category: literaturenote citekey: stipancicpedestriansafetysignalizedintersections2020 title: "Pedestrian safety at signalized intersections: Modelling spatial effects of exposure, geometry and signalization on a large urban network" authors: "Stipancic, Joshua; Miranda-Moreno, Luis; Strauss, Jillian; Labbe, Aurélie" year: 2020 date: 2020-00-00 2020 doi: 10.1016/j.aap.2019.105265 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2019.105265" zotero_key: W6ZI7S22 zotero_storage: 7GZJNNZD collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Stipancic, Joshua"

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Pedestrian safety at signalized intersections: Modelling spatial effects of exposure, geometry and signalization on a large urban network

Joshua Stipancica , Luis Miranda-Morenob, \*, Jillian Straussc , Aurélie Labbea

^a Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Côte-Sainte-Catherine, Montréal, Québec, H3T 2A7, Canada
^b Department of Civil Engineering and Applied Mechanics, McGill University, Room 268, Macdonald, Engineering Building, 817 Sherbrooke Street West, Montréal, Québec, H3A 0C3, Canada
^c Polytechnique Montréal, C.P. 6079, succ. Centre-Ville, Montréal, Québec, H3C 3A7, Canada

ARTICLE INFO

Keywords: Vulnerable road users Pedestrian injuries Bayesian models Crash modelling Signalized intersections

ABSTRACT

Intersections represent the most dangerous sites in the road network for pedestrians: not only is modal separation often impossible, but elements of geometry, traffic control, and built environment further exacerbate crash risk. Evaluating the safety impact of intersection features requires methods to quantify relationships between different factors and pedestrian injuries. The purpose of this paper is to model the effects of exposure, geometry, and signalization on pedestrian injuries at urban signalized intersections using a Full Bayes spatial Poisson Log-Normal model that accounts for unobserved heterogeneity and spatial correlation. Using the Integrated Nested Laplace Approximation (INLA) technique, this work leverages a rich database of geometric and signalization variables for 1864 intersections in Montreal, Quebec. To collect exposure data, short-term pedestrian and vehicle counts were extrapolated to AADT using developed expansion factors. Results of the model confirmed the positive relationship between pedestrian and vehicle volumes and pedestrian injuries. Curb extensions, raised medians, and exclusive left turn lanes were all found to reduce pedestrian injuries, while the total number of lanes and the number of commercial entrances were found to increase them. Pedestrian priority phases reduced injuries while the green straight arrow increased injuries. Lastly, the posterior expected number of crashes was used to identify hotspots. The proposed ranking criteria identified many intersections close to the city centre where the expected number of crashes is highest and intersections along arterials with lower pedestrian volumes where individual pedestrian risk is elevated. Understanding the effects of intersection geometry and pedestrian signalization will aid in ensuring the safety of pedestrians at signalized intersections.

1. Introduction

The obvious and oft-cited benefits of walking, related to personal and public health and environment, are tempered by the increased injury risk imposed on pedestrians. Between 2012 and 2016, nearly 1900 pedestrians were killed as a result of road traffic crashes in Canada (Transport Canada, 2017). Although pedestrian safety is often maintained through modal separation (in time or space), separation is often impractical or impossible to achieve at intersections where pedestrians face increased exposed to motor vehicles. Additionally, elements of geometry, traffic control, and built environment at urban intersections can further exacerbate crash risk (Schneider and Arnold, 2010; Elvik, 2009; Quistberg et al., 2015). In Canada, intersections account for 30% of all fatal and 40% of all serious injury crashes between pedestrians and motor vehicles (Transport Canada, 2019) and approximately 60% of pedestrian injuries in urban centres occur at signalized intersections (Fernandes, 2013). The necessity to provide adequate safety for pedestrians has led to the development of engineering countermeasures intended to enhance intersections, improve comfort, and increase safety. Countermeasures can include changes to geometry, built environment, traffic control, and/or traffic flow (Miranda-Moreno et al., 2011a, 2011b; Quistberg et al., 2015).

Evaluating the safety impact of countermeasures, or intersection features in general, requires methods to quantify relationships between different factors and pedestrian injury occurrence. For this task, statistical regression models have been popular in the existing pedestrian safety literature. Most commonly, these models consider the relationship between pedestrian and motor vehicle flows (traffic exposure) and pedestrian crash risk as summarized by Elvik (2009). Such regression techniques allow for the study of numerous other variables, including

E-mail addresses: joshua.stipancic@hec.ca (J. Stipancic), luis.miranda-moreno@mcgill.ca (L. Miranda-Moreno), jillian.strauss@polymtl.ca (J. Strauss), aurelie.labbe@hec.ca (A. Labbe).

^⁎ Corresponding author.

elements of geometry and signalization, while controlling for exposure. Several examples include Schneider and Arnold (2010); Miranda-Moreno et al. (2011a), 2011b, Pulugurtha and Sambhara (2011), and more recently Kröyer (2015). However, studies involving detailed intersection-level geometric data are rare in the pedestrian safety literature, with many city-level models using aggregate spatial data at the census tract or similar unit of analysis (Bhat et al., 2017; Xie et al., 2019). Although intersection-level models aid in the identification of risk factors and hotspots, by relying on small samples of intersections limited by available count data, many existing studies may introduce sample bias. Therefore, previously demonstrated relationships between intersection features and pedestrian injuries must be replicated. Furthermore, many studies relying on short-term pedestrian counts have failed to normalize the data by converting to average annual daily traffic (AADT), making raw counts not directly comparable between sites (Schneider et al., 2009).

This paper aims to address these limitations present in past research. More specifically, the purpose of this study is to develop a spatial pedestrian-vehicle crash frequency model to evaluate the effects of exposure measures, geometry, and signalization on safety using regression models of pedestrian injury occurrence. The specific objectives are to i) investigate effects of turning movements, ii) quantify the effects of intersection geometry and pedestrian signal phasing on safety, iii) examine the influence of spatial correlations on model performance, and iv) demonstrate the model's application in the network screening process (hotspot identification). A Full Bayes (FB) Poisson Log-Normal regression model is estimated on a large sample of urban signalized intersections in Montreal, Quebec, Canada for which rich geometric, signal, environmental, and flow data was collected. Expansion factors were developed using long-term counting stations to convert observed flows to AADT. Spatial correlations are introduced in the model to account for unobserved cofounders between neighbouring intersections and reveal the true effect of treatment-related factors. Finally, high-risk locations are identified using the posterior expected number of injuries.

2. Literature review

Traditionally, pedestrian safety has been measured using historical crash data (Cameron, 1982; Miranda-Moreno et al., 2011a, 2011b; Harwood et al., 2008; Lyon and Persuad, 2002; Brüde and Larsson, 1993; Shankar et al., 2003; Lee and Abdel-Aty, 2005; Murphy et al., 2017; Ni et al., 2016; Lee et al., 2019). Crash frequency models have been developed using macro-level (spatial zones) or intersection-level data. Although recent studies have considered alternative approaches including conflict analysis with video-based data collection, network screening and safety performance functions are still most commonly derived using the traditional crash-based approach. Count models for pedestrian count frequency have varied from simple to complex. An example of a simple Poisson model is found in Schneider and Arnold (2010). However, more recent studies have incorporated techniques to account for both unobserved and spatial heterogeneity. Narayanamoorthy et al. (2013) describe two techniques for incorporating spatial dependence; spatial lag or conditional autoregressive (CAR), choosing to implement a spatial lag model themselves. Bhat et al. (2017) used spatial random-coefficients model to estimate crash counts at the level of the census tract, accounting for both unobserved and spatial effects using a spatial autoregressive lag structure. Huang et al. (2017) developed a multivariate crash frequency model with a CAR structure for various modes, recognizing the significance of both spatial correlations between sites and modes within a single site. Xu et al. (2019) estimated a Bayesian Poisson-lognormal model of crash frequency accounting for unobserved heterogeneity and spatial dependence. Methods for incorporating unobserved and spatial heterogeneity in crash count models extend beyond pedestrian safety. Additional examples of various random parameter techniques are found in Anastasopoulos and Mannering (2009); Anastasopoulos (2016); Behnood and Mannering (2017); Xin et al. (2017); Fountas et al. (2018), and Cai et al (2018).

In terms of factors effecting crash frequencies, most studies have focussed on elements on traffic, including volumes and speeds, or elements of geometry and built environment. Generally, the literature has shown that aggregate volumes are significantly and positively related to the number of pedestrian injuries (Elvik, 2009). However, pedestrian injury rates (that is, the individual pedestrian risk) often decreases as pedestrian flow increases, popularly labelled the "safety in numbers" effect (Jacobsen, 2003; Elvik, 2009; Lee et al., 2019). In fact, reported elasticities from existing regression-based studies range from 0.2 to 1.2 for motor-vehicle flow and 0.3 to 0.7 for pedestrian flow (Schneider and Arnold, 2010; Elvik, 2009; Harwood et al., 2008; Miranda-Moreno et al., 2011a, 2011b; Lyon and Persuad, 2002; Geyer et al., 1982; Leden, 2002; Murphy et al., 2017; Ni et al., 2016). Positive elasticities indicate an increase in crash occurrence with increasing flow. Elasticities exceeding 1.0 would indicate an elastic relationship between crashes and flow, while the majority of the reported elasticities falling below 1.0 indicate an inelastic relationship (i.e. a decrease in crash rates with increasing flow). Posted speed limits and operating speeds have also been considered (Zeeger and Seiderman, 2002; Feng, 2001; Ewing and Dumbaugh, 2009; Fitzpatrick et al., 2006), with higher speeds typically positively related to pedestrian crashes. More recent studies (Kröyer, 2015; Chen et al., 2013) found that speed limit had, at best, a marginal effect on pedestrian safety.

Schneider and Arnold (2010) provide a review of literature on the influence of geometry and built environment on crashes, though many existing studies have quantified effects at an area-wide level (Graham and Glaister, 2003; Wier et al., 2009; Bhat et al., 2017; Xie et al., 2019) rather than at the site level. More recent studies have accounted for both site-level (i.e. geometry) and neighbourhood-level (i.e. density) factors using two-equation modelling frameworks (Miranda-Moreno et al., 2011a, 2011b), multilevel analyses (Morency et al., 2012; Heydari et al., 2017; Quistberg et al., 2015), or correlations between crash outcomes. Some key findings from the existing literature are as follows. The number of lanes and approaches have a significant impact on crash occurrence (Zeeger and Seiderman, 2002), with four-legged intersections having more crashes and injuries than three-legged intersections (Ewing and Dumbaugh, 2009; Miranda-Moreno et al., 2011a, 2011b; Morency et al., 2012; Lyon and Persuad, 2002). Quistberg et al. (2015) found wider roads were associated with more pedestrian crashes and that functional class influenced crashes, with arterials having the highest crash rates. Median type may significantly influence crash frequency (Zeeger and Seiderman, 2002; King et al., 2003; Bowman et al., 1994) by blocking certain interactions and providing a safe refuge for crossing pedestrians. Despite crosswalks being associated with improved pedestrian (Hauck and Bates, 1979; Retting et al., 1996) and driver behaviour (Knoblauch and Raymond, 2000), current research shows no clear benefit for pedestrian safety (Zegeer et al., 2005; Herms, 1970). In some cases, crosswalks are associated with increased crash rates (Zegeer et al., 2005; Koepsell et al., 2002). Curb parking often increases crash rates (Box, 2004; Agran et al., 1996; Humphreys et al., 1978). Schneider et al. (2009) found that more rightturn-only lanes, more residential driveways, and more nearby commercial properties significantly increased pedestrian crash risk.

The influence of traffic control on crash rates has been somewhat less studied, with most studies to date utilizing surrogate measures of safety (violations). Longer signal phases and pedestrian wait times have been associated with lower levels of comfort and more pedestrian violations (Cambron de Lavalette et al., 2009; Tiwari et al., 2007). Zhang et al. (Zhang et al., 2015) used both surrogate measures and crash data, finding that exclusive pedestrian phases decreased the probability of conflicts and pedestrian crashes. Though a recent study by Strauss et al. (2014) proposed a multimodal approach for safety analysis at intersections in Montreal, a relatively small sample of intersections was used, and the impacts of geometry and traffic control were not analyzed in depth. This highlights the first of several shortcomings present in the existing literature. Signalization, especially pedestrian traffic signals or phases, have rarely been incorporated into pedestrian crash models. Second, past studies have relied on relatively small samples of intersections, typically several hundred or less. Third, many features of interest are likely correlated with pedestrian or traffic volumes (for example, crosswalks are often installed in locations with the highest pedestrian demand). Not only is it necessary to control for exposure, but it is also necessary to normalize short-term counts using expansion factors, estimating models based on average flows, a step lacking form several past studies. Lastly, many existing pedestrian safety studies have ignored spatial correlations between neighbouring sites, shown to be crucial to model estimates in previous studies (Bhat et al., 2017; Xie et al., 2019; Graham and Glaister, 2003). This paper aims to address these limitations using the methods described in the following section.

3. Methodology

The methodology of this paper builds on methods previously proposed by Miranda-Moreno et al. (2011a,b) and Strauss et al. (2013). In these studies, regression techniques were used to study pedestrian and cyclist safety at urban intersections considering the effects of flow, geometric design, and built environment attributes. Compared to these studies, the primary developments herein are a significantly increased sample size, improved Bayesian modelling framework, and addition of spatial effects.

3.1. Data collection and preparation

This paper makes use of three primary sources of data; count data (including developed expansion factors), intersection feature inventory data, and injury data. Although there are several accepted counting schemes, this study utilized short-term 8 -h counts conducted in 15 minute intervals for each approach and turning movement. Counts were conducted on weekdays during the morning peak (6:00-9:00am), midday (11:00am-1:00pm) and the evening peak (3:30-6:30pm). Pedestrians were counted once for every unique crossing made (pedestrians crossing east-west and then north-south were counted twice). As counts were made across all weekdays and months, expansion factors were required to obtain AADT for pedestrians and vehicles. Similar to the approach used by Schneider et al. (2009) and (Strauss et al., 2013) for motor vehicle flows, expansion factors were obtained from permanent counting stations. For motor vehicles, permanent counting stations were used, while pedestrian counts were made using infrared sensors.

With regards to intersection features, this research utilizes an inventory of signalized intersections in Montreal compiled by the research team. Each studied intersection was visited and a variety of geometric, built environment, and signalization features were recorded. The inventory includes variables for number of approaches, presence of one-way approaches, number of lanes, road width and crosswalk length (measured using odometer wheels), presence and width of medians, signal type, presence and type of pedestrian phasing, and presence of left-turn lanes and phasing among others. Although pedestrian injury data can be compiled from several sources including police reports or insurance claims, this study uses injuries recorded in ambulance service reports. To assign crashes to individual sites, 20 m buffers were generated around each intersection and the total number of crashes in each buffer were counted.

3.2. Statistical modeling

Although several models for handling spatial dependencies have been demonstrated in the literature, count models (Poisson-Gamma and Poisson-Normal models and their derivatives) have been the most popular. Considering that full Bayes models may produce superior results (Miaou and Lord, 2003) and the limitations of traditional Monte Carlo Markov Chain (MCMC) estimation methods, this work proposes the use of a Bayesian Poisson Log-Normal spatial model with a CAR spatial structure estimated using the INLA technique. In this study, the number of pedestrian injuries (the response variable, Yi) at each intersection i, is assumed to follow a Poisson distribution,

$$Y_i \sim Poisson(\theta_i)$$ (1)

where θi is the mean number of injuries expected at intersection i. Although a negative binomial model was tested initially, it was consistently outperformed by the Poisson model, though the posterior distributions of the parameters changed only marginally. Mean pedestrian injuries are then modelled using a Latent Gaussian Model (LGM), which can be written as a structured additive model, in which μi is related to the various predictors through a link function g () such that

$$g(\theta_l) = \beta0 + \sum{k=1}^{K} \betak z{kl} + \sum{l=1}^{L} f^{(l)}(u{ll}) + \varepsilon_l$$ (2)

where ^β⁰ is the intercept, βk are the coefficients representing the linear effect of covariates zki (assuming K covariates in the model), f ( )^l are functions of covariates uli used to relax these linear relationships or introduce random effects, εi is the unstructured error component following a Normal distribution (Rue et al., 2009). In the case of a Poisson model, the link function is the natural logarithm and functions f ( )^l can take many forms, for example, allowing for spatial correlations (Latouche et al., 2007; Biangiardo and Cameletti, 2015). In this model, covariates zk include pedestrian and vehicle volumes, geometric data, and signalisation variables.

Furthermore, previous work has shown the ability of spatial correlations to reduce bias by accounting for unobserved cofounders between neighbouring sites (Bhat et al., 2017; Xie et al., 2019). This work proposes a modified version of the Besag–York–Molliè (BYM) model presented by Besag et al. (1991). In this model, the error component is decomposed into two discrete parts

$$\ln(\theta_i) = \beta0 + \sum{k=1}^{K} \betak z{ik} + u_i + v_i$$ (3)

where vi is a random effect that accounts for unobserved heterogeneity (effects of variables not captured in the model), following a Normal distribution with mean 0 and constant variance. Moreover, ui is a spatially structured site-specific random effect (to accommodate for correlation among neighbouring sites). Several structures can be specified for the spatial heterogeneity, u = … (, , ) u u ¹ ⁿ . Here, a proper version of the CAR structure is chosen

$$ui|u{-i}, \tau, d^{-} \mathcal{N}\left(\frac{1}{d+ni} \sum{i=j} u_j, \frac{1}{\tau(d+n_i)}\right)$$ (4)

where ni is the number of neighbours for intersection i, *u−ⁱ* represents all members of u excluding the i th, i ˜j indicates if links are neighbours, d > 0 controls the "properness", and τ > 0 is a scaling parameter (Biangiardo and Cameletti, 2015). Neighbours were defined using a proximity threshold. Specifically, two intersections are considered neighbours if d, the Euclidean distance, between them are 200 m or less. Other thresholds values were tested (100 m and 150 m) and were found to have minimal effects on modelling results.

Rather than estimating the LGM using a traditional MCMC approach, this study uses the Integrated Nested Laplace Approximation (INLA) approach, first proposed to perform Bayesian approximations on LGMs using a combination of Laplace approximations and numerical integration to estimate the posterior marginal of the latent field (Rue et al., 2009). The INLA approach can produce accurate approximations with a significant reduction in computational time (Schrodle and Held, 2011). The authors have demonstrated the applications of INLA in crash

Fig. 1. Sampled signalized intersections with pedestrian injuries and flows.

modelling in several studies on vehicle crashes (Stipancic et al., 2018; Stipancic et al., 2019). Estimation was completed in R using the R-INLA package (Schrodle and Held, 2011). Finally, sites are ranked using the posterior expected number of injuries (normalized by the observed pedestrian counts) and hotspots are identified.

4. Data description

4.1. Site selection

This study utilizes a large and unique sample of 1864 signalized intersections distributed across the island of Montreal, as shown in Fig. 1. Any signalized intersection with available count data was included, with the final sample representing nearly 80% of all signalized intersections in the city. The sample includes intersections from most of Montreal's boroughs and represents a mix of all possible combinations of intersecting (and signalized) arterial, collector, and local streets.

4.2. Injury data

The injuries included in this study include all reported accidents for which an ambulance was dispatched from January 1st, 1999 to July 31st, 2008. The distribution of injury counts is included in Fig. 2, and the spatial distribution of pedestrian injuries across the sampled intersections is provided in Fig. 1.

4.3. Exposure data

8 -h pedestrian and vehicle counts were conducted by the Montreal Department of Transportation, with most counts completed in 2008 or 2009. Expansion factors for motor vehicles were generated by the City of Montreal based on permanent counting stations from urban arterials. To generate expansion factors for pedestrians, infrared counters were installed at six sidewalk locations for one year between Summer 2010

Fig. 2. Distribution of pedestrian injury counts.

to Summer 2011, with pedestrian counts generated for each direction of travel. As with motor vehicles, these continuous long-term counts can be used to define the temporal distribution of pedestrian volumes, develop hourly, daily, and monthly expansion factors, and standardize the short-term counts. Each intersection with short-term counts is matched to a similar intersection with available long-term count data. Daily expansion factors are calculated by dividing the observed daily traffic volume by the AADT for the long-term site (similarly for monthly and yearly factors). Short-term counts are then divided by the appropriate daily, monthly, and yearly expansion factors to yield AADT for both pedestrians and vehicles. More information on expansion factors is provided in Gastaldi et al. (Gastaldi et al., 2014) and Beitel et al. (Beitel et al., 2018). The generated pedestrian expansion factors are shown in Fig. 3. In terms of hourly patterns, the weekday three-peak pattern is quite different from the weekend single peak. Pedestrian activity declines on weekends and during winter months. The normalized AADT

Fig. 3. Hourly, daily, and monthly expansion factors for pedestrian counts.

pedestrian flows are illustrated in Fig. 1.

Although vehicular volumes are typically considered using a single aggregate measure, this study adopts the method proposed for analysis of cyclist safety by (Miranda-Moreno et al., 2011a, 2011b). Vehicle flows are split by turning movement to observe the contribution of each movement to injury occurrence,

$$\ln(\theta_i) = \beta_0 + \beta_1 P_i + \beta2 V{li} + \beta3 V{ri} + \beta4 V{ti} + \sum{k=5}^{n\beta} \betak z{ki} + u_i + v_i$$ (5)

where Vli, Vri, and Vti are the AADT for left-turning, right-turning, and through vehicles respectively. Additional geometric and signalization variables are contained in zki. ui and vi are the spatial correlation and random effect defined in Section 3.2.

4.4. Geometric and signalization data

The McGill University intersection inventory is a rich dataset capturing features of interest at signalized intersections on the island of Montreal. The process of collecting and compiling the data for all 1864 intersections took approximately one year, with each intersection requiring, on average, one hour to visit, collect the data, and digitize the data. The inventory captures variables related to either geometry or signalization. Certainly, intersection geometry has an impact on pedestrian safety. One feature is the distance that pedestrians must travel in order to cross the intersection. It is hypothesized that the larger the crossing distance, the longer the pedestrian spends in the intersection, thereby increasing injury occurrence. Several unique variables present in the feature inventory describe crossing distance, namely:

Total Crosswalk Length: the sum of all crosswalk lengths (measured sidewalk to sidewalk) along every intersection leg.
Average Crosswalk Length: the average of all crosswalk lengths along every intersection leg.
Total Lanes: the sum of all approaching lanes along all legs. For example, a four-legged intersection between a three-lane one-way segment and two-lane two-way segment has seven total approach lanes (three approaches on the one-way and four approaches on the two-way).
Total Road Width: the sum of all road widths (measured curb to curb) along every intersection leg 15 m upstream of the crosswalk.

It should be obvious that these variables are highly correlated, and therefore only one should be included in the model to avoid potential issues with collinearity. Table 1 shows the correlations between the four variables and pedestrian injuries. Based on this result and additional exploratory analysis, Total Lanes was selected as the variables with the most explanatory power. This is logical, as each approach lane represents one source of potential conflicts, regardless of road width. Additional geometric variables include:

Table 1 Correlations of Crossing Distance Variables and Pedestrian Injuries.

Three-leg Intersection: indicates if the intersection has three legs.
Curb Extension: equal to 1 if Total Crosswalk Length–Total Road Width < 0 (crossing distance is reduced at the intersection) and 0 otherwise. Curb extensions are popular in Montreal and are a treatment used to extend sidewalks, reduce crossing distances, reduce vehicle speeds, and eliminate parking near the intersection.
Raised Median: indicates the presence of a raised median dividing opposing directions of traffic.
Commercial Entrances: the number of access points to commercial properties (gas stations, shopping malls, restaurants, etc.) within 25 m of the intersection. Intersections with four legs have a maximum of eight access points (one on both sides of every leg).
Number of Exclusive Turn Lanes: the total number of lanes used exclusively for one turning movement (either right or left turns).
Sides with Permitted Parking: the number of sides of all legs with permitted parking. Intersections with four legs have a maximum eight sides with permitted parking (one on both sides of every leg).
Sides with Restricted Parking: the number of sides of all legs with restricted parking. For four-legged intersections, Sides with Permitted Parking + Sides with Restricted Parking ≤ 8.

The intersection feature inventory also contains variables capturing elements of signalization and signal phasing present at each intersection. It is hypothesized that certain elements of signalization, especially those that provide priority to pedestrian movements, will decrease the occurrence of pedestrian injuries. Namely, the inventory contains the following variables:

All-red Phase: indicates a fully-protected pedestrian phase allowing pedestrians to cross in both directions while all vehicle movements are prohibited.
Half-red Phase: indicates a partially-protected pedestrian phase allowing pedestrians to cross in either direction before vehicles travelling in the same direction receive a green signal.
Straight Green Arrow: indicates a phase including a green straight arrow, where through vehicles are permitted while turning vehicles are prohibited.
Pedestrian Countdown Timer: indicates the presence of a countdown timer signaling the time remaining for pedestrians to cross.
Protected Left Turn Phase: indicates the presence of a protected left turn phase, where left turning vehicles can move without conflicting movements.
Restricted Left Turn Phase: indicates the presence of a permitted left turn phase, where left turning vehicles most give priority to conflicting movements.

A summary of all variables captured in the feature inventory is presented in Table 2.

Table 2 Summary Statistics from the Intersection Feature Inventory.

Variable	Mean	Std. Dev.	Minimum	Maximum
Injury
Pedestrian Injuries	2.22	3.19	0	29
Exposure
Pedestrian Flow	2887	5078	0	77736
Right-Turning Traffic Flow	2784	3422	0	46526
Straight Through Traffic Flow	21154	11469	0	76525
Left-Turning Traffic Flow	2608	3212	0	47783
Geometry
Total Lanes	0.68	2.58	0	18
Three-leg Intersection	0.24	0.43	0	1
Curb Extension	0.07	0.26	0	1
Raised Median	0.45	0.50	0	1
Commercial Entrances	0.92	1.43	0	8
Number of Exclusive Turn Lanes	0.25	0.82	0	1
Sides with Permitted Parking	3.14	2.48	0	8
Sides with Restricted Parking	4.27	2.37	0	8
Signalization
All-red Phase	0.06	0.24	0	1
Half-red Phase	0.21	0.41	0	1
Straight Green Arrow	0.25	0.43	0	1
Pedestrian Countdown Timer	0.46	0.50	0	1
Protected Left Turn Phase	0.41	0.49	0	1
Restricted Left Turn Phase	0.62	0.49	0	1

5. Results

5.1. Model interpretation

Results of the pedestrian crash model are contained in Table 3. Note that interpretation of the marginal effects for exposure variables is equivalent to the mean of the posterior distribution (because these variables are logarithmic). Additional marginal effects are interpreted as 1 − exp β( )^k , where βk is the mean of the posterior distribution. Considering the effects of pedestrian and vehicle volumes, the posterior mean of the coefficients is positive in all cases. Additionally, all volume covariates are statistically significant at 95% confidence, except for the right-turning vehicle volumes (it should be noted that this variable is significant at the 90% confidence level). As expected, increasing vehicular and pedestrian volumes are related to an increase in pedestrian injuries. Additionally, the elasticities are all positive but less than 1. This matches results found in much of the existing research (Schneider and Arnold, 2010; Elvik, 2009; Harwood et al., 2008; Miranda-Moreno et al., 2011a, 2011b; Lyon and Persuad, 2002; Geyer et al., 1982; Leden, 2002; Murphy et al., 2017; Ni et al., 2016). A 10% increase in pedestrian volumes results in a 4.30% increase in pedestrian injuries. Likewise, a 10% increase in right-turning, straight through, and left-turning vehicles results in a 0.43%, 3.54%, and 1.14% increase in injuries respectively.

Next consider the effects of geometric variables. Several statistically significant effects were observed as described below.

Total Lanes: The posterior mean is positive and statistically significant. Adding one additional lane increases pedestrian injuries by 13%. This variable is used to represent the total distance that must be travelled by pedestrians when crossing the street. As expected, a larger crossing distance requires more time to be spent mixing with traffic, which exposes pedestrians to more vehicle interactions, and thereby more crashes.
Curb Extension: The posterior mean is negative and statistically significant. The presence of curb extensions reduces pedestrian injuries by 24%. As curb extensions are a popular countermeasure for improving pedestrian safety, it is expected that their presence should reduce pedestrian injuries. This expectation is supported by the modelling results.
Raised Median: The posterior mean is negative and statistically

Table 3 Results of the FB Spatial Poisson Log-Normal Model for Pedestrian Injury Occurrence.

significant. The presence a raised median reduces pedestrian injuries by 24%. As in other studies (Zegeer et al., 2005; King et al., 2003; Bowman et al., 1994), the presence of a median is observed to significantly reduce pedestrian injuries. It has been suggested this effect occurs because certain medians provide refuge for crossing pedestrians.

Commercial Entrances: The posterior mean is positive and statistically significant. Pedestrian injuries increase by 9% for every additional commercial entrance. As in Schneider and Arnold (2010), more commercial entrances near the intersection increase the number of interactions faced by pedestrians, thereby increasing the number of crashes and pedestrian injuries.
Number of Exclusive Turn Lanes: The posterior mean is negative and statistically significant. Each additional exclusive left turn lane reduces injuries by 14%. Although the total number of lanes is positively related to pedestrian injuries, exclusive turn lanes are negatively related. This could be explained by exclusive turn lanes improving separation between movements and modes, effectively reducing the number of potential interactions.

No significant effect was found for the three-leg intersection or parking-related variables. It is interesting to note that for the specific case of Montreal, parking restrictions are often complex, being restricted for certain periods of the day or days of the week, and with paid parking often during specific periods. Perhaps a study with less complex parking restrictions or a data set with more detail regarding restrictions would yield different results. Finally, consider the statistically significant effects related to traffic and pedestrian signalization.

• All-red Phase: The posterior mean is negative and statistically significant. An all-red phase reduces injuries by 24%.

Half-red Phase: The posterior mean is negative and statistically significant. A half-red phase reduces pedestrian injuries by a factor of 19%. The presence of either an all-red or half-red phase is shown to significantly reduce pedestrian injuries, with the all-red phase being slightly more effective (it's posterior mean is lower than for the halfred phase). Both of these signal designs are intended to give pedestrian priority, and in doing so reduce crashes and pedestrian injuries overall.
Straight Green Arrow: The posterior mean is positive and statistically significant. Pedestrian injuries increase by 28%. in the presence of a straight green arrow.

No significant effect was observed for the presence of a pedestrian countdown timer or either protected or restricted left-turning phases.

Finally, consider the effect of spatial correlations. Although not presented here for brevity, a non-spatial model was also estimated and compared to the spatial model above. In general, the spatial model was observed to greatly improve model fit (DIC for the non-spatial model was 7276.4, compared to 6090.8 for the spatial model). Also, several variables which were significant in the non-spatial model became nonsignificant in the spatial model (specifically, Pedestrian Countdown Timer, Restricted Left Turn Phase, Sides with Permitted Parking, and Sides with Restricted Parking). However, the spatial model also had the effect of changing the posterior mean for right-turning vehicle volumes from negative to positive, as expected. Clearly, there are benefits to incorporating spatial correlations related to improved model fit and more accurate estimation of the effects of covariates.

5.2. Hotspot identification

Lastly, sites are ranked based on the posterior number of expected

Fig. 4. Hotspots identified by total number of expected injuries (a) and expected injury rates (b).

injuries and hotspots are identified. First, only the posterior expected injuries are used as the ranking criteria. Second, the posterior expected injuries are normalized using the observed pedestrian counts at each site to yield injury rates per 1000 pedestrians. The results of this analysis are demonstrated in Fig. 4, where the top 100 sites ranked by each method are visualized. Considering Fig. 4a, hotspots are largely identified in and around the city center in the borough of Ville-Marie, along with other centrally located boroughs of Plateau-Mont-Royal and Rosemont-La-Petite-Patrie to the north. These sites have the highest overall number of expected pedestrian injuries. However, centrally-located intersections also tend to have higher pedestrian volumes, reducing the individual risk faced by each pedestrian. This phenomenon is observed in Fig. 4a and b, in which almost no hotspots are chosen in Montreal's central neighbourhoods. Instead, when the injury rate is the selected ranking criterion, hotspots tend to be observed on arterials and collectors outside the city centre with high vehicular volumes, but few pedestrians.

As resources are always limited, funds intended for remediation of dangerous sites must be allocated effectively to maximize the benefit to society (reduction in pedestrian injuries). Clearly, the choice of the ranking criteria is extremely influential in terms of the identified hotspots, as revealed by Fig. 4. Ideally, several ranking criteria should be used, and their results should be compared. In this study, the total posterior expected crashes and expected crash rates were chosen and showed that either countermeasures aimed at reducing the total number of crashes at downtown intersections or countermeasures designed to reduce individual risk on high-volume arterials would be effective. Regardless of the chosen ranking criteria, this modelling approach allows for identification of hotspots based not only on observed historical crashes, but also characteristics of exposure, geometry, and signalization which increase the expected number of crashes.

6. Conclusions

This study presented a methodology to model the effects of exposure, geometry, and signalization on pedestrian safety at urban signalized intersections using a large inventory of intersections within the City of Montreal and a spatial FB spatial Poisson Log-Normal regression model estimated using the INLA technique. To generate the covariates, short-term vehicle and pedestrian counts were conducted across the 1864 studied intersections and corrected to AADT using expansion factors developed using permanent or long-term counters, a crucial step missing in many existing studies. This study contributed to and leveraged an intersection inventory with an incredibly rich set of geometric and signal characteristics for a large volume of signalized intersections within Montreal. Studies with such a large sample size and such a magnitude of geometric design and pedestrian traffic signal variables have rarely been reported in the literature. Models were estimated on 10 years of historical crash data. Model results largely confirmed the findings of existing studies or intuition. Pedestrian and vehicle volumes were shown to be positively related with pedestrian injury occurrence. Vehicular volumes were separated by turning movement to demonstrate the relative effect each movement has on pedestrian safety. Other than the variable for right-turning vehicles, all exposure measures were statistically significant at 95% confidence, with through vehicles having the greatest effect on safety. Furthermore, all elasticities were found to be less than one, supporting the safety-in-numbers effect found in previous studies.

Considering geometric features, curb extensions, raised medians, and exclusive left turn lanes were all found to significantly reduce pedestrian injuries. Curb extensions effectively shorten the crossing distance for pedestrians, while raised medians and exclusive turn lanes separate modes and movements and reduce potential interactions. The total number of lanes and the number of commercial entrances in the vicinity of the intersection were found to significantly increase pedestrian injuries. In terms of signalization, pedestrian priority phases significantly reduced pedestrian injuries, while the presence of a green straight arrow increased injuries. Clearly, providing pedestrian priority mediates collisions by separating pedestrian and vehicle movements and allowing pedestrians to traverse the intersection before motorists. Compared to a non-spatial model with identical covariates, the model with spatial correlations was shown to significantly improve model fit, while reducing the number of significant covariates. Importantly, the inclusion of spatial effects reduces potential biases due to unobserved similarities between neighbouring intersections, a noted source of error in previous studies. Lastly, the posterior expected number of crashes was used to rank sites and identify hotspots, first using the total crash count and second using the crash rates based on observed pedestrian volumes. The two ranking criteria were observed to produce different, yet complimentary, lists of high-risk intersections.

From a policy perspective, these results are of great importance. First, it is possible to identify the types of sites that should be targeted for remediation, based on the results of hotspot analysis. Using total crash count identified intersections close to downtown where the expected number of crashes is highest, while using crash rate identified intersections along arterials with lower pedestrian volumes where individual pedestrian risk is elevated. Second, the modelling results indicate the types of countermeasures that are effective in reducing pedestrian injuries. An all-red pedestrian phase was observed to have the greatest effect on pedestrian injuries, although the half-red phase was also effective. Clearly, the addition of pedestrian priority phases should be included in policy targeting pedestrian safety at signalized intersections, as it is currently only implemented at 27% of the intersections in the sample. In terms of geometry, curb extensions and raised medians significantly reduce injuries. These strategies can be implemented at new intersections or can be retrofitted to existing ones during reconstruction or rehabilitation. Curb extensions have a great potential, considering they are only implemented at 7% of the sampled intersections. A less invasive countermeasure could involve converting some traffic lanes to exclusive turn lanes, which also has the potential to reduce pedestrian injuries.

Several limitations related to this study should be noted. First, some of considered covariates may be endogenous. For example, intersections with curb extensions or pedestrian signals could be associated with either high pedestrian volumes or high injury risk or both. In other words, certain intersection characteristics may be predefined based on pedestrian activity and safety outcomes. Although initial analysis indicated a lack of endogenous effects, this could be explicitly tested in future work. Second, although vehicle turning movements were successfully disaggregated by turning movement, only the total number of pedestrian injuries at each intersection is known. To fully uncover the mechanisms between turning movements and pedestrian injuries, additional information related to the precise interactions (pedestrian and vehicle movements prior to a crash) would be beneficial. Use of the R-INLA framework limited the definition of neighbours to be based on Euclidean distance and a discrete threshold. Ideally, a distance-based neighbourhood structure could be used based on network distance and non-linear decay functions. This is a consideration for future work. Future work will also focus on similar models for an inventory of nonsignalized intersections within Montreal which has recently been completed. More recent crash data could be used to validate these results. Understanding the effects of intersection geometry and pedestrian signalization are critical for ensuring the safety of pedestrians at signalized intersections, which represent some of the most dangerous elements of the road network for vulnerable road users. It is expected that the results of this research will contribute to improving pedestrian safety at high-volume urban intersections within North America and around the world.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This project was funded in part by the Institute for Data Valorization

(IVADO), the Natural Sciences and Engineering Research Council of Canada, and the Fonds Québécois de la Recherche sur la Nature et les Technologies. The authors thank David Fernandes for helping in data preparation during his master's studies and Dr. Patrick Morency for their assistance and acknowledge Urgences-Santé and the Transportation Department of the City of Montreal who provided the injury and count data respectively.

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