iccsa geog an mod elke moons

Hot Spot Analysis: Improving a LISA for application

in traffic safety

Elke MoonsTransportation Research Institute

(IMOB)Hasselt University

BelgiumE-mail: elke.moons@uhasselt.be

ICCSA ConferenceGeog-An-Mod workshop

• Aim of the study

• Existing methods & applications to serve the purpose

• Application: Accidents on highways

• Conclusion

Overview

• Hot Spot Analysis: Why?– Traffic Safety: Top priority in National

Safety Plan– Belgium:

• poor performance; • risk of having a fatal accident (per VKD) is

33% higher than the European average• ambitious goal: reduce the number of fatal

accidents per year up to 500 by 2015

– Where are the dangerous locations and why are they hazardous?

1. Aim2. Methods3. Application4. Conclusion

• Aim: multiple– Identification– Ordering– Profiling– Selection

• Methods: many different methods are applied by different services which one to use? (purely observational methods, statistical methods, spatial methods, …)

1. Aim2. Methods3. Application4. Conclusion

• Definition of HS: Very broad! (Hauer, 1996; Elvik, 2007)

• Examples:– (increased) nr of accidents (w.r.t. comparison group)– (increased) risk on having an accident (w.r.t. comparison

group)– Taking severity into account

e.g. 1L + 3S + 5D > 15 hot spot– Observed versus expected number– Hot spot versus hot zone– Combinations are possible

• Geographical aspect is very important, though very often (Bayesian) statistical models are used!

1. Aim2. Methods3. Application4. Conclusion

• Idea: take geographical aspect directly into account

• Instead of concentrating all characteristics in one point, one looks also at the neighboring locations

• One needs to be able to localize accidents (!)

• Spatial autocorrelation– Look for relations between location in a study area that are close to

each other in space and they look alike or are each others opposite concerning the numerical variable under investigation

– At first, a point observations is returned, but one does take into account the neighboring points, consequently one combines indices that are alike to distinguish between hot zones and zones that are less dangerous

– Global measures: do the locations that pertain to the study area show a spatial autocorrelation together?

– Local measure: are there parts of the study area that show a spatial autocorrelation?

1. Aim2. Methods3. Application4. Conclusion

• Local: Local Indicators of Spatial Aggregation (LISA)– Local Moran index

– Disadvantage: not uniquely defined

• Nr of neighboring locations– Impossible to determine one optimal distance

– Varies according to type and characteristics of the road

• Weights are not uniquely defined– Uniform: ~ all 1 in neighborhood and 0 outside

– Logical: take distance into account, degressive weight wrt square of distance

– Fewer and shorter zones when compared to inverse of distance, but you have to most dangerous zones in this way

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1. Aim2. Methods3. Application4. Conclusion

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1. Aim2. Methods3. Application4. Conclusion

• Distributional properties are elusive

• Gaussian approximation does not work for Poisson processes such as accidents

• Use Monte Carlo testing to determine distributional properties

• New to the field:– Use of Moran’s I along the road network (accounts for

curvature, etc.)– Can account for crossroads/end of the road, etc. (see

further)– Locations without accidents also play an important role– From hot spots to a hot zone

• Correct use: i.e. take zero observations into account (otherwise wrong average & overestimation of importance of locations with accidents)

• Use of a reference value (for x-bar): Limburg, Flanders, Belgium

• Look only at locations and neighborhoods that positively reinforce (+/+) each other; there was doubt about -/+ & +/-, but if you would add accidents at location i (until you reach the average number), this would lead to a less extreme value (0) which is not desirable!

Adaptations

1. Aim2. Methods3. Application4. Conclusion

• Monte Carlo approach to determine the significant cut-off value (95%)– Because of the typical characteristics (many zero counts,

Poisson data = count data) of accidents, the distribution of the z-statistic was not correct (even far from!)

– Idea: • Distribute the total nr of accidents randomly over the

locations (e.g. for highways in Limburg 470 accidents over 3252 locations) and allow for a location to be selected more than once

• Repeat this multiple times (500) and determine each time for each location its Moran’s I

• Use the distribution of the obtained Moran values to determine the 95% cut-off value to localize the 5% most extreme Moran values (also only looking at positively reinforced values)

1. Aim2. Methods3. Application4. Conclusion

1. Aim2. Methods3. Application4. Conclusion

• Application to a straight part of the road

X X X X X X X X X X X X

Xi 1 0 0 0 1 2 3 2 1 0 0 0 0 4

A fixed length of 400m was used, weights are set equal to the average nr of accidents was set equal to 1 over a 3 year period and we look 200m to the left and right

2

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ij

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X X

1. Aim2. Methods3. Application4. Conclusion

1. Aim2. Methods3. Application4. Conclusion

What happens at the end of the road?

X X X X X X X XX

Vb. 1 0 0 0 3 2 1 2 3

1. Aim2. Methods3. Application4. Conclusion

What happens at a crossroad?

X X X X X XX

XX

XX

XX

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XX

1 0 0 1 2 3 2

10

01

2

03

01

0

1. Aim2. Methods3. Application4. Conclusion

– Data: 2003-2005 (variability!)– 3252 HM poles, 470 accidents– As a reference value: average nr of

accidents in Flanders: 0.1299(3978 accidents on 30621 HM poles)

– Average nr of accidents: 0.1556

Highways in Limburg

1. Aim2. Methods3. Application4. Conclusion

– Data: 2003-2005 (variability!)

– 3252 HM poles, 470 accidents

– As a reference value: average nr of accidents in Flanders: 0.1299(3978 accidents on 30621 HM poles)

– Average nr of accidents: 0.1445

– 1km to the left and right of each HM pole are considered to be neighbors, weights are inverse quadratic

1. Aim2. Methods3. Application4. Conclusion

• Cut-off value: 3.93, HS if Ii > 3.93

• Nr of hot spots in Limburg: 15

• Nr of hot spots if you would have used the normal distribution: 59 this clearly indicates the importance of the Monte Carlo approach!

1. Aim2. Methods3. Application4. Conclusion

1. Aim2. Methods3. Application4. Conclusion

Moran’s I: correct use

1. Aim2. Methods3. Application4. Conclusion

Moran’s I: Gaussian approximation

Province Nr of hot spots

Limburg 15

Flemish-Brabant 75

Antwerp 91

Eastern-Flanders 89

Western-Flanders 14

1. Aim2. Methods3. Application4. Conclusion

1. Aim2. Methods3. Application4. Conclusion

• General characteristics– 3856 locations– 1679 accidents between Hasselt and

Lummen on numbered roads– Average nr of accidents in study area:

0.4354

Application II: numbered roads between Hasselt and Lummen

1. Aim2. Methods3. Application4. Conclusion

• Nr of hot spots: 48

• Nr of hot spots if one would use the normal distribution: 114 emphasizes the importance of MC!

Moran’s I with MC approach

1. Aim2. Methods3. Application4. Conclusion

1. Aim2. Methods3. Application4. Conclusion

• Normal use of Moran’s I is due to sparseness and Poisson process impossible

• Simulation procedure to determine hazardous locations

• Necessary to allocate money in best possible way!

Conclusion

1. Aim2. Methods3. Application4. Conclusion

• Analysis on local roads: Basic Spatial Units of approximately 100m have been determined

• Compare results to results of network-constrained cluster methods, network K-function methods

• From hot spots to hot zones: first attempt

Future research

1. Aim2. Methods3. Application4. Conclusion

1. Aim2. Methods3. Application4. Conclusion

• Best weights: probably different for different road types

• Ideal number of neighbors to take into account

Open/unsolved issues

1. Aim2. Methods3. Application4. Conclusion

Thank you for your attention!