'Appropriate' Spatial Scale

What is the appropriate spatial scale for the analysis of spatial patterns?

Addresses, streets, neighbourhoods, regions, etc..

Could be a theoretical choice

E.g. we know individual houses are important

Or determined empirically

E.g. we only have data at the neighbourhood level

'Appropriate' Spatial Scale

But in some cases, there might be a need to find an 'appropriate' scale

In general: smaller is better (homogeneous events and population)

But: how small is too small

High-resolution data are hard / expensive to obtain (might be personally disclosive / commercially sensitive)

Small number problems / signal v.s. noise

Definition of the most appropriate scale: that which is as large as possible without causing the underlying spatial units to become heterogeneous with respect to the phenomena under study.

Method

Combines and adapts two existing methods:

Multiple-resolution goodness of fit procedure (Costanza, 1989) and a test for spatial (dis)similarity (Andresen’s S: Andresen, 2009; Wheeler et al.,2018).

1. Choose two similar crime datasets

Either split one data set into two, or choose two different years. Need to be structurally similar; differences due to randomness

2. Place a regular grid over the two data sets
3. Count the number of points in each cell from each data set
4. Remove cells with insufficiently low expected frequency
5. Calculate similarity using Andresen's Global S index
6. Repeat (2) using a smaller grid N times (until similarity is fairly constant)
7. Graph the similarity at different resolutions

Method

Calculating Similarity (Andresen's S)

For each grid cell, calculate the proportion of events from each data set (p1, p2)

Use Fisher's exact test to determine whether the proportions are similar

dissimilar -> 0, similar -> 1

Provides local (per cell) estimates of similarity ( S_L )

Global similarity ( S_G ) is the mean of all cells

Removing cells with low count

What about cells with too few events? Cannot just mark as 'similar'

Calculate expected number of events

E = row marginal * column marginal / grand total

Remove cells with E < 5 (by convention)

Method

All analysis uses the excellent Spatial Point Pattern Test ( sppt ) R library

github.com/wsteenbeek/sppt

Thanks Wouter!!

All code and are data available

github.com/nickmalleson/Multi-Scale-Error-Analysis

Similarity at different resolutions

Quiz

Similarity at different resolutions

What I expected

Similarity at different resolutions

WTF?

Similarity at different resolutions

Explanation

Case Study - Vancouver

Publicly-available crime data with good spatial accuracy

Chosen crimes: BNER, BNEC, TFV, TOB

Simulated Results

Crime data results

Well, what is the most appropriate resolution?

Discussion: Residential Burglary (BNER)

Peak in similarity with cells of ~20 hectares in size

Twice as large as a dissemination area / OA (smallest census unit)

20ha is the most appropriate scale?

Smaller is usually better, but <20ha noise might hide the signal

Note: burglary patterns were somewhat dissimilar

Discussion: Theft from Vehicle (TFV)

Similarity increases to ~20ha, then plateaus

No disadvantage to using smaller units

Although fewer cells have explanatory power with small cells

Discussion: Commercial Burglary (BNEC) and Theft of Bike (TOB)

Similarity peaks, then continues to rise

Even with 6ha cells there is still a discernible signal

Very tightly clustered crime pattern

Has explanatory power even at very small cells (in clustered areas)

References

Please see the GISRUK abstract at:

www.nickmalleson.co.uk/papers/2019-GISRUK-Presentation.pdf