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osamaevaluatingimpactbikenetwork2016.md

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category: literaturenote citekey: osamaevaluatingimpactbikenetwork2016 title: Evaluating the impact of bike network indicators on cyclist safety using macro-level collision prediction models authors: "Osama, Ahmed; Sayed, Tarek" year: 2016 date: 2016-00-00 2016 doi: 10.1016/j.aap.2016.08.010 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2016.08.010" zotero_key: B8T9C534 zotero_storage: TQQR9S9V collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Osama, Ahmed"

status: converted

Contents lists available at ScienceDirect

Accident Analysis and Prevention

jour nal home page: www.elsevier.com/locate/aap

Evaluating the impact of bike network indicators on cyclist safety using macro-level collision prediction models

Ahmed Osama, Tarek Sayed∗

Department of Civil Engineering, The University of British Columbia, 6250 Applied Science Lane, Vancouver, BC, V6T 1Z4, Canada

a r t i c l e i n f o

Article history: Received 30 March 2016 Received in revised form 4 August 2016 Accepted 6 August 2016 Available online 24 August 2016

Keywords: Graph theory Bike network indicators Bike kilometers travelled Macro-level collision prediction models Cyclist-Vehicle collisions

a b s t r a c t

Many cities worldwide are recognizing the important role that cycling plays in creating green and livable communities. However, vulnerable road users such as cyclists are usually subjected to an elevated level of injury risk which discourages many road users to cycle. This paper studies cyclist-vehicle collisions at 134 traffic analysis zones in the city of Vancouver to assess the impact of bike network structure on cyclist safety. Several network indicators were developed using Graph theory and their effect on cyclist safety was investigated. The indicators included measures of connectivity, directness, and topography of the bike network. The study developed several macro-level (zonal) collision prediction models that explicitly incorporated bike network indicators as explanatory variables.As well,themodels incorporated the actual cyclist exposure (bike kilometers travelled) as opposed to relying on proxies such as population or bike network length. The macro-level collision prediction models were developed using generalized linear regression and full Bayesian techniques, with and without spatial effects. The models showed that cyclist collisions were positively associated with bike and vehicle exposure. The exponents of the exposure variables were less than one which supports the "safety in numbers" hypothesis. Moreover, the models showed positive associations between cyclist collisions and the bike network connectivity and linearity indicators. In contrast, negative associations were found between cyclist collisions and the bike network continuity and topography indicators. The spatial effects were statistically significant in all of the developed models.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Many cities worldwide are recognizing the important role that cycling plays in creating green and livable communities and have implemented policies to encourage cycling. However, vulnerable road users such as cyclists are usually subjected to an elevated level of injury risk which discourages many road users to cycle. As such, developing a safe and efficient bike network can attract more road users to cycle for a range of activities.

Road safety has often been managed in a reactive manner where existing problems, that occur after a road has been designed and built, are targeted. Recently, researchers have advocated a more proactive approach that addresses road safety before problems emerge (de Leur and Sayed, 2003). This can be achieved by making safety a priority from the outset of the transportation and land use planning process. One main obstacle associated with the delivery of

E-mail addresses: ahmed.osama@eng.asu.edu.eg (A. Osama), tsayed@civil.ubc.ca (T. Sayed).

a proactive road safety measure is the lack of reliable tools to evaluate road safety in a proactive manner (de Leur and Sayed, 2003). The main goal ofthis paper is to develop empiricaltools that can be used for proactive cyclist safety evaluation. Macro level collision prediction models (CPMs) have been widely used as a decision tool for the proactive safety evaluation of transportation networks. CPMs attempt to explain the relationship between collisions occurrence and various network characteristics (traffic, geometry, etc.). They have diverse applications such as: evaluating the effectiveness of safety improvement measures, detection and ranking of accidentprone locations, and estimating the safety potential of facilities (Sawalha and Sayed, 2001). Among the macro-level CPM studies thatinvestigated cyclist collisions, some have focused on bike route types (Harris et al., 2011; Chen et al., 2012; Teschke et al., 2012; Kaplan and Prato, 2015), while others have focused on zonal characteristics such as the built environment and land use (Siddiqui et al., 2012; Wei and Lovegrove, 2013; Chen, 2015). Although important efforts were utilized in these studies to associate wide range of variables to cyclists' collisions, none of the previous studies comprehensively addressed the impact of the bike network structure on cyclist safety. The study of networks is an area of research under

∗ Corresponding author.

which any transport network can be visualized as a graph that is composed of a set of links and nodes. Accordingly, various network properties can be investigated based on the relationship between the network elements (i.e. the links and nodes); and new network indicators can be estimated.

This study discusses the development of macro level CPMs for 134 traffic analysis zones (TAZs) at the city of Vancouver, British Columbia. The models are developed using generalized linear modeling (GLM) and full Bayesian (FB) techniques, and explicitly incorporate new indicators related to the connectivity, directness, and topography of the city of Vancouver bike network. In addition, the actual cyclist exposure (bike kilometers travelled and vehicle kilometers travelled) is used as opposed to relying on exposure proxies such as the population or the bike network length. Spatial effects among the different TAZs are also studied using the developed Bayesian models.

2. Literature review

2.1. Safety models for cyclists

Various studies have discussed cyclist safety at an aggregate level. Jacobsen (2003) examined the relationship between the number of vulnerable road users (pedestrians and cyclists) and their collisions with motor vehicles based on five data sets from different locations worldwide. Results showed that, at the population level, the number of motorists colliding with vulnerable road users would increase at approximately 0.4 power of the number of people cycling or walking. Robinson (2005) studied three datasets from Australia, and concluded similar results to the Jacobsen's study. Kim et al. (2007) explored various crash, roadway, land, and environmental factors contributing to the injury severity of cyclists, who were involved in cyclist-motorist crashes in North Carolina. Their results showed that several factors increased the probability of a fatal injury in a crash, including head-on collisions, speeding, inclement weather, no streetlights, morning peak, truck involvement, intoxicated drivers/cyclists, and age. Kim et al. (2010) also discussed results from macro level CPMs, which suggested that demographic variables, accessibility variables, bus route length, and number of intersections were positively associated with cyclist-vehicle collisions. Wei and Lovegrove (2013) developed community-based negative binomial models for cyclistvehicle collisions. The models revealed an increase in the cyclist collisions with the increase of the total lane kilometers, bike lane kilometers, bus stops, traffic signals, intersection density, and arterial–local intersections percentage. More recently, Chen (2015) indicated that zonal bike crash frequencies are spatially correlated. His study included some cycling related variables that had not been investigated in prior studies such as bike trips vs. total trips, zonal mean of the driving speed limits, zonal mean slopes, and densities of street trees and parking signs. He found that the zonal mean of driving speed limits,total number oftrips, length of on-arterial bike lanes, entropy of mixing land use, and density oftraffic signals were positively associated with cyclist collisions. Lastly,Kaplan and Prato (2015) modeled the frequency and the severity of crashes involving cyclists and motorists in the Copenhagen region by estimating a link-based multivariate Poisson-lognormal model. The model underlines the relevance of infrastructure, land use, and spatial effects to explain the variation in the number of cyclist–motorist collisions. They showed thatthe number of crashes was nonlinearly related to the average bike and vehicle daily traffic, which confirms the safety in numbers hypothesis (Elvik, 2009; Jacobsen, 2003). Kaplan and Prato (2015) also found that bike paths are associated with less crashes, which agrees with recent studies that show that cycling facilities increased actual and perceived safety (De Rome et al., 2014; Kaplan et al., 2014), and is in disagreement with past literature that assume that cycling in mixed traffic is safer than cycling on bike infrastructure (Pucher et al., 1999; Rodgers, 1997).

2.2. Graph theory

Graph theory concepts originated from the "Seven Bridges of Konigsberg" problem, which was solved by Euler in the 18th century. Garrison and Marble (1962) applied graph theory to transportation networks, and were able to develop indices for connectivity. Kansky (1963) presented indices that characterized network connectivity and complexity. More recently, Gattuso and Mirello (2005) were able to evaluate the topology and geography of metro networks in some European cities and New York City based on graph indicators. Derrible and Kennedy (2010) presented a new methodology to draw metro networks as graphs, and accordingly they were able to create directness and structural connectivity indicators. Quintero-Cano et al. (2014) introduced a novel approach to redraw transit networks as graphs, and hence they were able to include new connectivity indicators. Those indicators were used in developing macro-level CPMs to assess the safety of Metro Vancouver transit network (Quintero et al., 2013).

Previous studies that developed macro-level bike collision models used proxies for the cyclist exposure due to data limitations, e.g. (Wei and Lovegrove, 2013; Amoh-Gyimah et al., 2016). Moreover, many of the studies did not use any exposure measure for motorized traffic, e.g. (Siddiqui et al., 2012; Chen, 2015). These two limitations can lead to biased results since exposure is one of the most important factors affecting collision occurrence. As well, although some studies investigated the association between road network patterns and the safety of vulnerable road users (Zhang et al., 2015; Wei and Lovegrove, 2012), almost none of the former macro-level cyclist safety studies incorporated a comprehensive set of indicators, representing the bike network structure, and their impact on cyclist safety. This study attempts to address these shortcomings in order to develop reliable and rigorous macro-level cyclist safety models.

3. Data collection

3.1. Data sources

In this study, zone-level CPMs are developed based on 134 TAZs at the city of Vancouver. The CPMs included explanatory variables that represent the cycling network attributes. Exposure due to bike and vehicle traffic volumes is also included. Data is compiled for analysis using ArcGIS after being extracted from four main sources:

  • 1. Insurance Corporation of British Columbia, a public automobile insurance company, provided the collisions data for the city of Vancouver for a 5 years period (2009–2013). Only cyclistvehicle collisions are included in the analysis, as shown in Fig. 1, to prevent any bias that may occur if other types of collisions are considered. A 5 years period is selected to obtain an adequate sample size of collisions. The sample included 3 severity levels, i.e. fatality, injury, and property damage only. However the total number of collisions is used in the analysis in order not to reduce the sample size. The data did not include collisions between cyclists-pedestrians and cyclists with each other. Although this can be a limitation (Chen, 2015), it should be noted that these collisions are typically rare and not usually reported in Vancouver.
  • 2. Translink, the Metro Vancouver transportation authority, provided geocoded files of the bike network, the street network, and the TAZs boundaries. Moreover, Translink provided the out-

Fig. 1. Heat Map of 2009–2013 cyclist-motorist collisions at the city of Vancouver TAZs.

put of the Emme2 transportation planning model for the travel demand in year 2011. Translink used the 2011 household travel survey to calibrate the model, and the 2011 cordon counts to validate the model assignments.

  • 3. Acuere consulting Inc. provided the Vancouver Cycling Data Model (VCDM, 2011) illustrated in Fig. 1. The VCDM used bike counts between 2005 and 2011 to estimate the annual average daily bike traffic (AADB) over the city of Vancouver bike network (El Esawey et al., 2015). The available data covered more than 810,000 hourly volumes over seven years. The model was efficient in estimating the AADB on most of the bike network links (3180 links, or more than 70% of the network).
  • 4. City of Vancouver Open data Catalogue (http://vancouver.ca/ your-government/open-data-catalogue.aspx) provided the digital elevation model and contour maps (1-m resolution) for the city of Vancouver.

3.2. Analysis variables

Definitionsof the variables that are used in the analysis, as well as their summary statistics, are shown in Table 1. The independent variables are divided into two main categories: exposure and cycling network.

3.2.1. Collisions

Cyclist-motorist collision is the only dependent variable. Collisions are aggregated at the different TAZs according to their geo-spatial locations. A methodological question arises concerning how to assign the collisions occurring along the zonal boundaries. Different approaches were attempted in the literature. Some previous studies recommended dividing boundary collisions in a way that can result in a better goodness of fit for the collision prediction models. However, other researchers argue that since it is difficult to know the exact location of the boundary collisions and how they affect different traffic zones, a reasonable way of dividing boundary collisions is to relate them to the exposure in each zone. Lovegrove and Sayed (2006) aggregated boundary data in an automatic geospatial way to develop a macro-level collision prediction models for the Great Vancouver Regional District. Wei (2010) made use of five boundary data aggregation approaches (the oneto-one ratio method, the half-to-half ratio method, the geospatial method, the vehicle kilometer travelled (VKT) ratio method, and the total lane kilometers (TLKM) ratio method) for the geocoded data on the TAZ boundaries, and investigated how the different methods affected the CPM results. Cui et al. (2015) proposed a collision density ratio method to aggregate boundary collisions into neighborhoods, and they used ground truth data to evaluate their method. In this study, we followed an approach using BKT proportions among the neighboring zones as a way to fairly divide and represent boundary collisions, since more bike kilometers travelled will be associated with more cycling activities and therefore more bike collisions (as revealed in the previous studies and the models developed in this study). This approach is similar to the VKT ratio method (Wei, 2010), but using BKT ratios instead of VKT ratios. Boundary collisions were first identified and the ratio between the zones BKT was calculated. The boundary collisions were then assigned to the zones according to the calculated BKT ratio.

3.2.2. Exposure

Three exposuremeasures are used in this study, i.e. BKT andVKT, along with the EXP variable, which is the multiplication of both. BKT is obtained using the Vancouver cycling data model, which provided the modeled cyclist trips on the city of Vancouver road segments (El Esawey et al., 2015). The trip count at each segment is multiplied by the corresponding segment length to obtain link BKT, which is then aggregated for each TAZ. VKTs of the different TAZs are obtained using the Emme2 model.

3.2.3. Network indicators

The first step in calculating the network indicators is to characterize the transportation network as a graph (i.e. set of links and nodes)in order to collectthe basic measurements ofthe graph characterization (e.g. number of nodes, number of links, length of links, etc.). The links represent the bike network infrastructure (e.g. bike lanes), and the nodes represent the intersections between the bike links. Since a zonal level of aggregation is selected, a technique is developed for splitting the entire bike network into smaller zones. The links and nodes are distributed between the different TAZs according to their geospatial location. However, if a link is found to pass through two zones, then it is divided between the two adjacent zones using a weight that is relative to the link's length within each zone.

Using the graph representation, several indicators can be estimated. For this study, the indicators are divided into three main categories: connectivity, directness, and topography.

Table 1 Variables Definition and Data Summary (n = 134 TAZ).

| Variable | Description | Mean | SD | Min | Max | | |-------------------------|--------------------------------------------|---------|---------|--------|----------|--| | Area | | | | | | | | Ar | Area of TAZs (km2) | 0.87 | 0.74 | 0.052 | 5.31 | | | Collisions | | | | | | | | Coll | Cyclist-motorist Collisions over 5 Years | 12.71 | 13.48 | 0 | 78 | | | Exposure | | | | | | | | VKT | Vehicle Kilometer Travelled in a Zone | 4290.43 | 3327.54 | 189.46 | 22288.79 | | | BKT | Bike Kilometer Travelled in a Zone | 1047.77 | 2109.96 | 0 | 21462.77 | | | EXP | (VKT*BKT) for Each Zone | 6.47E06 | 25.9E06 | 0 | 292.7E06 | | | Cycling Network | | | | | | | | Connectivity Indicators | | | | | | | | InterD | Intersections Density | 74.28 | 33.80 | 6.08 | 235.95 | | | Conn | Degree of Bike Network Connectivity | 0.38 | 0.11 | 0 | 1 | | | Cov | Degree of Bike Network Coverage | 0.34 | 0.19 | 0 | 1 | | | NetD | Bike Network Density | 5.38 | 3.78 | 0 | 21.91 | | | Comp | Complexity of the Bike Network | 0.99 | 0.14 | 0 | 1.66 | | | Directness Indicators | | | | | | | | Lin | Linearity | 0.98 | 0.03 | 0.84 | 1 | | | AvgEdLen | Average Edge Length (Continuity) | 0.084 | 0.032 | 0 | 0.37 | | | AvgVerLen | Average Length per Vertex | 0.13 | 0.054 | 0 | 0.62 | | | Topography Indicators | | | | | | | | L | Total Length of Bike Network Links (km) | 3.37 | 2.52 | 0 | 17.40 | | | WSlope | Average Weighted Slope of the Bike Network | 2.52 | 0.90 | 0.63 | 6.65 | |

3.2.4. Connectivity

Connectivity includes five different measures: network density, degree of connectivity, network coverage, intersection density, and complexity. Each indicator represents a specific perspective of the bike network connectivity. Network density describes how well the bike network covers a specific area or a region. The degree of connectivity represents the extent to which the bike network is saturated with links that are connecting various graph nodes. Coverage is used to representthe bike network coverage ofthe existing street network. Intersection density measures the quantity ofintersections (necessary for access) withinanarea.Complexitydescribes the ability of network nodes to carry higher number of links. The indicators are quantified as follow.

Network density is the ratio between the total length of the bike links in a TAZ and the corresponding TAZ area. This measure was used in previous studies for measuring the connectivity of both the pedestrian and cyclist networks (Matley et al., 2000; Dill, 2004).

Degree of connectivity represents the ratio between the actual number of bike links in a TAZ and the maximum possible number of links in the TAZ. Assuming a planar graph, the maximum possible number of links within a graph is calculated according to the graph theory using Eq.(1), where n is the number of nodes within a graph.

$$l_{\text{max}} = 3(n-2) \tag{1}$$

The value of the degree of connectivity is bounded between 0 and 1. A completely connected network will have a degree of connectivity equal to 1, while a completely disconnected network will have a degree of connectivity equal to 0. The degree of connectivity indicator has been used in previous studies for evaluating transit networks (Derrible and Kennedy, 2011; Quintero et al., 2013). However, two deficiencies are noticed upon applying the indicator to this study. First, the equation form that is used to calculate lmax should vary from a zone to another according to the graph shape. Moreover, the equation is not valid when the number of nodes is less than 3.

Therefore, anew indicator that canbetter representthe bikenetwork connectivity is suggested. The indicator is called the degree of network coverage and is calculated using Eq. (2) (Yigitcanlar and Dur, 2010).

$$Cov = \frac{Number of Bike Links in TAZ}{Number of Street Links in TAZ}$$ (2)

Degree of network coverage simply assumes that lmax is the total number of street links in the TAZ. This assumption is more practical than the one in Eq. (1), because the maximum possible number of bike links shall not exceed the number of street links in any zone (assuming that the number of off-street bike paths is not high enough to void this statement). However, this indicator is reliable only if the complete layer of the road network is available, and if not, degree of connectivity can be used. Fig. 2 shows the bike network along with heat maps for both the connectivity and coverage for different TAZs.

  • Intersectiondensity is calculatedas the ratio betweenthenumber of intersections within the zonal bike network and the area of the corresponding TAZ. This indicator aggregates all intersections without distinguishing between their different types.
  • The lastindicator in this category is complexity, which represents the degree of network complexity. Complexity is defined as the average number of bike links per node (Kansky, 1963), as shown in Eq. (3).

$$Comp = \frac{Number of Bike Links in TAZ}{Number of Nodes in TAZ}$$ (3)

Networks with a complex structure will have high complexity value, while those with simple structures will have low complexity value.

3.2.5. Directness

For the network directness category, new indicators are developed. This paper focused on three main aspects of directness; i.e. linearity, orientation, and continuity.

Scheltema (2012) defined linearity within a network as the ratio between a crow line and its effective straight line. However, in macro level studies, many of those effective straight lines tend to set out of the zone that they used to be within, which would

Fig. 2. (a) Connectivity of the Bike Network at City of Vancouver TAZs. (b) Coverage of the Bike Network at City of Vancouver TAZs.

give biased results upon analysis. For calculating orientation and continuity, Scheltema (2012) proposed manual methodologies by counting every turn along the key bike routes to quantify orientation, and by counting every crossing along the key bike routes to characterize continuity. Nevertheless, such methodology is inconvenient for macro level studies as it consumes considerable time and effort.

Therefore, new ways to calculate directness need to be applied in the context of macro-level studies. Three graph indicators are developed in this study: average edge length, average length per vertex, and linearity. Both average edge length and average length per vertex can characterize the continuity ofthe bike network since they explicitly representthe average length ofthe network link free frominterruptions, while the linearity indicator is able to characterize both linearity and orientation within the bike network since it penalizes irregularities and curvatures in the network. The method of quantifying the average edge length, average length per vertex, and linearity is described as follow.

  • Average edge length is calculated as the ratio between the total length of the zonal bike network and the number of links in the corresponding TAZ, while average length per vertex is calculated as the ratio between the total length of the zonal bike network and the number of nodes within the TAZ (Kansky, 1963).
  • Linearity is calculated using Eq. (4) as the ratio between the modified bike network length and the original bike network length in the TAZ, where the modified bike network is a hypothetical network in which all non-straight links are drawn straight maintaining the original nodes (assuming thatthe drawn straightlinks canbepractically built withinthe TAZ). Fig. 3 shows thedifference between the straight and non-straight links, where non-straight links represent any curved or irregular links. A lower value of linearity represents more non-linearity in the existing network.

$$Lin = \frac{Total \ Length \ of \ the \ Modified \ Bike \ network \ in \ TAZ}{Total \ Length \ of \ the \ Bike \ Network \ in \ TAZ} \tag{4}$$

To modify the non-straight links, the entire bike network is exported from ArcGIS to AutoCAD software to manage the separation of the non-straight links from the straight links, and then modifying them into straight ones. Afterwards, the network is imported back to ArcGIS to aggregate the length of the modified

Fig. 3. Linearity (a) Straight Links (b) Non-Straight Links (Curved or Irregular).

bike network links and measure the linearity at each zone using Eq. (4). Fig. 4 shows the non-straight links within the city of Vancouver bike network after being imported from AutoCAD.

3.2.6. Topography

Lastly, the total length of the bike network links and the average weighted slope of the bike network at each TAZ are included as indicators in the topography category. Total length of the zonal bike network represents the size of the bike network infrastructure within a TAZ. Average weighted slope of the zonal bike network gives an indication of the average absolute steepness of the bike network within each zone.

  • Total length of the bike network is calculated by aggregating all the bike network links (regardless of their types, i.e. separated, on-street, etc.) within each TAZ.
  • The zonal average weighted slope of the bike network is calculated according to the following steps. First, the bike link slopes are computed (assuming absolute values) using the contour map of the city of Vancouver, as shown in Fig. 5, and the slope at each link is given a weight relative to its length. Then the average weighted slope of the links is calculated for each TAZ, using Eq. (5); where l represents the link length and s represent the link's slope.

Average Weighted Slope in TAZ = $$\frac{\sum{1}^{n} l{1} * s{1} + l{2} * s{2} + ... + l{n} * s{n}}{\sum{1}^{n} l{1} + l{2} + ... + l_{n}}$$ (5)

Fig. 4. Non-Straight Links in the City of Vancouver Bike Network.

Fig. 5. Slopes of the Bike Network Links.

4. Methodology

4.1. Macro level CPMs

Macro-level CPMs require sufficient data of sound quality to developgood-fit reliablemodels. The way in whichdata is extracted and aggregated influences whether underlying causal mechanisms are concealed or revealed in the resulting models (Davis, 2004). Many studies have shown that using improperly aggregatedmacrolevel data, correlated by geographic area, may conceal causal associations between collisions and explanatory variables, leading to biased results (Kmet et al., 2003; Davis, 2004).Aggregation bias is a phenomenon that can produce a statistically significant association suggesting a causal relationship that is in direct contradiction to the true underlying causal association (Lovegrove and Sayed, 2006). In order to minimize the aggregation bias, itis recommended to use as large data set as possible, stratify classes of possible models, and then identify a member of each class that best fits the data (Davis, 2004).

The macro-level CPMs developed in this study first use the GLM approach to investigate the impact of each network indicator exclusively on crash frequency before integrating the various network indicators into combined models. GLM approach, which assumes a non-normal distribution error structure, is widely used for the development of CPMs since conventional linear regression models lack the distributional property to adequately describe collisions. This inadequacy is due to the random, discrete, nonnegative, and typically sporadic nature that characterizes the occurrence of collisions (Miaou and Lum, 1993; Sawalha and Sayed, 2006, 2001). A Negative Binomial error distribution assumption has become the standard for CPMs developed using the GLM approach (Hauer et al., 1988; Sawalha and Sayed, 2001). The model form used for CPMs should generally satisfy two conditions (Sawalah and Sayed, 2006). Firstit should not yield negative results in terms of predicting negative collisions and also should predict zero collisions for zero traffic exposure (when there are no vehicles or bikes on the road). As well, there need to be a link function to transform the model into a linear form. Based on empirical studies (Miaou and Lum, 1993; Sawalha and Sayed, 2001), a commonly used model form includes an exposure measure (e.g. vehicle kilometers travelled) raised to some power and multiplied by an exponential function including the other non-exposure explanatory variables. The model can be expressed mathematically as shown in Eq. (6).

$$E(Y) = a_0 V^{a1} \exp(\Sigma b_j x_j)$$ (6)

Where E(Y) is the predicted collision frequency, V is the measure of the traffic volume (VKT, BKT, etc.), xj represents any other explanatory variables, and a0, a1, and bj are the model parameters. The recommended statistical methodology to add explanatory variables into a CPM is a forward stepwise procedure (Sawalha and Sayed, 2001). Variables are added one by one, and their significance is tested. Variables representing exposure must be included first.

Two statistical measures are used to assess the goodness of fit of the GLM models, including Pearson chi square (-2) and scaled deviance (SD) statistics (Sawalha and Sayed, 2001). For a well-fitted model and a relatively large number of observations, the expected value of Pearson -2 and SD will be approximately equal to the number of degrees of freedom (Sawalha and Sayed, 2001).

4.2. Full Bayes CPMs with spatial effects

Incorporating spatial effects intheCPMs isusuallyundertakenin a FB analysis context which is more suitable for spatial models due to its ability to implement complex correlation structures (Aguero-Valverde and Jovanis, 2008). Recently, Bayesian analysis using FB hierarchical statistical models has become more popular due to its flexibility and its ability to use prior information, which results in improving the accuracy of the parameter estimates. Moreover, FB analysis can provide more accurate measures of uncertainty on the posterior distributions of the parameters' estimates (El-Basyouny and Sayed, 2009, 2010).

Zone-based Poisson lognormal models that account for spatial effects are used in this study to handle the over-dispersion in count data, and account for both the unstructured and structured (spatially correlated) heterogeneities. The development of FB models in this study followed the procedure described by El-Basyouny and Sayed (2009). Yi is assumed to be the number of collisions at zones i, and Yi is assumed to follow a Poisson distribution with a parameter i as shown in Eq. (9). i is considered itself a random variable and modeled according to Eq. (10).

$$Y_i \sim Poisson(\lambda_i)$$ (9)

$$ln\lambda_i = a_0 + a_1 ln(VKT_i) + a_2 ln(BKT_i) + \Sigma_i b_i X_i + \mu_i + s_i$$ (10)

where a0 is the intercept, a1, a2, andbi aremodelparameters,VKTi is the vehicle exposure variable, BKTi is the bike exposure variable, Xi represents the explanatory variables, i accounts for the unstructured heterogeneity among zones, and si accounts for the spatially correlated (structured) heterogeneity among zones.

The unstructured heterogeneity follows a lognormal distribution as implied by Eqs. (10) and (11), while the spatial effects are accounted for by Gaussian CAR techniques, and Si is calculated according to Eq. (12).

$$u_i \sim normal\left(0, \sigma_u^2\right)$$ (11)

$$Si | S{-i} \sim normal(\tilde{s}_i, \frac{\sigma_s^2}{n_i}), \quad \tilde{s}i = \sum{j \in C(i)} \frac{s_j}{n_i}$$ (12)

Where 2 u2 u is the unstructured heterogeneity variation, 2 s is the spatial variation, and nini, C(i), and S−i represent the number of neighbors of zone i, the set of neighbors of zone i, and the set of all spatial effects except Si, respectively.

Eq. (12) is based on an adjacency-based proximity measure, where the conditional variance is inversely proportional to the number ofneighboring zones, and the conditionalmeanis themean of the adjacent spatial effects.

The effects of spatial correlation are calculated by computing the spatial variation proportion of the total random effects variationaccording to Eq.(13). Significant spatial correlationexists when s is found to be greater than 0.5 (Aguero-Valverde and Jovanis, 2008). This implies that the neighbors of zones with high predicted collision frequencies will likely have high predicted collision frequencies and vice versa.

$$\Psi{s} = \frac{\sigma{s}^{2}}{\sigma{s}^{2} + \sigma{u}^{2}} \tag{13}$$

Although including spatial effects usually increases the models' goodness of fit, the inclusion of spatial correlation can sometimes affect the estimation of parameters by making some variables nonsignificant although those variables were significant in the CPMs without spatial effects (Karim et al., 2013).

Markov chain Monte Carlo (MCMC) is applied using WinBUGS tool to sample the posterior distribution and estimate the FB model parameters. MCMC methods use sampling to generate sequences of random points, the distribution of which converge to the target posterior distributions. A subsample is used for the purpose of monitoring convergence, and then excluded as a burn-in sample. Parameter estimation, performance evaluation, and inference are obtained by the following iterations.

Obtaining FB estimates requires the specification of prior distributions for the parameters reflecting the prior knowledge about the considered parameters. The prior may be informative or vague depending on the availability of the prior information. A diffused normal distribution with a zero mean and a large variance is the most commonly used prior to estimate the regression parameters (El-Basyouny and Sayed, 2009), For the dispersion parameter, 2 u , under the Poisson lognormal model, the commonly used prior is a gamma distribution with parameters (-, -), where the value of is a small number, e.g. 0.001 (Karim et al., 2013). For the Gaussian CAR models developed in this study, the prior distribution of 2 is assumed to be a gamma distribution with parameters (1 + li/2, 1 + n/2), where li is the term contributed by each zone and is calculated by Eq. (14).

$$l_i = n_i s_i (s_i - \bar{s}_i) \tag{14}$$

Two chains are used to run each model, and 20,000 MCMC iterations are discarded as burn in samples. The summary statistics of each chain are then estimated, and the convergences of the developed models are thoroughly checked to ensure that the posterior distribution has been found in order to begin parameter sampling. Convergence can be checked in several ways. First, two or more parallel chains with diverse starting values are tracked so that full coverage of the sample space is ensured. Brooks–Gelman–Rubin statistic can be also used, where convergence occurs if the value of the Brooks–Gelman–Rubin statistic is less than 1.2 (El-Basyouny and Sayed, 2009). Moreover, convergence can be checked by visually inspecting the MCMC trace plots of the model parameters. As a rule of thumb, convergence occurs when the ratios of the Monte Carlo errors relative to the respective standard deviations of the estimates are less than 0.05.

After obtaining convergence, additional 20,000 iterations are performed for each chain and the significance of the parameter estimates is tested using the 95% credible intervals. The FB model goodness of fitis judged by the Deviance Information Criteria (DIC). Spiegelhalter et al. (2002) proposed the DIC as a measure of model complexity and fit. As a goodness of fit measure, DIC is a Bayesian generalization of Akaike's information criteria that penalizes larger parameter models. According to Spiegelhalter et al. (2003), it is difficult to determine what would constitute an important difference in DIC; however, differences of more than 10 might definitely rule out the model with the higher DIC, and differences between 5 and 10 are considered substantial.

5. Results

Using the methodology discussed in the previous section, macro level CPMs are developed incorporating exposure and network indicators. Table 2 shows the developed negative binomial GLM CPMs, while Table 3 shows the FB models incorporating spatial effects. The goodness of fit statistics and the explanatory variables significance are provided in both tables. The models show good fit; with almost all the explanatory variables being statistically significant at the 5% level.

5.1. Exposure

Cyclist-vehicle collisions are found positively associated with both bike and vehicle exposure measures, which is reasonable and consistent with results from previous studies (Miranda-Moreno et al., 2011; Strauss et al., 2013; Hamann and Peek-Asa, 2013; Kaplan and Prato, 2015). The exponents of the exposure variables are less than one, which suggests that higher number of bikes on road, as well as more vehicle congestion, would reduce cyclist crash risk. The results are in line with a recent macro-level study by Prato et al. (2016), and agree with the "safety in numbers" hypothesis (Jacobsen, 2003). The results also agree with the studies that concluded the presence of positive associations between congestion and lower crash rates (e.g. Reynolds et al., 2009).

In order to incorporate the bike network indicators into the CPMs, three exposure measures are used (i.e. BKT, both BKT and VKT, and EXP) to develop three models for each network indicator. The model that yields the highest statistical significance for the network indicator is the one reported in the results.

5.2. Connectivity

The CPMs show that there is a positive association between the cyclist-vehicle collisions and various connectivity measures (i.e. InterD, Conn, Cov, and NetD). The positive association between intersection density and bike crashes reported in this study is similar to that reported in Siddiqui et al. (2012), Strauss et al. (2013), and Wei and Lovegrove (2013) studies. This can be attributed to the higher cyclist-vehicle interactions at the intersections, which would lead to an increased collision risk.

To the best of the authors' knowledge, the safety effect of bike network's degree of connectivity, coverage, density, and complexity had not been investigated in previous studies. The degree of connectivity andthedegree of coverage are relatedto thenumber of bike network links, network configuration, and street network coverage; and are found to be positively associated with bike crashes. This is likely due to the fact that more links between nodes indicate more frequent routes, which would lead to higher exposure to conflicts and consequently higher collision potential. Similar results were found for transit networks, where the degree of connectivity was foundpositively associated withcollisions frequency (Quintero et al., 2013). As for network density, a higher value implies better zone coverage, as well as better network connectivity (Dill, 2004). Therefore, it is plausible that the relationship between network density and collisions is similar to the one between degree of connectivity and collisions. Lastly, a model is developed to evaluate the impact of bike network complexity on the frequency of cyclist collisions. Although the model resulted in a positive association between complexity and cyclist collisions, the complexity variable is found statistically non-significant, and therefore was not reported in the results.

5.3. Directness

The average edge length variable is found to have a negative association with cyclist collisions, while the average length per vertex is found to be statistically non-significant. The results imply that a higher average edge length, which indicates longer links without hindrances or discontinuities, is presumably more convenient and safer to the cyclists. The association between average edge length and collisions agrees with the safety study done by Quintero et al. (2013) on Metro Vancouver transit network. On the other hand, linearity is found positively associated with cyclist collisions. This positive association may be attributed to the tendency of motorists and cyclists to speed more on straight links, which would increase crashes risk. However, such result needs further investigation.

5.4. Topography

The length of the zonal bike network is found negatively associated with cyclist-vehicle collisions. This agrees with recent studies that concluded that more bike infrastructure would increase cyclist safety (De Rome et al., 2014; Kaplan et al., 2014; Prato et al., 2016). As well, a negative association is found between the weighted slope of the zonal bike network and cyclist collisions. This may be explained as cyclists' speed is usually reduced at climbing slopes, which would lower crash risk. This result is consistent with a study by Chen (2015), who used a zonal mean slope variable to represent the average absolute slopes of the TAZs. Although the variable used in Chen's study was non-significant at 95% level, it showed negative association between zonal mean slope and cyclist crashes.

5.5. Combined models

Lastly,three models (A, B, and C) are builtto combine the significant cyclingnetwork attributes into aggregateCPMs. The procedure for selecting the combined model variables is a forward stepwise procedure. The order in which the variables are added is based on their p-value, from lowest to highest. Whether to keep or remove a variable from a model is decided based on two conditions. First, the variable's parameter needs to be significant. Second, the variable should exhibit low correlation with other variables that already exist in the model. The relationships between the various network attributes and cyclist collisions in the combined models are found similar to those in the models relating the attributes individually to cyclist collisions.

Models incorporating spatial effects are then developed for the combined models using a full Bayesian Poisson-lognormal approach. Spatial effects are found highly significant (i.e. =0.99) in all the developed models indicating the presence of spatial correlation. This highlights the importance of accounting for spatial autocorrelation in the macro-level CPMs investigating cyclist safety. Model A is found to have the best fit (lowest DIC) among the three reported combined models, which agrees with the GLM model results. The inclusion of spatial effects caused two network indicators (i.e. network density and average weighted slope) to become non-significant. All the other network indicators are significant at either 95% or 90% levels.

6. Summary and conclusions

The study developed zone-level CPMs relating bike network indicators and cyclist-vehicle collisions. Both generalized linear

Table 2 Negative Binomial GLM Estimates.

Model Coll= K df SD X2 P-Value
Exposure
0.184BKT0.643 2.52 131 142.57 125.16 a0, BKT < 0.001
0.239VKT0.484 1.31 132 149.82 132.40 a0 = 0.081, VKT < 0.001
0.040BKT0.59VKT0.22 2.43 130 142.60 118.71 a0, BKT < 0.001, VKT = 0.0084
0.016EXP0.45 2.27 131 144.42 117.33 a0, EXP <0.001
Cycling Network
Connectivity Indicators
0.016 BKT0.58VKT0.28exp(0.006InterD) 2.63 129 141.88 111.10 a0, BKT, VKT < 0.001, InterD = 0.0038
0.012BKT0.61VKT0.27exp(1.80Conn) 2.56 129 141.83 117.48 a0, BKT <0.001, VKT = 0.001,
Conn = 0.018
0.010 EXP0.46exp(0.65Cov) 2.28 130 143.17 112.76 a0, EXP <0.001, Cov = 0.061
0.0098 EXP0.46exp(0.046NetD) 2.38 130 143.01 111.80 a0, EXP < 0.001, NetD = 0.009
Directness Indicators
0.28BKT0.63exp(-4.76AvgEdLen) 2.38 130 142.31 125.13 a0 = 0.005, BKT < 0.001,
AvgEdLen = 0.024
0.23*10−4 BKT0.60VKT0.18exp(7.81Lin) 2.70 129 142.82 122.79 a0, BKT < 0.001, VKT = 0.023, Lin = 0.001
Topography Indicators
0.020 BKT0.61VKT0.31exp(−0.063L) 2.50 129 143.07 121.32 a0, BKT, VKT < 0.001, L = 0.049
0.053BKT0.58VKT0.24exp(−0.17WSlope) 2.46 129 140.73 115.68 a0, BKT < 0.001, VKT = 0.003,
WSlope = 0.029
Combined Models
A) 0.19*10−4 BKT0.58 3.03 127 141.39 121.23 a0, BKT < 0.001, VKT = 0.0017,
VKT0.25exp(0.005InterD + Lin = 0.001, InterD = 0.014,
7.51Lin-0.14WSlope) WSlope = 0.067
B) 0.032BKT0.60 2.70 127 140.37 117.27 a0, BKT < 0.001, VKT = 0.002,
VKT0.26exp(1.64Conn-3.58 Conn = 0.03, AvgEdLen = 0.09,
AvgEdLen-0.17WSlope) WSlope = 0.02
C) 0.032EXP0.52 exp(0.043NetD-0.08L) 2.56 129 143.38 118.14 a0, EXP < 0.001, NetD = 0.01, L = 0.008

Table 3 Combined FB Models with Spatial Effects.

Variable Combined Model A Combined Model B Combined Model C
Estimate SD Bayesian
Confidence Interval		 Estimate SD Bayesian
Confidence Interval		 Estimate SD Bayesian
Confidence Interval
2.5% 97.5% 2.5% 97.5% 2.5% 97.5%
Intercept −11.96* 2.09 0.98 0.98 −4.21* 0.78 −5.75 −2.66 −1.17* 0.31 −1.78 −0.57
BKT 0.46* 0.054 0.35 0.56 0.46* 0.05 0.36 0.57
VKT 0.39* 0.086 0.22 0.56 0.39* 0.08 0.22 0.55
EXP 0.45* 0.04 0.37 0.54
InterD 0.0035* 0.001 0 0.007
Conn 1.06** 0.64 −0.19 2.31
NetD 0.016 0.018 −0.019 0.053
AvgEdLen −5.07* 2.05 −9.21 −1.71
Lin 7.96* 1.95 4.14 11.79
L −0.052** 0.028 −0.10 0.002
WSlope −0.034 0.065 −0.16 0.09 −0.06 0.06 −0.19 0.07
DIC 741.66 745.37 745.83
0.992 0.001 0.988 0.995 0.992 0.001 0.99 0.995 0.992 0.001 0.989 0.995

* Significantly different from zero at 5%.

regression, and full Bayesian techniques incorporating spatial effects were used to build the CPMs. The CPMs incorporated network structure indicators that were obtained from the graph characterization of the bike network. The indicators were divided into three categories: connectivity, directness, and topography. As well, the models included measures of actual cyclist exposure (bike kilometers travelled) as opposed to relying on proxies such as population or bike network length.

The results showed that the cyclist-vehicle collisions were positively associated with the different exposure variables used (i.e. BKT, VKT, and EXP). Collisions were also found positively associated with the bike network linearity and the various connectivity measures used in the study (i.e. degree of connectivity, network coverage, network density, and intersection density). On the other hand, cyclist-vehicle collisions were found negatively associated with bike network continuity, length, and average weighted slope. FB models incorporating spatial effects confirmed the aforementioned results, and showed considerable spatial autocorrelation between the random effects among the studied TAZs.

The non-linearity of the exposure measures shows that the cycling environment can be safer with higher number of cyclists. This can be attained by promoting the health and economic benefits of cycling as well as designing streets to be more convenient for active transportation commuters by adopting complete street policies. The results also revealed the significantimpact of bike network indicators on cyclist safety. This indicates that any suggested policies for increasing the number of cyclists should be accompanied by risk mitigation measures. Improving the quality of the

** Significantly different from zero at 10%.

bike network can play an important role in improving cyclist safety and motivating more commuters to cycle. Such improvement can include expanding the bike network infrastructure and reducing the discontinuities on the bike network.

It is worth noting that the study has some limitations. The study investigated bike collisions, traffic exposure, and bike network data using a sample of medium-low bike-use communities. Therefore, data need to be collected from high bike use communities (e.g. European cities) to validate the conclusions of this study. Moreover, the study included only cyclist-vehicle collisions due to data limitation. Investigating other cyclist related collisions such as cyclist-pedestrian and cyclist–cyclist collisions would be interesting. Boundary collisions in this study were divided between zones in proportion to their bike kilometers travelled. A detailed investigation of other techniques of assigning boundary collisions would be useful. Finally, the study investigated the impact of the bike network structure on cyclist safety without considering the bike and road network patterns that may affect the characteristics of traffic flow and travel behavior. Incorporating road network patterns and variables that are related to the built environment (e.g. transit stops, traffic signals, etc.) and land use could provide further insights on cyclist safety.

References