Ch 5 Practical Point Pattern Analysis Spatial Stats & Data Analysis by Magdaléna Dohnalová

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 doesn’t –Global technique

In fact, what we need to know is..  Where the pattern deviates from expectations >>> CLUSTER DETECTION  Where are the Clusters?

Case Study: Sellafield 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

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

GAM…how the  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

Pattern of Circles used by GAM

About Cluster Detectors  More recent genetic algorithms (intelligent) –Map Explorer (MAPEX) & Space Time Attribute Creature (STAC)  Data Availability –When aggregate data -> 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

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

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

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!

Point Pattern Analysis: Proximity Polygons  Delaunay proximity polygons –Distribution of area –The number of neighbors –Lengths of Edges –Minimum Spanning Tree (from Gabriel graph)

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)

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.