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
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.
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).
Either split one data set into two, or choose two different years. Need to be structurally similar; differences due to randomness
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 ( SL )
Global similarity ( SG ) 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)
All analysis uses the excellent Spatial Point Pattern Test ( sppt ) R library
All code and are data available
Publicly-available crime data with good spatial accuracy
Chosen crimes: BNER, BNEC, TFV, TOB
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
Similarity increases to ~20ha, then plateaus
No disadvantage to using smaller units
Although fewer cells have explanatory power with small cells
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)
Is smaller really better?
Yes! Environmental criminologists can relax...
High-quality, disaggregate data are always preferable
Rather, we propose a framework to explore the scale at which the broader spatial pattern might be overcome by noise
In cases where space is important for the phenomena
Caveat: Meaningful spatial units
Grid cells are not meaningful
Better to use a geography that links to the underlying phenomena
E.g. illuminating work on street segments
Future work could explore this
Data Assimilation for Agent-Based Models (dust)
Main aim: create new methods for dynamically assimilating data into agent-based models.
Uncertainty in agent-based models for smart city forecasts
Developing methods that can be used to better understand uncertainty in individual-level models of cities
Bringing the Social City to the Smart City