Lecture 5 - Hot Spot Analysis

Question 1

DENSITY-BASED POINT PATTERNS

Answer 1

how we quantify depends on how we group/classify data

density depends on the sensitivity of the study region definition

density-based point pattern measures characterize patterns based on 1st order properties

Question 2

DENSITY BASED MEASURES

Answer 2

1. Quadrat counts

2. Kernel density estimation

Question 3

PROBLEMS WITH COUNTING METHODS (KDE & quadrats)

Answer 3

1. a cell may not contain any incidents but can have a high score (because of the way density is smoothed out with the kernel)
2. changes in cell size/search distance can result in different surfaces (local vs global)
3. edge/border effects
4. legend can be confusing

Question 4

APPLICATIONS (examples)

Answer 4

examples:
chernobyl radiation over weeks after
density of walmart vs starbucks vs mcdonalds
air pollution emissions
turtle populations
crime hot spots

Question 5

STATISTICAL SIGNIFICANCE

Answer 5

Ratio = KDE result / KDE background population

Mathematical equations to density

Map results by mean or standard deviation

Can map / animate hot spots over time to see how it moves

Question 6

What is a hot spot?

Answer 6

a cluster of incidents or high values

Question 7

First order effects

Answer 7

Global effect

The driving process

Question 8

Second order effects

Answer 8

Local effect

The local distribution - secondary processes (spatial autocorrelation)

Question 9

Quadrat count method

Answer 9

Use a quadrat (grid) to count the density by counting each square - used often in ecology (count dominant landcover/plant species in each square)

Two types:
Exhaustive census approach
Random sampling

Question 10

Quadrat: exhaustive census approach

Answer 10

• uniform grids drawn across study area and thematically mapped
• choice of origin, orientation and size affects observed frequency distribution
• commonly used in spatial crime and epidemiology studies

Problems:
-quadrat is too large / small

Question 11

Quadrat: random sampling approach

Answer 11

• possible to increase the sample size by adding more quadrats
• may describe point pattern w/o having complete data on the entire pattern
• common in field biology work

Question 12

Quadrat shapes

Answer 12

• squares
• hexagonal
• triangular

hexagons are fairly common because they have lots of neighbours

Question 13

Kernel Density Estimation

Answer 13

• Kernel = group of cells around a central point
• calculates density using a kernel function
• creates raster surfaces - using a neighbourhood of values (Kernel)
• larger Kernel = smoother and less detailed
• smaller Kernel = patchier but better detailed
• ArcGIS has an algorithm to calculate optimum kernel size

Question 14

KDE process

Answer 14

fit a weighted cone over each point, the cone has distance decay with more density in the middle than extremes, KDE algorithm sums across the study region all the cones to create a new raster surface

it is a VISUAL estimate of density but not a statistical test of density

Question 15

Bandwidth

Answer 15

Bandwith = radius

• use to make the kernel wider or narrower
• useful to look for local or global trends (local = small bandwidth, global = large)

Question 16

spurious ‘noise’ and border effects

Answer 16

spurious ‘noise’ = lone points at the edge generate density which is unreliable, the solution to use adaptive kernel estimation (alter bandwidth as a function of the density of underlying points)

boundaries = may be missing contributions from the edge, solution to adopt edge correction or refine boundary inwards by a distance equal to the bandwidth

Question 17

KDE core considerations

Answer 17

• what constitutes a hot spot?
• defining hot spot thresholds (symbology/classification)
• what can you control? cell size and kernel distance (bandwidth)
• need to statically test significance
• to test significant use ratio = KDE result / KDE background population