Lecture 4 - Point Pattern Analysis Flashcards
What is Point pattern analysis (PPA)
Do the observed events show a systematic pattern - either clustered or regularly distributed? Or are they random?
PPA is concerned with locations of events, and answering questions about the distribution of those locations, specifically whether they are more or less clustered than a totally random distribution.
PPA is sensitive to the definition of the study area, a regular pattern may appear clustered at the wrong scale.
Methods to describe point patterns
Centrographic Statistics: simple measures of spatial distribution:
- mean center
- central feature (centroid)
- standard distance deviation
- standard distance ellipse
- density kernel estimation
Methods to quantify point patterns
Distance based point pattern measures:
- nearest neighbour distance
- G function
- K function
- nearest neighbour index
Density based point pattern analysis:
-kernel density estimation
Spatial dependence & independence
No point pattern is completely spatially random
PPA parameters
scale proximity times natural background variation pattern clustered dispersed exploratory approach - find a pattern then look for cause
Alternative to PPA
aggregate data into areas or polygons (MAUP problem)
A priori
Preserve the original location of events in space
What do we need for PPA (5)
- pattern should be mapped on a plane
- determine the study area objectively (no arbitrary boundary/change area –> will change the result)
- all entities in the study area should be included
- 1 to 1 correspondence between objects and events
- proper event locations
The Texas Sharp Shooter
drawing the target ring around the bullet hole that is already there
Point distribution types /94)
Random
Uniform
Clustered
Normal
Point distribution types: random
equal probability to have a point in any location, any point’s position is not affected by other points
Point distribution types: uniform
every point is as far as possible from all neighbors
Point distribution types: clustered
Many points concentrated close together (hot spots) with large areas containing few/no points (cold spots)
Point distribution types: normal
the concentration of points around a locus follows a Gaussian curve (think like a hot spot that is filtered/faded out)
Complete spatial randomness
- EQUAL PROBABILITY - any point has equal probability to be in any position / each area has an equal chance to receive a point
- INDEPENDENCE - the position of any point is independent of positions of any other point
First order effect
Global Effect - a trend for the whole study region
- assumption of equal probability of each area receiving an event not often sustained
- values of variables not independent of their spatial location
- large or global scale variation (differences in intensity)
Second order effect
Local Effect - covariance (or correlation) between values of the process at different regions in space
- assumption that event placements are independent of each other not often sustained
- smaller-scale variations: correlation between local sites, the occurrence of 1 event at a location increases probability of other events nearby
- remember: spatial autocorrelation - interactions between entities
Spatial processes that lead to clustering
Socio-economic processes lead to the clustered distribution of variables values:
-grouping (of similar people in localised areas)
-spatial interaction (people near more likely to interact & share)
-diffusion (neighbours learn from each other)
-dispersal (people move to usually short distances, carry their knowledge)
spatial hierarchies (economy-based influence on binding people together)
Measures of centrality
mean centroid weighted mean centre central feature centre of minimum distance
Measures of dispersion
- standard distance
- standard deviational ellipse
Mean centre
- single point sum measure ofr location of a set of points
- simply the mean of x and y coordinates for the set
- distance points have large effect
- used to track distribution changes/compare distribution of different feature types
example applications:
- cirime type (burglaries vs robberies)
- gender distribution
- biology (summer vs winter observed species)
- economic activity over time
- trip destinations (dif times of day)
Weighted mean centre
- geographic centre of set of points adjusted for the influence values associated with each point
- produced by weighting each x,y coordinate by another variable
- centroids derived from polygons can be weighted by any characteristic of polygon (i.e. population)
Nearest neighbour index
- measures distance between each feature’s centroid and its nearest neighbour’s centroid location
- <1 means clustered and >1 means distributed
- example with villages in Slovaki some dispersed on the plane others clustered in the valleys
