time problem
• Snapshot effect
• Aggregation over time, similar to MAUP

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Extension of Basic Point Pattern

• Multiple Sets of Events
• Contingency table analysis
• Chi-Square Test
• Discards location information
• Cross Functions (G and K functions)
• Cumulative Nearest-Neighbor function
• Distance from event in each pattern (G)
• Events counts within in distance to the other (K)
• Random if events are independent of each other

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Extension of Basic Point Pattern

• When was it Clustered?
• Clustering in space and time together!
• Knox test
• Distance in space (near-far) and time
  (close-distant)
• Contingency table Chi-square
• Threshold decision similar to MAUP
• Mantel Test
• Distance and space distance for all objects
• Modified K function
• Combining two K functions in Contingency table
• Test difference between the two

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Point Pattern Analysis Proximity Polygons

• Using DENSITY and DISTANCE
• Geographical Space is not random!
• Delaunay triangulation of proximity polygons
• Neighborhood relations are defined in respect to
  local patterns!

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Point Pattern Analysis Proximity Polygons

• Delaunay proximity polygons
• Distribution of area
• The number of neighbors
• Lengths of Edges
• Minimum Spanning Tree (from Gabriel graph)

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Point Pattern Analysis Distance Based Methods

• Distance Matrices
• Large amount of data (not the most efficient but
  convenient for computer calculations)
• Underlines shortest distance (nearest neighbor
  G function)
• Convert to Adjacency Matrices (K function)
• Derived Matrices (F function)

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Questions

• What are the two major questions we ask about
  clusters?
• What is the final product of GAM?
• What are the main challenges in cluster
  detection?
• What are the strengths of using Proximity
  Polygons for cluster detection? Describe the
  minimum spanning tree.