TRANSPORTATIONSPATIAL NESTED SCALES FOR ROAD ACCIDENTS
IN THE PERIPHERY OF BRUSSELSNathalie ECKHARDT

Isabelle THOMAS

Department of Geography, U.C.L
Louvain-la-Neuve, Belgium

Department of Geography, U.C.L
Louvain-la-Neuve, Belgium
National Fund for Scientific Research
Brussels, Belgium
Centre of Operation Research and Econometrics
Louvain-la-Neuve, Belgium(Received October 12, 2004)

This paper tests the usefulness of a multilevel model (MLM) for explaining the spatial occurrence of road accidents; it also shows and confirms
how far the characteristics of the geographical environment influence the location and concentration of road accidents at two levels of spatial aggregation. The results are compared to those obtained from a more classical logistic regression. The analysis is performed on the southern periphery ofBrussels (Belgium). The main conclusions are: (1) that MLM is a potentially useful technique for modelling road accidents, but that hierarchical levels
are not easy to define for spatial data and so MLM are less useful than other regression techniques for modelling spatial occurrences of road accidents; (2) that the characteristics of the environment and the road itself significantly influence the occurrence of road accidents, and changes in thesecharacteristics are quite important elements in the explanation, leading to the suggestion that road users do not adapt their behaviour sufficiently tochanges in road conditions. Hence, concentrations of road accidents often correspond to places where improvements could be made in terms of roaddesign, signalling and land-use planning.
Key Words: Multilevel model, Geography, Environment, Accidents, Brussels

1. INTRODUCTION
The main research objective of our team is toanalyse the spatial aspects of road-accident occurrence atseveral scales of analysis1-4. The present contribution
aims at modelling the spatial occurrence of road accidents
by considering different nested levels of spatial data aggregation.
Multilevel analysis is a recent technique that enables the relationships/interactions between variables atseveral levels of data aggregation to be examined simultaneously5,6. It attempts to solve the dilemma of the spatial scale, that is to say the use of scales in analysing thecharacteristics of accidents at a local level, taking into
account the broader spatial context in which these accidents occur. Up to now, applications have mainly been
limited to the social and behavioural sciences. Let us
mention here the well-known example of school test results, which can be explained by the individual characteristics of the scholars, but also by the characteristics ofthe class (group) as well as the school or even its environment7. Multilevel models are specifically dedicated tothe concept of the integration of contextual effects andso to hierarchical models6,8,9. In spatial analysis, multi-

66 • IATSS RESEARCH Vol.29 No.1, 2005

level models enable the researcher to go beyond the scale
defined a priori by territorial executives (for example),and to attempt to capture the continuous character of
space, taking into account the nested nature of spatial
scales6,10.
In the field of road safety, two recent papers haveused multilevel modelling. Jones and Jorgensen11 consider road accident casualties, and show that the risk offatality is associated with casualty age and sex, as wellas the type of vehicles involved, characteristics of the
impact, attributes of the road section on which it took
place, time of day, and whether alcohol was suspected.
The multilevel analysis shows that 16% of the unexplained variation in casualty outcomes was between accidents, whilst approximately 1% was associated with thearea in which each incident occurred. Gee and Takeuchi12
analyse the cross-sectional relationship between traffic
stress and neighbourhood conditions, depression andhealth status by means of multilevel analyses. They showthat perceived traffic stress is associated with both general health status and depression in multilevel models,with people reporting traffic stress having lower healthstatus and more depressive symptoms.
In this paper, we aim at showing the utility of multilevel analysis for understanding the spatial aspects of

SPATIAL NESTED SCALES FOR ROAD ACCIDENTS IN THE PERIPHERY OF BRUSSELS

road safety, and more particularly to show how far thecharacteristics of space (environment and infrastructure)
can influence the location of accidents at different levelsof measurements in a periurban environment. By doing
so we expect to partly solve some data aggregation problems, well-known in spatial analysis13,14 as well as in roadaccident analysis15,16. The analysis is here conducted ondata from the suburbs of Brussels (southern periphery);the modelling results are interpreted in terms of operational results and are also compared to those obtained bymeans of a more “classical” logistic regression3.
This paper is organised as follows. The model is
described in Section 2 and choices related to the data are
discussed in Section 3. Empirical results are reported in
Section 4. Two levels of aggregation are considered: thehectometre (100m) of road and the commune; we aim atunderstanding why accidents are concentrated in somehectometres and why these hectometres are located in
specific communal environments. Our conclusions anddiscussion are to be found in Section 5.

2. MULTILEVEL ANALYSIS
Let us first justify our modelling choices by briefly
defining the type of model (Section 2.1), its advantages
in terms of accident modelling (Section 2.2) as well as
the methods used for estimating the parameters (Section
2.3). We refer to the literature for further model definition and formulation6,7,9,17,18.
2.1

Definition
Multilevel modelling (MLM) is a type of regressionthat has mainly been developed since the 1980s; it is designed to handle hierarchical and clustered data. Such data
involve group effects on individuals, which may not be
assessed validly by traditional statistical techniques. Thatis, when grouping is present, observations within a groupare often more similar than would be predicted on apooled-data basis, and hence the assumption of independence of observations is violated. MLM uses variables
at several levels of aggregation to adjust the regressionof the base-level dependent variables on the base-level
independent variables. In our case, for instance, we could
predict accident occurrence from the characteristics of thehectometres or from larger environments such as communes. MLM is related to structural equation modellingin that it fits regression equations to the data, then tests
alternative models using a likelihood ratio test.

N. ECKHARDT, I. THOMAS

MLM specifies the expected direct effects of variables on each other within any one level, and cross-levelinteraction effects between variables located at different
levels. Hence, mediating mechanisms are postulated; they
allow variables at one level to influence variables at another level (e.g. better road infrastructure may influenceroad-user behaviour and hence prevent accidents at places
other than that where the road enhancement has been effected). MLM tests multilevel theories statistically, by simultaneously modelling variables at different levels
without having recourse to aggregation or disaggregation.
In our case, the global problem is to model the relationship between the place of an accident and the context inwhich it occurs. We hence aim to detect the amount ofcontext contribution and its effect on the total variationof the “individual behaviour”, and to identify whichmacro characteristics are responsible for the context effect. This means conceptually introducing a multilevelapproach in which road accidents are grouped together
at different spatial levels; in our case, variables from twolevels will be jointly analysed in a unified framework.
The multilevel model is therefore a model with asingle dependent variable (Y) measured at the base level(e.g. the accidents are taken individually). As in ordinary
least squares (OLS) regression, there may be one or more
independent variables collected at the base level. In addition, there will be at least one broader level of aggregation, with at least one explanatory variable (for instance,
the environment or the socio-economic characteristics of
the ward). In an OLS model, base-level data are analysed
for all groups pooled together (e.g. all hectometres, allcommunes). In a MLM, the regression is performed separately for each group. This produces different regression
coefficients and different intercepts (e.g. for each blackzone or each commune) and also explains why MLMs arecalled “random coefficient models”. Such models usually
use maximum likelihood algorithms to estimate the parameters (coefficients) (see http://www2.chass.ncsu.edu/
garson/pa765/multilevel.htm).
Let us briefly summarise the formulation. Yij is thevariable to be explained. We consider here a model at twolevels of observation (see Section 2.2): the hectometre i(Level 1) localised in a municipality j (Level 2). The general shape of the linear model includes an explanatory
variable at Level 1 related to the hectometre (Xi), and acontextual variable at Level 2 related to the commune(municipality) and denoted Zj. Then
Yij = β 0 + β i X i +Γ j Z j (µ 0j+ µ ij∗X ij+ εij)

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where β 0 + β i X i +Γ j Z j is the fixed part of the modeland (µ 0j + µ ij ∗X ij + εij ) is the random part. β 0 is the intercept. β i is the angular coefficient of the right-hand sideof the regression; it is the coefficient of the explanatory
variables at Level 1 (Xi); Γ j is the coefficient of the Level
2 explanatory variable (Zj). Error terms (residuals) areassociated with β 0 and β i at the contextual level (µ 0j andµ ij); they represent the deviation of the municipality jfrom the average coefficient. These contextual residuals
are assumed to follow a normal distribution law with nullaverages, variances σ0µ 2 and σiµ 2 and covariance σ0iµ .
Level 1 residuals (εij) have a null-average and equal σ0ε2variances. Hence, this formulation allows every municipality j to have its own constant (β0) and angular coefficient (βi). This heterogeneity of the regression coefficients
between municipalities can later be tested and explainedby Level 1 and Level 2 variables. In other words, the outputs of a multilevel model include: (1) a fixed part containing the regression coefficients and the corresponding
p-value for the significance levels, at Level 1, Level 2,
and for the cross-level interactions; (2) a random part containing regression coefficients and p-values for estimating the variances of Level 1 variables and intercepts; and(3) standardised (beta) coefficients which, as in OLS regression, allow us to compare the relative importance of
the independent variables and interactions. Most software
packages also produce a measure of deviance.
2.2

Advantages of spatial analysis
Two types of errors are avoided when different levels of aggregation are considered simultaneously6,19-21: theecological error which consists of using a global aggregated statistical measure to reveal individual behaviour;and the atomist error, which considers the characteristics of the individual but ignores the context in which thehuman behaviour occurs. This is also true for road accidents: indeed it seems fallacious to isolate the accident
from its environment, or the society in which it occurred.
The purpose of this paper is to determine the direct effect of the explanatory variables measured at a low levelof aggregation and at a higher level of aggregation, andto see if the explanatory variables at the aggregated level
moderate the relationships occurring at the individuallevel, or vice versa.
Levels of analysis are often hierarchically organised:
items at one level interact and create a higher homogeneity8. This hierarchical structure leads to a correlationof the observations that violates the hypothesis of the independence of residuals (classical regression techniques)
and leads to an underestimation of the standard deviations

68 • IATSS RESEARCH Vol.29 No.1, 2005of the regression coefficients. MLMs take this correlation into account in the estimation of the standard deviations of the regression coefficients by including terms oferror at the contextual level. With regard to our study,
this dependence is spatial and means that the observations
supply less information than if they were randomly distributed, as is assumed in the OLS method22.
Additional advantages of MLM are: (1) regression
coefficients are specific to each level of analysis thanks
to the contextual residuals; (2) it is possible to test
whether the variance in the contextual terms of error issignificantly different from 0 (likelihood tests); (3) coefficients of determination (R2) can be computed for eachlevel of analysis by comparing the residual variances withthe variances of an “empty model” (without explanatory
variable) for each level; and (4) it is possible to attributethe residual variance of the classical multiple regression
to various levels of analysis6,10. The assumptions for theapplication of MLMs are in general less restrictive thanfor more traditional regression techniques6,7,9,10; the maindifficulty with MLMs is the definition of the hierarchical levels of observation and the associated variables (seeSection 3.2).
2.3

Estimating the parameters
Homoscedasticity (equal variances) is often violated
in hierarchical situations: OLS techniques are hence inappropriate. Multilevel linear models are often best estimated by the Newton-Raphson algorithm that is based on
maximum likelihood and generalised least squares. The
restricted maximum likelihood method is often used. The
values of the regression coefficients are first computedon the basis of the first analysis of the matrix of variancecovariance. The matrix is then re-estimated, using the firstvalues of the coefficients. Finally, the estimation of thecoefficients is improved by the new variance-covariancematrix until convergence. In this way, the fixed and random parts of the model are more effectively estimatedthan with OLS.
Several software packages, such as HLM and MlwiN,
are available23,24. SAS was used (Proc Mixed, Proc
Nlmixed) for the research reported in this paper; this package enables the more classic regression models to be considered as well as the hierarchical formulations. Several
models can be implemented with Proc Mixed: simple random-effects only, simple mixed with a single fixed andrandom effect, split-plot, multilocation, repeated measures, analysis of covariance, random coefficients, andspatial correlation.

SPATIAL NESTED SCALES FOR ROAD ACCIDENTS IN THE PERIPHERY OF BRUSSELS

3. METHODOLOGICAL CHOICES
3.1

Road safety in the studied area
Brussels is the capital city of Belgium, located in
the centre of the country and containing approximately
1 million inhabitants. As in most urban areas, the city
sprawls far beyond its administrative boundaries. Walloon
Brabant corresponds to an administrative entity (province)
located in the south of the city; it is mainly peri-urban
but its landscape results from its historical evolution. Up
to the 18th century, it was mainly rural, with many small
villages. During the 19th century, industries located in thewest (ironworks) and centre (paper mills). Railways andbetter roads later increased the accessibility. In the firsthalf of the 20th century, industries started closing one after the other. In the sixties, the region was increasingly
polarised by Brussels: as in many European cities, people
started to move from the centre of Brussels to the countryside, while keeping their jobs in the city. Later on auniversity was created in Louvain-la-Neuve and several
industrial parks were planned all over the area. Hence,the southern periphery of Brussels is now characterisedby old villages and small towns, a new town and many
allotments, old industrial locations as well as new planned
ones (industrial parks), highly urbanised communes close
to Brussels as well as more residential areas, woods andagriculture as well as employment and commercial centres. The result is a mosaic of landscapes, a polynuclear
structure and quite an interesting spatial pattern25,26. Ourstudied area is hence by definition periurban; its particular structure makes it quite interesting as links between
urban sprawl, travel practises and road safety have been
little dealt within the literature27.
In Belgium, any road accident that occurs on a public road and that involves casualties must be officially reported. Location is accurately known on numbered roads:
there is a stone marker every hectometre (100 meters);
numbered roads are motorways, national and provincial
roads linking towns together. On other roads, location is
identified by postal addresses that are often less accurate.
This analysis is limited to accidents with casualties on
numbered roads; the hectometre is the smallest spatial
unit for which accident data are spatially and officiallyavailable.
Walloon Brabant has 460.4km of numbered roads
including 37.7km of motorway. In this paper, a black zone
is defined by means of local spatial autocorrelation indices2,28,29 as a set of contiguous hectometres with a highnumber of accidents. Black zones vary in length and in-

N. ECKHARDT, I. THOMAS

tensity, and some black zones may include a hectometrewith no or very few accidents. These black zones charcterise the same places from year to year30, despite themany socio-economic changes in this studied area. 47%of the road hectometres did not register any accidents.
Black zones represent 38% of the total number of accidents but only 12% of the total number of hectometres.
In this paper, the period under study is 1998-2000, a period long enough to minimise random fluctuations, but
short enough to limit changes in road traffic conditions.
Some 2,363 accidents were registered on numbered roads
during this period; in total, 1,388 hectometres out of 4,604
experienced at least one accident with casualties.
3.2

Levels of analysis and dependent variables
The definition of the hierarchical levels is not aseasy as for some topics in human sciences. It is a compromise between the significance and the availability ofthe data.
Ideally, accidents should be considered as the firstlevel of analysis. However, accident data are collected byhectometre (no GPS was available). Moreover, mostenvironmental variables are also only available for
hectometres or segments of roads rather than for pinpoint
locations on the road. Let us here add that some environmental characteristics are collected at the time and placeof an accident and are reported on the statistical form
filled in for each accident with casualties. These could
have been used for characterising the places at which accidents took place, but their quality is doubtful31 and we
do not have any comparable information about places
where no accidents occurred. Hence the lowest aggregated level of analysis used here is the hectometre.
Initially, we decided to take the road segment (several hectometres long) as the second level of analysis.
However, it was not easy to choose the “best” length forthis segment and to justify it. Thresholds would have beenquite artificial and such segmentation does not correspondto any official definition; explanatory data are not available at this level, and they would have had to be a combination of data available at the hectometre level. Hence,
the municipality j (commune) was chosen as the second
level of analysis. It is not directly related to the road network itself, but to its global environment. A lot of data
are available at this level of administrative aggregation,
which corresponds quite well to mobility patterns in Belgium.
Three dependent variables are used and modelled
separately: Y1 takes the value 1 when a hectometre belongs to a black zone and 0 otherwise. It enables us to
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understand why some hectometres are more dangerous
than others. Y2 is the total number of accidents observedin each hectometre of road, and Y3 is a measure of therisk of accident, roughly estimated as the total numberof accidents divided by the average daily traffic intensity.
Y2 has the advantage of giving the real number of accidents: some hectometres can belong to a black zone (Y1)
without any accidents being recording2, and, on the contrary, a hectometre with several accidents can be surrounded by hectometres with no accidents and hence notbelong to a black zone. The absolute number of accidents(Y2) is interesting for some public authorities (such as the
emergency services), while for others, the relative number (Y3) is important. For each Y variable, the situation on
motorways is modelled separately because traffic has adifferent structure (two separate lanes, etc.) on motorways.
3.3

Explanatory variables
The purpose here is to identify environmental conditions associated with road safety/danger at two nested
levels of analysis. Most explanatory variables are selectedfrom official data bases (Belgian National Institute of Statistics, Ministry of Equipment and Transport) or constructed by means of G.I.S. techniques from official IGN
maps32; some of these variables are identical with (orclose to) those used by Flahaut3. They are briefly described below.
Let us remind that our objective is not here to get
an exhaustive list of all the potential explanatory variables. Our choice was guided by former published studies and constrained by data availability as well as the
structure of the studied area. We are conscious that thischoice biases the results of the analysis and limits the conclusions. However, most results presented hereunder are
consistent with former published results. There is indeed
a large number of papers in the literature justifying the
choice of roadway geometrics or the characteristics of theadjacent environment of roads for explaining road accidents occurrences. Roadway geometrics include variables
such as the road type (functional or physical), the number of lanes and their width, the horizontal curvature andthe vertical grade33-36. Spatial environment can be apprehended in various ways : land use37, roadside features(guardrail, bridges, etc.)38, residential development27,39,
human activities39,40, social disparities41,42.
Most explanatory variables used at Level 1 describe
the environment of the hectometre itself: the physicalcharacteristics of the road, land use or natural environment of the hectometre (see Table 1). Changes in environmental conditions are also considered by means of

70 • IATSS RESEARCH Vol.29 No.1, 2005

so-called “transition variables” which pinpoint road andenvironmental discontinuities that could influence drivers’ ability (or inability) to cope with changes. These variables are referenced by the absolute distance to the spatial
discontinuity and are recorded as _dist. If the change iswithin the hectometre, the distance is recorded as 0
metres. A maximum of 200m is considered on numberedroads and 300m on motorways. Information on traffic,
speed limits and the physical characteristics of the roads(type of road, type of surface, adherence of the road,presence of rutting or obstacles) were made available
by the Ministry of Equipment and Transport (MET).
Traffic density is measured by the 1999 average daily
number of vehicles in both directions, including all typesof vehicle, between 6 a.m. and 10 p.m. Traffic density ismeasured for well-defined hectometres and extrapolated
to larger road segments, but is never known at the timeand place of the accident. It is a daily average. As in manyother countries, traffic is macroscopically measured43.
Land use variables refer to human activities or to measurable characteristics of the physical environment (e.g.
% of area built-up, level of afforestation along the road at
a distance of 50m). These are constructed on the basisof 1:50,000 digital maps provided by the National Geographic Institute. Finally, the orientation, bends and slopesof the roads are obtained from measurements made on
digitalised topographic maps by means of appropriate GIS
techniques. These characteristics of the roads can potentially influence the visibility and the behaviour of road
users. Most variables are (0,1) variables.
At level 2, explanatory variables mainly pertain to
the socio-economic characteristics of the population living, working or shopping in the commune (Census
data)41. Table 2 contains the definitions of the variables
used in this paper. As in most human geography studies, it is difficult to estimate the population at risk who
is really present in the municipality or traversing it. We
limited ourselves to proxies that are officially available.
Structural variables were also taken into account: thelevel of urbanisation44 and the rurality (as expressed by
the ratio of agricultural areas to the total land area of amunicipality). We also expected that the morphology ofthe built-up environment could influence accident occurrence; morphology was estimated by fractal dimension25,26. Let us remind that the fractal dimension (D)describes the extent to which a mass (here the built-up
area) is concentrated within a zone. Fractal dimension is
not equal to density26. Thus for spatial mass distributions,
D can be interpreted as a measure of mass concentration
in a given area. It can be shown that a value of D close

SPATIAL NESTED SCALES FOR ROAD ACCIDENTS IN THE PERIPHERY OF BRUSSELS

N. ECKHARDT, I. THOMAS

Table 1 Explanatory variables at Level 1
Variables
Road use

Physicalcharacteristicsof the road

Land-use

LandscapeDescription

TRAFFICLogarithm of the average daily volume of traffic (Source: MET)

VMAX

Maximum speed limit (Source: MET)VMAX_distDistance to a change in speed limit (in meters): >200; 200; 100; 0 m and 300 m on
motorways. Written as VMAX(>200)_dist etc.

LANES

Number of lanes: (1) 1+1; (2) 2+2; (3) 2; (4) 3

LANES_dist

Distance to a change in road type in terms of number of lanes: >200; 200; 100; 0 m and 300 m
on motorways. Written as LANES(100m)_dist etc.

SURFACEType of surfacing (1) BE: concrete; (2) HFN: conventional asphalt; (3) HOM: thin asphalt;(4) HON: draining asphalt

SURFACE_dist

Distance to a change in surfacing: >200; 200; 100; 0 m for numbered roads and 300 m on
motorways

RUT

Presence (1) / absence (0) of ruts

JUNCT_dist

Distance to major crossroad: >200; 200; 100; 0 m on numbered roads and >300 ; 300 m on
motorways

ADHERENCE

Adherence of the road surface: (0) good or normal; (1) bad or very bad

PROX_ACCES

Proximity (<300 m) to entry/exit. (0,1) On motorways only

BZONE

Hectometre belonging (1) or not (0) to a black zone

BUILT

Estimated % of built-up area (from the road to 50 m from it): <20; 20; 25; 30; 40; 50. Written as
Built30 etc.

BUILT_dist

Distance to transition in density of built-up area (BUILT): >200; 200; 100; 0 m (>300; 300 m on
motorways)

WOODS

Estimated % of wooded area along the road (at 50 m): < 20; 20; 25; 30; 40; 50. Written as Woods30
etc.

FIRMS

Proximity of firms or large supermarkets (50 m) (0,1)

OBSTA _dist

Distance to an obstacle such as a bridge pillar: >200; 200; 100; 0 m (>300; 300 m on motorways)

AGGLO

Inside/outside an urban agglomeration (F1/F3 road sign)

DIRECTION

Road segment direction: (1) Others (N-S); (2) E-W≤22.5°; (3) 22.5°<E-W45°

RELIEFAt the top of a slope; at 100 m from the top; at the bottom of a slope; at 100m from the bottom; other

Table 2 Explanatory variables at Level 2
Variables

Description

MIXITY

Number of jobs/number of inhabitants in a commune in 2001 (= level of mixing of the activities and hence traffic).

ATTRACT(Numbers of jobs + number of inhabitants)/surface of the commune in 2001 (= attractivity of the commune)

EMPLOYDENS(Working population residing in a commune + population working in the commune) / total surface of the commune

MOBILITY

Working population residing in commune i / Total resident population in i

ROADLENGTH

Total number of hm of roads in the commune (logarithm)

URBE

Level of urbanisation

DCORR

Fractal dimension of the built-up area obtained by correlation

RURALITE

Area devoted to agriculture in 2001 / total area (%)

to 2.0 describes a fairly homogeneous distribution. The
lower the value of D, the more the mass is concentrated:thus a dimension close to 0.0 corresponds to a concentration of the mass in one isolated point (one farm in the
middle of fields), while the value 1.0 corresponds to aline (houses along a road), but also characterises a hierarchical spatial distribution of masses. No value smallerthat 1.0 was obtained in this study. Such values wouldrefer to structures composed of a disconnected set ofpoints. It is possible that road safety is affected bywhether built-up areas are distributed homogeneously or
heterogeneously throughout the neighbourhood. D is heremeasured by correlation25 and denoted DCORR.

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4. MODELLING RESULTS
Section 4.1 and Table 3 contain the results for accidents occurring on numbered roads (regional roads)
with the exception of motorways, which are reported in
Section 4.2 and Table 4. The three dependant variables
are analysed separately. The exploratory data analysis
conducted on the explanatory variables is not reported
here; it was mainly based on correlation coefficients andodd ratios, and enabled the number of explanatory variables to be reduced and their “best” formulation to be selected.
4.1

Accidents on numbered roads
Proc Nlmixed uses a non-linear formulation of themodel. It requires initial values for the parameters to be
specified, so that the model converges. Convergence isdue to the fact that maximum likelihood estimation is an
iterative algorithm which may require many runs before
reaching stable coefficient estimates. Our first estimate
was β0 = -2.05; this initial value was introduced into the“empty” model (Table 3, Column 2). The intra-municipal variance (Level 1) is an indicator of the variability
between hectometres, whereas the inter-municipalities
variance (Level 2) concerns the variability between municipalities. The total residual variance of the empty model
was 7.77. The intra-class correlation ρ µ =σ µ02
σ µ 02 + σ ε 0 2

indicates the proportion of the variance due to the communes (Level 2); ρ here is equal to 24.95% (σ0µ2 = 1.94).
For the hectometres (Level 1) ρ ε =σ ε 02= 75.05%
σ µ 02 + σ ε 0 2( σ0ε2 = 5.83). The smaller the intra-class correlation,
the better the standard errors of the parameters are estimated11. Let us also mention the pseudo-coefficientof determination (R2), which indicates the weight of the
explanatory variables at every level by comparing theresidual variances to those of the empty modelσ ε 0 actuel 2
σ µ 0 actuel 2
and R 22 = 1 − σ).
(R 12 = 1 − σ2
2
ε 0 ancienµ 0 ancien

Pseudo R-squared (denoted R2) should not be comparedto the R2s obtained by OLS. There are analogous, but notequivalent.
The empty model contains no explanatory variables.
It simply results in a partition of the total variation between the intra- and inter-level constituents. The purposeis then to reduce these variances by introducing explana-72 • IATSS RESEARCH Vol.29 No.1, 2005

tory variables. The explanatory variables that make a significant contribution to the equation related to Y1 (being
or not being part of a black zone) only explain 5.15% of
the variance (Table 3, Column 3). However the decomposition by level of observation leads to a larger R2 at
the municipal level (R 22 = 23.19%). Let us here note that,quite surprisingly, the variance observed at the hectometre
level (5.88) is almost the same than that observed in theempty model (5.83). At this stage of the analysis, this is
not easy to explain. MLM models are perhaps not the best
way to model Y1. Interpretation of the coefficients may
be meaningless.
Y2 is the total number of accidents observed on eachhectometre of road. Table 3 shows that its variability between communes is small (σ0µ2= 0.0001; ρµ = 0.01%);
communes can therefore be considered as homogeneousin this respect. Compared to the empty model, the X variables have a greater explanatory power at the municipal
level (R22 = 66.30%) than at the hectometre level (R21 =9.07%). Several variables explain the variation of Y2, including the quality of the adherence of the road surface(ADHERENCE). We suspect the role of this variable to be
associated with users’ behaviour; given the many recent
technical improvements to motor vehicles, drivers may
take greater risks because they feel more confident whendriving vehicles equipped with these safety features evenin difficult conditions45. When adherence is not good,road conditions seem not to be manageable by road users for one reason or another (weather conditions,infrastructural or behavioural circumstances), leading toan accident. As expected46,47, Y2 is also high when thehectometre is located in the vicinity of a junction(JUNCT_dist). We know that better signalled intersections
are a short-term solution for avoiding black zones, withroundabouts being a solution in the longer term. Traffic
density (TRAFFIC) also has a significant positive influence
on Y2, confirming former results such as those recently
published by Hiselius48, Golob43 or Davis15. As expected,
the total number of accidents (Y2) is higher in urban agglomerations (AGGLO), which also confirms the effect ofdensity and/or mobility27,43. We see from Table 3 that
Y2 is once again higher close to places where driving
conditions change (LANES 0, 100_dist; VMAX 0_dist). Theselatter are quite interesting because they identify road
discontinuities that are potentially dangerous: narrowingof the road, agglomerations, etc. We know from experience that better warning signs are an easy short-term solution for reducing risks at these transition places47.
However, in the longer term, they should be accompanied by changes in infrastructure and environment.

SPATIAL NESTED SCALES FOR ROAD ACCIDENTS IN THE PERIPHERY OF BRUSSELS

N. ECKHARDT, I. THOMAS

Table 3 MLM for accidents on numbered roads
Y1
Variables

β0

Y2

Y3

Empty Model

MLM

Empty Model

MLM

Empty Model

MLM–2.05***–13.71***

0.21***–1.97***

0.47***–1.47**

Level 1 variables
AGGLO

0.38***

TRAFFIC

1.52**

0.18***

0.53***VMAX (0m) _dist

0.19***LANES(3)–0.75***LANES (0m) _dist

0.34**LANES(100m)_dist

0.31***

RUT–0.31**

JUNCT (0m) _dist

1.33***

0.32**

JUNCT(100m)_dist

2.15***

0.35***ADHERENCE

0.75***

0.23***

0.35***

BZONE

0.75***

BUILT30

0.32***

0.54***WOODS25

0.50*

FIRMS

0.47**DIRECTION (3)–0.29**

Level 2 variables
EMPLOYDENS

2.64***–0.97***

DCORR

2.82***

Variance σ0ε2 (level 1)

5.83

5.88

1.11

1.01

3.79

2.98

Variance σ0µ2 (level 2)

1.94

1.49

0.00030.00010.00020.0002

Total variance

7.77

7.37

1.11

1.0088

3.79

2.98

ρε

75.05%

79.78%

99.98%

99.99%

99.99%

99.99%

ρµ24.95%

20.21%

0.02%

0.01%

0.01%

0.01%
21.34%

2
1

–

–

–

9.05%

–

R22

–

23.19%

–

66.3%

–

–

R2total

–

5.15%

–

9.07%

–

21.34%

R***significant at 99.9%; ** significant at 99%; * significant at 95%

Y3 is a simple measure of risk: the total number ofaccidents observed in a hectometre of road divided by theaverage daily traffic intensity. The scale effect is here due
to hectometres only. Some 21.34% of the variance is explained. This means that infrastructure and environment
play a limited but significant role in accident risk. Y3 isalso explained by distance to crossroads (JUNCT_dist), location within urban agglomeration (AGGLO), bad adherence of the road surface (ADHERENCE), built-up (BUILT30)
and wooded (WOODS25) environments. There is also an unexpected negative effect of rutting (RUT) (β = -0.31): therisk of accidents is small where rutting occurs. This might
be explained by the fact that, in the area we studied, rutted roads often correspond to roads with dense traffic andhence congestion. We know that congestion leads to moredamage-only accidents (fewer casualties). But ruttedroads may also correspond to small roads between hamlets with little traffic, where vehicles do not necessarily
adapt their speed. Variables measured at the municipality level have a very small but significant explanatory
power for the risk of accidents. However DCORR, which
is an index of urban morphology, plays an interestingrole: the greater the uniformity in the built space (no hierarchy), the greater the risk of accidents. This is quite
an important and novel finding in terms of planning. Specific spatial organisations (morphologies) may affect therelative speed of vehicles. Moreover, the risk of accidents also decreases when population density increases:
IATSS RESEARCH Vol.29 No.1, 2005 •73

TRANSPORTATION

the greater the density, the greater the activity and traffic and hence congestion or speed limits. These latter reduce the risk of accidents; as already discussed49, thisshould be taken into account when considering mobility
problems within urban areas.
We can here conclude that the utility of MLM formodelling the occurrence of accidents is limited: effects
of scale are small. In all cases, one level of analysis ispredominant, although this may differ for different dependent variables. In the model for the number of accidents (Y2), the significant variables explain 66.3% of thevariance at the level of the commune, whereas in themodel for the risk of accidents (Y3), the explanatory variables account for 21.34% of the variance at the level ofthe hectometre. In the first model, for the occurrence of
black spots (Y1), the variation is mainly at the level ofthe hectometre, but the explanatory variables account for23.19% of the variance at the municipal level. The effect of scale in this case is shared between hectometres(79.78%) and municipalities (20.21%). Although MLM
is known to be helpful in revealing differences in variance among units of analysis at different levels, it is lessinteresting than expected in this frame of application (seeSection 5).
The explanatory variables that are significant in all
three models are proximity to crossroads (JUNCT_dist), theadherence of the road (ADHERENCE), and measures of traffic density (TRAFFIC or EMPLOYDENS). This confirms resultsof other published studies (see references mentioned). The
quality of the road surface is a risk factor that deserves
particular attention in the maintenance of roads, especiallyin a peri-urban context. At the municipal level the riskof accidents increases with the urban morphological indicator (DCORR) and decreases with population density.
4.2

Accidents on motorways
Given the characteristics of motorway traffic (separate lanes, few entries/exists, minimum/maximum speed
conditions, etc.) and the specificities of road accidents on
this kind of road, models were computed separately forthis type of road accidents. The results are given in Table
4.
The first analysis, for the existence of a black spot(Y1), shows an increase in the total residual variance for
the MLM compared to the empty model (from 17.81 to
55.46) (Table 4, Columns 2 and 3); this means that, overall, the significant explanatory variables do not improvethe explanation of whether or not a particular hectometreis part of a black zones of the motorway. The fact that ahectometre belongs to a black zone is not to be explained

74 • IATSS RESEARCH Vol.29 No.1, 2005

by the here used explanatory environmental variables.
The model related to the number of accidents byhectometre (Y2) is reported in Columns 4 and 5 of Table
4. The introduction of explanatory variables in the model
now reduces the total variance (from 1.43 to 1.23); thisis exclusively due to Level 1 variables (R21 = 14.24%).
Hence, the effect of scale is here mainly due to thehectometres. This is quite obvious for motorways where
entries/exists are sparse compared to the scale of the communes. Let us have a look at the explanatory variables.
Traffic density has a positive relationship to accidents:
the larger the traffic volume, the larger the number of accidents. We know that his relationship is true on average: traffic varies with the time of the day leading tocongestion at some periods. Let us remember that accidents on motorways often only involve one road user andare often associated with a loss of control and/or travelling in excess of the speed limit38,50,51, which occur whentraffic is not dense (often at night). Distance to a change
in surface (SURFACE200m_dist), distance to a change inmaximum speed limit (VMAX 0 and 100m_dist) are once
again sources of changes in road behaviour; they shouldbe the focus of planners’ attention, as they normally correspond to roadworks on motorways or places close tocities. Better road signs avoid these situations; speed limits signs are indeed a safety measure and their use has
already often been debated52. The nearness of firms/department stores (FIRMS) is also a risk factor at the entranceof cities; this risk factor could be avoided by better land
use/infrastructure planning. Surfacing of type HFN and
the variable BUILT<20 have negative coefficients: asphalt
with the conventional texture and sparsely built-up environments are factors of road safety rather than danger.
Modelling of the risk of accidents (Y3) is reported
in Columns 6 and 7 of Table 4. It turns out that the effect of scale is once again only due to hectometres, andthat 13.14% of the variance is explained by the explanatory variables introduced. The MLM adds very little inthis case because the variance associated with one of thelevels (here Level 2) is almost equal to 0. Significant explanatory variables are the distance to a maximum speed(VMAX 0 or 100_dist), membership of the hectometre ofa black zone (BZONE) and the type of surfacing (HFN).
Hence, on motorways, Level 2 is useless in modelling Y2 and Y3 because variables describing the municipal level only apply to those sections of the motorways
that are located near Brussels. It might have been betterto choose another contextual environment because themunicipal effect only represents a small part of the effects of scale on motorways. For Y1, the effects of scale

SPATIAL NESTED SCALES FOR ROAD ACCIDENTS IN THE PERIPHERY OF BRUSSELS

N. ECKHARDT, I. THOMAS

Table 4 MLM for accidents on motorways
Y1
Variables

β0

Y2

Y3

Empty Model

MLM

Empty Model

MLM

Empty Model

MLM–5.27**

92.91**

0.75***–11.22***

1.54***

4.85*

Level 1 variables
TRAFFIC–21.47**

2.55***VMAX (0m)_dist

2.38***

4.07***VMAX (100m) _dist

1.83**

3.71**LANES(4)–2.44**

3.74***SURFACE (HFN)–0.41***SURFACE(200m)_dist

1.06**

PROX_ACCES (300m)–0.49*

1.29**

BZONE

1.70***

BUILT (20%)–2.63**

FIRMS

2.46**

0.48*

Level 2 variables
EMPLOYDENS

7.19*

MIXITY–5.31**ATTRACT

–6.88*

Variance σ0ε2 (niv 1)

12.02

30.14

1.43

1.23

4.78

4.15

Variance σ0µ2 (niv 2)

5.79

25.32

0.00020.00020.00020Total variance

17.81

55.46

1.43

1.23

4.78

ρε

67.47%

54.35%

99.98%

99.98%

99.96%

100%

ρµ

0.04%

–
13.14%

4.15

32.51%

45.65%

0.02%

0.02%

2

R1

–

–

–

14.24%

–

R22

–

–

–

–

–

–

R2total–––14.24%–

13.14%***significant at 99.9%; ** significant at 99%; * significant at 95%

are shared between hectometres (54.35%) and municipalities (45.65%), but no variable explains the total variation,
which increases when explanatory variables are introduced. None of the explanatory variables recurs in eachmodel, but each is useful in defining sensitive places on
motorways (such as, for example, the zones with different speed limits, the changes in type of road, the surfacing of roads, etc.). To sum up, when modelling thepresence of a hectometre in a black zone on motorways(Y1), variations are shared in a more or less equivalent
way between hectometres (ρε = 54.35%) and municipalities (ρµ = 45.65%). The introduction of explanatory variables does not improve the predictive power of the model.
When modelling the number of accidents (Y2), the variation occurs at the level of the hectometres and 14.24%(R2total) is explained. When the dependent variable is thenumber of accidents divided by the average traffic intensity (Y3), the effect of scale is only due to hectometresbut only 13.14% of the total variation is explained.
4.3

Comparing MLM to logistic regression results
Multilevel results are not really comparable to other
regression results13,14. MLM relies on complex, particular distributions of relationships across and within levels.
MLM outcomes are hence less general since each best-fitting model may be very specific to the dataset used. Let
us here roughly compare Y1 modelling results obtainedon numbered roads with those obtained by Flahaut3 bymeans of a more classical logistic regression (Table 5)
using the same area of study and almost (but not exactly)
the same explanatory variables. We see that (1) infrastructure and land-use have a smaller power of explanation in
the MLM model (smaller pseudo R2), and that (2) the explanatory effect of the variables is only slightly different. Similar effects are to be found for traffic density,
crossroads, adherence, built-up areas, and proximity of
IATSS RESEARCH Vol.29 No.1, 2005 •75

TRANSPORTATION

firms/department stores. MLM modelling adds variables
such as the orientation of the roads and the number oflanes; at the municipal level, MLM adds population density, which confirms other density effects measured at thehectometre level and other published papers already mentioned. In the logistic model, distances to changes in
speed limit or in the number of lanes as well as the typeof road surface play a more determining role also confirming the importance of speed variance.
Table 5 Comparing multilevel and logistic modellingof Y1 on numbered roads
Variables

Multilevel model

TRAFFIC++VMAX (0m) _dist

Logistic model
+++
+++

LANES

---

LANES (0m) _dist+

SURFACE++JUNCT (0m) _dist+++

ADHERENCE++++BUILT (30%)

+++

+++

FIRMS

++

+++

DIRECTION--EMPLOYDENS (level 2)

+++

+++

(+ a positive relationship; - a negative relationship.
+++/---significant at 99.9%; ++/-- significant at 99%; +/- significant at 95%).

Operationally, both modelling approaches lead to
specific results, but, on average, road accidents data in
Brabant Walloon seem to have a strong spatial structurethat comes through in both modelling procedures. Results
are quite stable, confirm common practise and should
hence be better integrated into land use planning and roadinfrastructure enhancement policies.

5. CONCLUSIONS
The importance of MLM in understanding contextual effects on road safety lies in its ability to meaningfully specify the latent structure of relationships, which
involve individuals and their environments. This paper
considered the spatial occurrence of road accidents bymeans of MLM. Three dependant variables were studied
separately. Explanatory components were limited to infrastructure and environment; the choice of the data wasconstrained by the availability of the data, the character-76 • IATSS RESEARCH Vol.29 No.1, 2005

istics of the studied area as well as recent published results. Due to the nature of the road accident and data limitations, only two levels of analysis were taken into
account: the hectometre and the commune. In spite ofthese many limitations, we can conclude that:(1) MLM enables the relative importance of spatial levels in the explanatory process to be assessed. In ourcase, the commune has, on average, less importancein the explanation than the hectometre: road accidents
occur at micro-locations (hm) which can be analysedin a broader spatial context, but this context does notseem to correspond to the commune. If communes
are useful official statistical and administrative units,
they vary in size and shape (modifiable areal unit
problem) and are not suitable for explaining the locations and spatial concentrations of road accidents.
This level is not appropriate for taking into accountthe complex relationships in which a car/road user isinvolved in an accident. Unfortunately, in road accident analysis, the choice of the spatial level of observation is not as straightforward as in human andbehavioural sciences. In both road accident and mobility analyses, there is often a compromise between
data availability and meaning. In this case hectometresand communes were the only possible choices. MLM
for road accidents is not straightforward to apply for
spatial analysis.
(2) If the level of spatial explanation is not high, it ishowever significant and corroborates former published results. Environment and infrastructure explain
between 5% and 21% of the total observed variationin road accidents in Brabant Walloon. We are conscious that our models are mis-specified: we didn’t
take into account the many other factors that could
interact (user behaviour, mobility patterns, etc.).
Given these results, the physical characteristics of theroad, as well as its environment, should be better andfurther integrated into safety and land-use policies.
Let us here however add that the assessment of environmental accident factors can, however, been discussed: circumstances can be present and regarded asrisk factors, but not necessarily as accident factors
and causes36.
(3) Three different dependent variables were analysed:
whether or not a hectometre belongs to a black zone;
the number of accidents per hectometre; and the riskof accidents, defined as the number of accidents divided by the average traffic volume. Each Y variable
has a specific meaning for police forces, emergency
services or road engineers/planners. In our analysis,

SPATIAL NESTED SCALES FOR ROAD ACCIDENTS IN THE PERIPHERY OF BRUSSELS

each model has also a specific form, with a difference combination of independent variables.
(4) Most explanatory variables are associated withhectometres. Many are related to changes in road conditions. The importance of these changes in road conditions in the explanation reveals the inability of theroad user to adapt his or her behaviour to changes inroad conditions and road infrastructure53. In-depth
analysis of each sub-type of accident should increase
our understanding of each type of circumstance, but
this is far beyond the scope of this paper. All theseassociations show that spatial concentrations of roadaccidents often correspond to places where improvements could be made in terms of road design, signalling and land-use planning. This corroborates
previous results on road accidents and road geometry33,34,47,54.
(5) The introduction of a morphological index (fractal dimension) is quite novel in measuring land use andmore particularly in explaining road safety. Further
analyses will be performed with this variable. In thispaper we showed that homogeneity in texture leads
to greater danger. Specific spatial organisation (morphology) may affect the relative speed of vehicles aswell as the mobility patterns. This should be taken
into consideration when considering safety and mobility problems within urbanised areas.
(6) Multilevel results are not really comparable to other
regression results. MLM outcomes are less generalsince each best-fitting model may be very specific forthe dataset used. In our case, logistic regression seems
to be easier to use and could be extended to cope with
autocorrelation3. Other analytical methods, such as aweighted geographic regression21 (which is based on
the hypothesis that the variations between variables
measured in different places cannot be constant in thespace), may however also be interesting to use. Instead of considering the local variations as averages
and as unobservable, weighted regression allows us
to measure local variations and to map them. However, the quality of the spatial data for this type ofanalysis is a strong preliminary condition.
The findings of this paper are both suggestive andlimited in that they are based on only one data set, andonly consider the environment and infrastructure as explanatory variables. Our modelling results depend
strongly upon the many choices made, and these arestrongly related to data availability. Neither the social
characteristics of the road users nor the technical char-

N. ECKHARDT, I. THOMAS

acteristics of vehicles are considered here. The interactions between social, technical and spatial variables are
not taken into account. Our paper shows the importanceof the hectometre as a basic spatial unit and the limited
usefulness of multilevel models in analysing road accident locations. Other statistical techniques may be better
suited to this task. Spatial concentrations of accidents arecharacterised by specific accident circumstances, which
require different counter-measures to reduce their number (e.g. improvements in terms of road design, signalling,
and local environment). There is no unique combinationof characteristics associated with road accident locations:
it is a complex phenomenon of which only a very few
aspects have been considered here.

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ACKNOWLEDGEMENTS
This work was funded by the Federal Scientific Policy in
Belgium (project CP/10/342). We would like to thank Benoît
Flahaut and the anonymous referees for helpful comments on earlier versions of this paper.