Lecture 3 - Spatial Autocorrelation

Question 1

What is spatial autocorrelation?

Answer 1

Spatial autocorrelation helps us understand the extent to which an object is similar to other nearby objects

We assume that everything is randomly distributed and that values at one location do not depend on its neighbour’s values. Locations of values can be changed without affecting data distribution (null hypothesis)

There is SA when there is any systematic pattern in spatial distribution of a variable. Need to test this with statistical measurement techniques, not just based on a visual assessment.

Question 2

SA EXAMPLES

Answer 2

Housing market, elevation change, temperature, vegetation, population, animal species, health, crime, income, air pollution, soil type

Examples from slides: socioeconomic deprivation, police station areas with violent crimes, allergies (hay fever) and industry pollution, gas prices, happiness map

Question 3

Spatial autocorrelation relationships

Answer 3

• Positive when neighbouring locations are similar (clustering of low or high values)
• Negative when neighbouring areas are unsimilar (chess board - grid of hot and cold spots).
• Random when there is no SA.

Question 4

DIAGNOSTIC MEASURES (statistical tests for autocorrelation)

Answer 4

• Joins count statistics
• Moran’s I
• Geary’s C
• Variogram clouds

Testing if distributions of point events/areal units relation to each other (statistically significant)

Question 5

How to determine signficance of SA

Answer 5

Run Moran’s I and look at Z score and p-values (probability of null hypothesis being true) when p-value is very low we can reject null hypothesis and say there is significant spatial autocorrelation.

Need to measure and test strength so we can determine if pattern is random or dependent on something.

Question 6

Null hypothesis

Answer 6

A hypothesis saying that there is no statistical significance between two variables.

• Everything is randomly distributed.
• Values at one location do not depend on neighbouring values.
• Locations of values can be altered without changing data distribution.

The researcher tries to disprove.

Question 7

SA Order Effects

Answer 7

First Order: variation due to underlying properties (one causes the other)
Second Order: variation due to interaction (one thing happens which causes an effects which then causes another thing to happen)

Question 8

SA Method / Steps

Answer 8

• Choose a neighbourhood criterion (which areas are linked?)
• Assign weights to linked areas (create spatial weights matrix)
• Statistically test data using spatial weights matrix to assess autocorrelation

Question 9

Spatial Weights Matrix

Answer 9

Two methods: Binary (contiguity based) or Variable weighting (distance based)

Question 10

Binary SWM

Answer 10

• If zones are adjacent they get a value of 1, if not value of 0
• Table is created
• Contiguity orders (closeness/in contact)

Question 11

Variable SWM

Answer 11

• Distance between points/polygon centroids
• Measurement type - distance to some or all points?
• Can use different distance type measurements: Euclidean, travelling, inverse, etc

Question 12

Rooks vs Queens

Answer 12

For contiguity (binary) matrix
(think chessboard) for first order:
-Rook’s is above, below and right, left (only neighbours sharing edges) (4 neighbours - each gets 0.25 weight)
-Queen’s includes the same plus diagonals which share a vertex (8 neighbours - each gets 0.125 weight)

For second order, third order, etc we include more neighbours by the same methods (neighbours of neigbhours either via rooks or queens)

Question 13

Moran’s I

Answer 13

Looks at a variable in different locations to see if they have similar values. Compares the mean of the variable (spatial lag) to the local value. To identify if there is positive, negative or random. Values of I are typically between -1 to +1. Where -1 is dispersed, 0 is random, +1 is clustered.

Create a scatter plot to see if values are clustered high-high, low-low, high-low, etc.

Test significance with permutations of the data from the set distributed randomly to see if how it compares with the Moran’s I value measured

Question 14

Moran’s scatterplot

Answer 14

Upper left (low-high)
Upper right (high-high)
Lower left (low-low)
Lower right (high-low)