Lecture 4 - Point Pattern Analysis

Question 1

What is Point pattern analysis (PPA)

Answer 1

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.

Question 2

Methods to describe point patterns

Answer 2

Centrographic Statistics: simple measures of spatial distribution:

• mean center
• central feature (centroid)
• standard distance deviation
• standard distance ellipse
• density kernel estimation

Question 3

Methods to quantify point patterns

Answer 3

Distance based point pattern measures:

• nearest neighbour distance
• G function
• K function
• nearest neighbour index

Density based point pattern analysis:
-kernel density estimation

Question 4

Spatial dependence & independence

Answer 4

No point pattern is completely spatially random

Question 5

PPA parameters

Answer 5

scale
proximity
times
natural background variation
pattern
clustered
dispersed
exploratory approach - find a pattern then look for cause

Question 6

Alternative to PPA

Answer 6

aggregate data into areas or polygons (MAUP problem)

Question 7

A priori

Answer 7

Preserve the original location of events in space

Question 8

What do we need for PPA (5)

Answer 8

1. pattern should be mapped on a plane
2. determine the study area objectively (no arbitrary boundary/change area –> will change the result)
3. all entities in the study area should be included
4. 1 to 1 correspondence between objects and events
5. proper event locations

Question 9

The Texas Sharp Shooter

Answer 9

drawing the target ring around the bullet hole that is already there

Question 10

Point distribution types /94)

Answer 10

Random
Uniform
Clustered
Normal

Question 11

Point distribution types: random

Answer 11

equal probability to have a point in any location, any point’s position is not affected by other points

Question 12

Point distribution types: uniform

Answer 12

every point is as far as possible from all neighbors

Question 13

Point distribution types: clustered

Answer 13

Many points concentrated close together (hot spots) with large areas containing few/no points (cold spots)

Question 14

Point distribution types: normal

Answer 14

the concentration of points around a locus follows a Gaussian curve (think like a hot spot that is filtered/faded out)

Question 15

Complete spatial randomness

Answer 15

1. EQUAL PROBABILITY - any point has equal probability to be in any position / each area has an equal chance to receive a point
2. INDEPENDENCE - the position of any point is independent of positions of any other point

Question 16

First order effect

Answer 16

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)

Question 17

Second order effect

Answer 17

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

Question 18

Spatial processes that lead to clustering

Answer 18

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)

Question 19

Measures of centrality

Answer 19

mean
centroid
weighted mean centre
central feature
centre of minimum distance

Question 20

Measures of dispersion

Answer 20

• standard distance

- standard deviational ellipse

Question 21

Mean centre

Answer 21

• 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)

Question 22

Weighted mean centre

Answer 22

• 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)

Question 23

Nearest neighbour index

Answer 23

• 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