Prediction of drivers and pedestrians' behaviors at signalized mid-block Danish offset crosswalks using Bayesian networks

Journal of Safety Research 69 (2019) 75–83

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Journal of Safety Research journal homepage: www.elsevier.com/locate/jsr

Prediction of drivers and pedestrians' behaviors at signalized mid-block Danish offset crosswalks using Bayesian networks Boniphace Kutela, a,⁎ Hualiang Teng b a

Department of Civil and Environmental Engineering and Construction, University of Nevada, Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV 89154-4015, United States USDOT Railroad University Transportation Center, Commissioner, Nevada High Speed Rail Authority, Director, Railroad, High Speed Rail and Transit Initiative, Department of Civil and Environmental Engineering and Construction, University of Nevada, Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV 89154-4015, United States

b

a r t i c l e

i n f o

Article history: Received 19 September 2018 Received in revised form 29 January 2019 Accepted 28 February 2019 Available online 9 March 2019 Keywords: Drivers yielding compliance Pedestrians' behaviors Bayesian networks

a b s t r a c t Introduction: This study presents the prediction of driver yielding compliance and pedestrian tendencies to press pushbuttons at signalized mid-block Danish offset crosswalks. Method: It applies Bayesian Networks (BNs) analysis, which is basically a graphical non-functional form model, on observational survey data collected from five signalized crosswalks in Las Vegas, Nevada. The BNs structures were learnt from the data by the application of several score functions. By considering prediction accuracy and the Area under the Receiver Operating Characteristic (ROC) curves, the BN learnt using the Bayesian Information Criterion (BIC) score resulted as the best network structure, compared to the ones learnt using K2 and the Akaike Information Criterion (AIC). The BIC scorebased structure was then used for parameter learning and probabilistic inference. Results: Results show that, when considering an individual scenario, the highest predicted yielding compliance (81%) is attained when pedestrians arrive at the crosswalk while the flashes are active, whereas the lowest predicted yielding compliance (23.4%) is observed when the pedestrians cross between the yield line and advanced pedestrian crosswalk sign. On the other hand, crossing within marked stripes, approaching the crosswalk from the near side of the pushbutton pole, inactive flashing lights, and being the first to arrive at the crosswalk result in relatively high-predicted probabilities of pedestrians pressing pushbutton. Furthermore, with a combination of scenarios, the maximum achievable predicted yielding probability is 87.5%, while that of pressing the button was 96.3%. Practical applications: Traffic engineers and planners may use these findings to improve the safety of crosswalk users. © 2019. National Safety Council and Elsevier Ltd. All rights reserved.

1. Introduction The risk of fatal crash involvement is observed to be higher for pedestrians and bicyclists than vehicle occupants. In fact, general traffic safety statistics in the United States revealed a decline of fatalities by 18% for a period of 10 years (2006–2015), although pedestrian and bicyclist fatalities increased by about 12% and 6%, respectively, for the same period (Highway Traffic Safety Administration, 2014; Pedestrian and Bicyclist Crash Statistics, 2017). Of all states, Nevada is ranked number 3, with a pedestrian fatality rate of 2.47 fatalities per 100,000 people. As the most populated city in Nevada, Las Vegas has experienced escalating pedestrian and bicyclist fatality rates for the past seven years, and the forecast projects even more fatalities in the next years (Wright, 2017). The lives of pedestrian and bicyclists are more imperiled when there is unsafe interaction between them and drivers. To separate such interaction, signalized or un-signalized crosswalks, which are found to improve pedestrian safety (Highway Traffic Safety ⁎ Corresponding author. E-mail addresses: [email protected] (B. Kutela), [email protected] (H. Teng).

https://doi.org/10.1016/j.jsr.2019.02.008 0022-4375/© 2019. National Safety Council and Elsevier Ltd. All rights reserved.

Administration, 2014), have been provided at intersections or midblock locations. For signalized crosswalks, various forms of lighting signals have been considered; however, the Overhead Flashing Beacons (OFBs), Circular Rapid Flashing Beacons (CRFBs), and Rectangular Rapid Flashing Beacons (RRFBs) (Pécheux, Bauer, & Mcleod, 2009; Shurbutt & Van Houten, 2010) are the most common in the United States. The communication between pedestrians and drivers at a signalized crosswalk is channeled through warning lights, which most of the time need to be actuated by using a pushbutton. The objective of this study is to model the behaviors of pedestrians and drivers at signalized crosswalks using the Bayesian Networks approach. Specifically, this study estimates the probabilistic association between various crosswalk and traffic characteristics, drivers yielding compliance, and pedestrians' tendency to press a pushbutton. The study uses observational survey data collected from five signalized Danish offset mid-block crosswalks equipped with OFBs, CRFBs, and RRFBs located on two major arterials in Las Vegas, Nevada. Contrary to most of the previous studies, which evaluated the yielding compliance using parametric approach, this study applies the Bayesian Networks, which is a probabilistic approach that allows simultaneous evaluation of both drivers' and pedestrians' behaviors. Through BNs, the

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probabilistic prediction of yielding compliance of drivers to pedestrians, as well as the probability of the pedestrian pushing a flashing light button at a crosswalk, are evaluated. This study attempts to answer prediction questions about crosswalks equipped with OFBs, CRFBs, and RRFBs. For instance, given the pedestrian has activated the lights, what is the likelihood that the driver(s) will yield? Moreover, given the prevailing traffic flow conditions, what is the probability that a pedestrian will activate the warning lights? To the authors' best knowledge, no study has attempted to answer such questions using the methodology applied in this study. The rest of the paper is organized as follows: the literature review from previous studies is first presented; followed by the methodology and discussion of the results; finally, the conclusion is drawn and recommendations are provided. 2. Literature review Although various signalizations have been implemented at the crosswalks, the RRFBs, CRFBs, and OFBs are the most recent and widely applied. In assessing their performance, researchers have focused on the interaction between the pedestrians and drivers. Regardless of the methodological approach, the concentration has been on driver yielding behaviors and pedestrian activation of warning lights. In general, researchers have come to an agreement that regardless of the type of flashing lights at the crosswalk, a dependency exists between the yielding tendency and lighting activations (Al-Kaisy, Miyake, Staszcuk, & Scharf, 2016; Fitzpatrick, Potts, Brewer, & Avelar, 2015; Hunter, Srinivasan, & Martell, 2012; Shurbutt & Van Houten, 2010). Although researchers indicate that there is an increase in the driver yielding rate when the crosswalk lights are activated, findings among researchers deviate significantly. For example, Hunter et al. (2012) in St. Petersburg, Florida reported a 54% yielding rate after installation of RRFBs, while Ross, Serpico, and Lewis (2011) in Bend, Oregon, with 211 crossings incidents at three crosswalks, reported an average of 84.3% yielding tendency after installation of an RRFB. As high as a 92% yielding rate was observed when the RRFB was activated, while as low as 45% was reported when the RRFB was not activated (Foster, Monsere, & Carlos, 2014) on a five-lane arterial with a 35 mph speed limit in Portland, Oregon. The linear mixture model developed by Potts et al. (2015) showed that an activated RRFBs or CRFBs results in 3.68 more yielding likeliness compared to when not activated. The dependency between lighting activation and yielding tendency pleads for another question to be asked by researchers about how often pedestrians press the pushbuttons. In an attempt to answer that question, a study by Levelt (1992) in Toulouse, France which reported as low as 18% pushbutton attempts at a crosswalk, was among the early studies focused on this matter. A higher activation rate was observed at an intersection by Foster et al. (2014) in Portland, Oregon; however, the rate depended on the state of incoming traffic. Their study noted that 160 out of 170 pedestrians (92%) pressed the pushbutton when there were incoming vehicles, while when there was no oncoming traffic 13 out of 18 pedestrians did. The low rate of pushbutton use has called for improvements in pushbutton position (Al-Kaisy et al., 2016) and design (Huang & Zeegar, 2001). However, Huang and Zeegar (2001) revealed that even design improvement by illuminating the pushbutton did not improve the activation tendency, as pressing tendency declined from 16.9% to 12.7% in Windsor, Ontario. In modeling driver and pedestrian behaviors at signalized crosswalks, most of the previous studies used binary logistic regressions (Fitzpatrick, Brewer, & Avelar, 2014; Kim, Brunner, & Yamashita, 2008; Potts et al., 2015; Rosenbloom, 2009). However, literature suggests that Bayesian Networks (BNs) perform either the same or better than logistic regressions (Lee, Abbott, & Johantgen, 2005; Witteveen et al., 2018; Zhang et al., 2016). Contrary to logistic regressions, BNs do not require a specific function form in presenting the probabilistic relationship between a set of random variables. They are graphical models, with nodes that represent the random variables and arcs representing

the relationships. The BNs relax the statistical assumptions such as linearity and additivity, which are more complex in logistic regressions (Lee et al., 2005). Such a relaxation enables BNs to capture the complex relationship between the variables (Zhang et al., 2016) and produce models with better performance. The BNs approach is relatively new in transportation research. It has been applied in studies related to traffic congestion, safety, and route choices (Kidando, Moses, Sando, & Ozguven, 2018; Kim & Wang, 2016). It is apparent that researchers have attempted to explain the interactions between drivers and pedestrians at signalized crosswalks. However, the probabilistic relationship between the two has not been explored extensively, especially when driver actions and crosswalk user actions have to be predicted simultaneously. This is, linking pushbutton activation, yielding compliance and other external factors simultaneously. These relationships can be probabilistically explained by using different approaches, Bayesian Networks (BNs) being one of the approaches. 3. Methodology This section avails detailed information about the study locations, data collection strategies, Bayesian Networks (BNs) structure learning, as well as parameter learning form the collected data. 3.1. Study setting and design This study involved five signalized Danish offset midblock crosswalks that have dissimilar characteristics. The land use areas where the crosswalks are located include residential, commercial, and education institution (University), while the warning lights include the OFBs, RRFBs, and the combination of the two (CRFBs & RRFBs). Four of the crosswalks are located on Maryland Parkway, while the fifth is on Charleston Boulevard. Both roadways are observed to have high pedestrian activities; Maryland Parkway being the second to Las Vegas Boulevard for pedestrian activities (RTC, 2017). Regardless of the location and warning type, each crosswalk is a Danish offset type (Fig. 1), with six lanes (three in each direction), low variability Annual Average Daily Traffic (27,000–29,000 vpd on Maryland Pkwy and 33,000 vpd on Charleston), and similar speed limits (30–35 mph) (NDOT, 2014). Therefore, the influence of these factors to pedestrian and driver interactions is assumed to be uniform for all sites. To evaluate driver and pedestrian interactions, first, the effective crosswalk area was defined, and the distinct crossing zones were identified. For this study, the effective crosswalk area is defined as the distance between two advance pedestrian crosswalk signs. The effective crosswalk area is then subdivided into three zones: Zones “a,” “b,” and “c.” Zone “a” was the marked stripes, zone “b” was the distance between the marked strips and yield line, while zone “c” was defined as the distance between the yield line and advanced pedestrian crossing sign. The lengths of these zones vary per crosswalk: zone “a” varies between 12 and 15 ft., zone “b” spans between 25 and 40 ft., while zone “c” ranges between 150 and 360 ft. Second, the researchers defined the “yielding” scenarios. For this study, drivers were considered yielded to pedestrians if they stopped or reduced speed within 5 s from the moment a pedestrian requested to cross by either pushing a button or waiting at the sidewalk. The basis for the 5 s assumption was on the perception reaction time of 2.5 s, provided by the AASHTO (2001), and an additional buffer of 2 s. 3.2. Data collection and descriptive statistics Data collection were performed for 33 days within a six-month period (January–May 2017) using printed spreadsheets. Each site received two rounds of data collection per day, each round spanned for 1 h. During data collection, different times of the day were considered for different purposes, such as time to go to work, lunch time, low visibility

B. Kutela, H. Teng / Journal of Safety Research 69 (2019) 75–83

77

(a) Typical Danish offset crosswalk(FHWA 2013) Designated pedestrians’ path

Advanced pedestrian crossing sign (APCS) Yi eld lin e

Yi eld lin e

Vehicular traffic flow

c

Vehicular traffic flow

Raised median a

b

Advanced pedestrian crossing sign (APCS)

b

c

(b) Defined zones within Danish offset crosswalk(Kutela and Teng 2018) Fig. 1. Defined pedestrian crossing zones at a typical Danish crosswalk (FHWA, 2013; Kutela and Teng, 2018).

(night) time, etc. The times for data collection were; morning (7:00 a.m.–11:00 a.m.), afternoon (12:00 p.m.–2:00 p.m.), evening (3:00 p.m.–6:00 p.m.), and night (7:00 p.m.–9:00 p.m.). The data collection were on an alternate basis; this is to say, if data collection were performed at one site in the morning, the same site was revisited in the evening or night of the same day. A total of 5041 observations were collected. The site with minimum observation was Charleston and 11th street with 666, while 1411 was the maximum number of observations at one site, Maryland and Del Mar. Other sites with their respective observations are Maryland & Reno (1053), Maryland & University (1216), and Maryland & Dumont (695), making a total of 5041 observations. Several variables of interest were recorded during data collection. Table 1 presents the descriptive statistics of the variables of interest that were used in this study. It can be observed from this that about 65% of the drivers yielded to pedestrians, while 56% of pedestrians pressed the button to activate the warning lights. 3.3. Bayesian Networks (BNs) As described earlier, BNs do not require a specific function form, but a graphical model that consists of nodes that represent random variables and arcs representing variables relationship. The tail side of the arc defines the “parent” node, while the arc's head is the “child” node (Markov & Russell, 2007). The Markov property defines the relationship between the parent and the child node; this property states that every random variable Xi has a direct dependence on its parents ΠXi (Korb & Nicholson, 2004), which for discrete variables can be written as:

is referred as Directed Acyclic Graphs (DAGs). Two optimization search based algorithms: score-based (SB) and constraint-based (CB), have widely been implemented in structure learning (Korb & Nicholson, 2004). The CB algorithms use hypothesis tests such as chi-square, to evaluate independence of the nodes (Korb & Nicholson, 2004). The CB-based algorithms are faster than the score-based algorithms, but are less favored since they are prone to locating wrong directions of

Table 1 Variables used in the Bayesian Network model. Variable name

Abbreviation Category

Count Percent

Drivers behavior Yield compliance

m_yield

Yielded Did not yield

3256 1785

64.6% 35.4%

Pedestrian Bicyclist Pressed Did not press Approaching from far side Approaching from near side First to arrive Not first to arrive Within marked strip Between strip and yield line Between yield line and APCS One person Two people Three or more people

4841 200 2824 2217 1580

96.0% 4.0% 56.0% 44.0% 31.3%

3461

68.7%

4098 943 3605 993

81.3% 18.7% 71.5% 19.7%

443

8.8%

4031 759 251

80.0% 15.1% 5.0%

2964 666 1411 341 4700 1316 3735 3415 1626

58.8% 13.2% 28.0% 6.8% 93.2% 28.5% 71.5% 66.5% 33.5%

Pedestrians' traits and actions Pedestrian type ped Pushbutton pressing

pressed

Approaching side

far_side

Arrival sequence

first_arrive

Crossing zone

zone

Number crossing

P ðX 1 …::…:X n Þ ¼

n Y

P ðX i jΠXi Þ

ð1Þ

i¼1

In performing a BNs analysis, two main sequential steps are crucial; structure learning and parameter learning (Wu, et al., 2014). The BNs structure can be found manually if the analyst has the knowledge of the dependencies of the variables (Kim & Wang, 2016); alternatively, learning the structure from the set of data is an available option (Demiroluk et al., 2014). Regardless of the learning option used, no cycle should be introduced when nodes are connected; this condition

numb_cat

Infrastructure and traffic characteristics Treatment type flash_type OFB RRFB CRFB & RRFB Incoming vehicles no_veh Absent Present Warning lights status flashing Already flashing Not flashing Traffic lights grn_lights Green lights downstream Red lights

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the arcs. In contrast, score-based algorithms evaluate all possible DAGs to determine the best available DAG given the objective functions, which is referred to as the scoring functions (SFs). In determining the best attainable DAG, the score based algorithm may use either Bayesian Information Criterion (BIC), Akaike Information Criterion (AIC), or Kfold cross-validation among others (Korb & Nicholson, 2004); the structure with a low score is preferred. For the AIC, BIC and K2 of the Bayesian Networks structure (S), given data (D) can be expressed as (De Campos, 2006; Liu, Malone, & Yuan, 2012): AIC ðS=DÞ ¼ −2 log likelihood þ 2 number of parameters

ð2Þ

BIC ¼ ln ð#of observationsÞ  numberof parameters−2 maximum likelihood

ð3Þ

    K2Score X i ; Ss; D ¼ log S2s; D qi n X X 4 þ i¼1

j¼1

ðr i −1Þ!  log  Nij þ r i −1 !

! þ

ri X

!3 log Nijk ! 5 



k¼1

ð4Þ

The log likelihood is defined as:   X n X N   S ¼ LL log P Dij =PAij D i j

ð5Þ

where Dij is the number of observations Xi in data Dj, and PAij is the number of instances of Xi's parents in Dj. Ss is the BNs structure, D is the data, Nijk is the number of instances in the dataset, n is the number of discrete variables in the BNs structure, ri is the number of values of the attribute Xi,qi = the number of possible values of its parent Pa(Xi) attribute, and Nij is the number of instances in which attributes Xi with its parents j. When the structure is completely determined, parameter learning, which is basically the estimation of the Conditional Probability Distribution (CPD) of the variables, can then be performed given the dataset. The Maximum Likelihood (ML) approach is preferred for parameter learning due to its ease of implementation, compared to the Bayesian approach which requires some prior knowledge (De Campos, 2006; Koller & Friedman, 2009). Once both structure learning and parameter learning have been performed, the predictive inference can be performed. The predictive inference involves computing the posterior probability of a variable X (event) given evidence (e) P(X/e). The BNs performance was assessed by using receiver operating characteristics (ROCs) and prediction accuracy (Goutte & Gaussier, 2005). The ROC is the graphical approach that provide the tradeoff between the sensitivity (true positive rate) and specificity (1-true positive rate; Fawcett, 2006). The area under the ROC curve (AUC) is the easily interpretable part of the ROC. The perfect model has the AUC equals to 1, thus, the model with AUC that is close to 1 implies the better the model performance. On the other hand, the perfect model has a prediction accuracy equal to 100%, the closer to 100% the prediction accuracy, the better the model. The entire analysis was performed in R version 3.5.1 environment (R Core Team, 2018). Several packages were using for analysis, the bnlearn (Scutari, 2010) was used for BNs structure and parameter learning. Other packages include, caret (Kuhn, 2017) and pROC package (Robin et al., 2018) which were used for prediction accuracy and the AUCs computations respectively. To perform the prediction, data were divided into two portions whereby 60% of the data were used for model training purpose and 40% was used for model testing. Finally, the entire dataset was used to build a model that was used for prediction inference.

4. Results discussion 4.1. Models' performance comparison The BNs structures were found by using a score-based algorithm, whereby AIC, BIC, and K2 scores were applied to determine the best structure. It was found that the network learnt using BIC (Fig. 2) had the highest average prediction accuracy (77.8%). The model performed slightly better for predicting pedestrian pressing pushbutton (79.4%) than driver yielding compliance (76.2%). The AIC and K2-based models had average prediction accuracies of 69% and 71.8%, respectively. Considering the ROCs (Fig. 3), the BIC based model outperformed the AIC and K2 based models. It can be observed that the BN structure found using the BIC score has the highest AUC for pedestrian pressing pushbutton (0.859), as well as for driver yielding compliance (0.8112). The lowest AUC was 0.3537, which was from the BN structure found using the K2 score. The AIC score-based BN structure had a relatively high AUC (0.8179) for pressing pushbutton, but a relatively low AUC (0.5) for motorist yielding. In this study, the BN model aims at predicting both yielding and pressing pushbutton. Therefore, the model with the highest average prediction accuracy and highest average AUC was considered for the parameter estimations. This is, the BN found by the BIC score (Fig. 2). The parameters of the BNs, which is the conditional probability table (CPT) for each node, were found from the dataset with 5041 observations, using the BNs structure retrieved by the BIC scoring function (Fig. 2) with the application of the Maximum likelihood (ML). Although the BNs provide the parameters of all the nodes available in the structure, this study is interested in the “hypothesis nodes.” These are nodes that have a direct dependence on drivers' yielding compliance (m_yield) and pedestrians' actions toward the pushbutton (pressed). Therefore, in querying probabilities for yielding the child node was “m_yield,” while for pushbutton pressing the child node was “pressed” (Fig. 2). The prediction inference presents the evaluated individual scenario and a combination of scenarios to the probability of drivers to yield or pedestrians to press the pushbutton. In addition, the prediction inference results present the magnitude of the impact of the given scenario compared to the competing scenario(s). The next segment discusses in detail the prediction inferences for yielding and button pressing. 4.2. Prediction inference The prediction inference involves valuing the probability of the occurrence of an event given a set of evidence. Here the evidence is defined as something that has been observed (e.g., active warning lights), while an event is the impact of the observed evidence (e.g., drivers' yielding). Then, the prediction of drivers to yield can be expressed as: P ð Yield ¼ ?j evidence ¼ iÞ

ð6Þ

Whereby i is a scenario of a given variable (e.g., green lights scenario for traffic lights downstream). To perform this analysis, a set of hypothesis variables (evidences) are linked to an event, the query set up is such that the prevailing roadway characteristics, traffic flow, and human traits are assumed to be observed, while the probability of yielding and button pressing are to be determined through querying. In addition, a sensitivity analysis is performed to evaluate the impact of scenario change in the same variable. The sensitivity analysis can be expressed as: Sensitivity value ¼ P ðYield ¼ ?j evidence ¼ iÞ−P ðYield ¼ ?jevidence≠iÞ

ð7Þ

B. Kutela, H. Teng / Journal of Safety Research 69 (2019) 75–83

79

Fig. 2. BIC-based network structure.

compared to when the button was not pressed. This finding suggests that, provision of automatic detectors that trigger the lights after detecting crossing pedestrians would increase the yielding compliance up to 20.9%, holding other factors. Additionally, the predicted yielding probabilities, due to traffic lights status and number of pedestrians crossing, were relatively high with small sensitivity values.

The sensitivity analysis is one of the strengths of the BNs analysis over the other methods. Typical questions to be answered are, given the warning lights are active and inactive, what is the change in probability of yielding? The query for all the evidence was performed and results were presented in Table 2. Focusing on the probability of drivers to yield, results in Table 2 revealed that crossing zones, warning light status, pushbutton pressing, and treatment type not only have relatively high magnitudes of predicted probabilities, but also high sensitivity values. For instance, the predicted yielding probability if the pedestrians observed to cross through the marked strips is 70.6%. However, if they cross between the yield line and APCS this probability falls to 23.4%, making a 47.2% sensitivity value. Therefore, encouraging pedestrians and bicyclists to properly use the crosswalks would extensively raise the yielding compliance. The maximum predicted yielding probability (81.1%) is observed when the flashing lights are active at the moment pedestrians arrive at the crosswalk. This variable has a relatively high sensitivity value (25.7%). Drivers are predicted to have a higher yield compliance in the presence of CRFB & RRFB combined than either OFB or RRFB only. The comparison between the predicted probabilities in the presence of OFB only and RRFB only shows that the predicted probability for RRFB (50.7%) is lower than that of OFB by 8.6%. This finding is contrary to most previous studies (Fitzpatrick et al., 2015; Shurbutt & Van Houten, 2010). To add to the list, the probability of yielding, given the pedestrians pressed a pushbutton, is 72.1%, which is higher by 20.9%,

- Implies no direct dependence, base is the base scenario used for comparison

Compared to the predicted yielding probabilities, the probabilities to press the pushbutton, given the same evidence in crossing zones, are relatively small but have high sensitivity values. The predicted probability to press the button, given that the pedestrians were observed to cross within the marked stripes, is found to be 67.8%, which is higher by 65%, compared to when the pedestrians or bicyclists are observed to cross between yield line and APCS (2.8%). Also, if pedestrians crossing between marked stripes and yield lines was observed, the predicted probability to press the button declined to 31.9%; this is a 36% difference from the predicted probability of the same if the pedestrian crossing through the marked strip was observed. The arrival sequence difference resulted into about a 45% difference in predicted probabilities to press the button. The person who is first to arrive at the crosswalk is expected to have a 63.0% chance to press the button. The warning lights status at

1.00

Scores

0.75 Sensitivity

AIC-Pressed, AUC = 0.8179 AIC-Yield, AUC = 0.5 BIC-Pressed, AUC = 0.859

0.50

BIC-Yield, AUC = 0.8112 K2-Pressed, AUC = 0.7495

0.25

K2-Yield, AUC = 0.6463

0.00 0.00

0.25

0.50 1-Specificity

0.75

1.00

Fig. 3. Receiver Operating Characteristic (ROC).

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Table 2 Predicted probability for yielding and button pressing. Variable

Observed evidence

Predicted probabilities Yield

Crossing zone

Warning lights status Traffic lights downstream Number crossing

Pushbutton pressing Treatment type

Pedestrian type Incoming vehicles Approaching side

Arrival sequence

Within marked strip Between strip and yield line Between yield line and APCS Already flashing Not flashing Green lights Red lights One person Two people Three or more people Pressed Did not press OFB RRFB CRFB & RRFB Pedestrian Bicyclist Absent Present Approaching from far side Approaching from near side First to arrive Not first to arrive

Table 3 Predicted probabilities for combined scenarios.

Sensitivity Press

(a) Predicted yielding probabilities Sensitivity

sn

Number crossing

Crossing zone

Already flashing

Traffic lights

Yielded

67.8% base 31.9% −36.0%

Treatment type

Pressed

70.6% base 51.0% −19.6%

1

No

Yes

Red

96.3%

2.8%

−65.0%

2

Zone “a”

Yes

No

Red

95.7%

81.1% 55.4% 59.7% 67.5% 61.6% 64.9% 67.8%

base −25.7% base 7.9% base 3.3% 6.2%

28.4% 63.7% – – – – –

base 35.3% – – – – –

3

Zone “b”

No

Yes

Red

94.7%

Zone “a”

No

No

Red

94.7%

Zone “a”

Yes

No

Red

93.2%

Zone “a”

Yes

Yes

Red

90.5%

72.1% 51.2% 59.3% 50.7% 75.0% – – – – –

base −20.9% base −8.6% 15.6% – – – – –

– – – – – 56.2% 39.2% 46.2% 55.7% 36.4%

– – – – – base −17.0% base 9.5% base

One person Three or more Two people Two people Two people Two people One person One person One person One person

Zone “a”

23.4% −47.2%

CRFB &RRFB CRFB &RRFB OFB

Zone “a”

No

Yes

Green

90.5%

Zone “a”

Yes

Yes

Green

89.9%

Zone “c”

No

Yes

Red

88.7%

Zone “b”

No

Yes

Green

88.2%

–

63.8% 27.4%

– –

– –

63.0% base 18.1% −44.9%

Already flashing No No No No No Yes No Yes No No

Far side No No Yes Yes No No No Yes No No

Pressed

–

the moment the crosswalk user arrives at the crosswalk revealed that if the flashes are active at that moment, the probability that the button will be pressed is 28.4%, while when the flashes are inactive, the probability rises to 63.7 making a 35.3% difference. The 27.4% sensitivity value was observed when the approaching side was considered. In this case, when pedestrians approaching the crosswalk from the near side was observed, the probability of pressing the pushbutton was estimated at 63.8%, compared to 36.4% when the pedestrians approached the crosswalk from the far side of the pushbutton. This observation is very important to practitioners, as proper location of the pushbutton pole would improve yielding compliance up to 27%, given that other factors are kept constant. The analysis results also reveal that, if the person is a pedestrian, the probability of pushing the button is predicted to be 56.2% compared to 39.2% when the observed person is a bicyclist. Also, the absence and presence of incoming traffic accounted for only a 9.5% difference in the predicted probabilities of pushing the button, whereby the presence of the incoming traffic resulted in a high (55.7%) predicted probability. In addition to assessing the influence of the individual factor of drivers' yielding and pedestrians' button pressing, presented in Table 3, the impact of concurrent scenarios was assessed. There are situations in which multiple scenarios coexist at the same time. For instance, one might be interested in determining the likelihood of drivers yielding given that two pedestrians who did not press the pushbutton are crossing between marked stripes and the yield line in a crosswalk equipped with an OFB while the warning flashes are inactive, and the traffic lights downstream are green. Such a query can be performed by constructing a joint probability of the event given the scenarios to be tested. Table 3 shows the top 10 combinations of scenarios that results in the highest likelihood of driver yielding compliance as well as pedestrians and bicyclists pushing button. With the combination of scenarios, the maximum possible driver yielding compliance of about 96.3% can be attained. This maximum yielding compliance is expected when the following evidence exist: the treatment type is CRFB & RRFB, whereby one person who did not press the pushbutton is crossing through the marked stripes while the flashes were already active, and the traffic

4 5 6 7 8 9

CRFB &RRFB OFB CRFB &RRFB CRFB &RRFB CRFB &RRFB OFB

10 OFB

(b) Predicted pushbutton pressing probabilities First to Incoming sn Ped/bike Crossing zone arrive traffic 1 Ped Zone “a” Yes Yes 2 Bike Zone “a” Yes Yes 3 Ped Zone “a” Yes Yes 4 Bike Zone “a” Yes Yes 5 Ped Zone “a” Yes No 6 Ped Zone “a” Yes Yes 7 Ped Zone “a” No No 8 Ped Zone “a” Yes No 9 Ped Zone “b” Yes Yes 10 Bike Zone “a” No Yes

87.5% 72.2% 70.1% 68.7% 68.6% 64.3% 63.0% 58.8% 51.5% 50.0%

lights downstream are red. Otherwise, a 87.5% chance of button pressing can be reached if a pedestrian who approaches the crosswalk from the near side of the pushbutton is first to arrive at a crosswalk whose warning lights are inactive while there is an incoming traffic and crosses through the marked stripes. There is a trend that can be established. For instance, the top yielding compliance scenarios show that among 10 observations presented, the following scenarios appear most frequently: Crossing zone = Zone a, already flashing = Yes and, Traffic lights = Red. In contrast, the following scenarios are observed to be dominant for button pressing tendency: driver type = pedestrian, crossing zone = Zone a, first to arrive = Yes, already flashing = No, Far side = No. Therefore, to have the maximum possible yielding compliance and button pressing tendency, the combination of scenarios that are practically possible should be maintained. The strength of association between a given scenario and an event (yielding) was further evaluated using the odds ratio. The odds of occurrence of an event is defined as the ratio of the probability of occurrence of an event and no occurrence of the same event. The ratio of the odds, known as the “odds ratio” (OR), denotes the odds that an event or outcome will occur given a particular exposure exists, compared to the occurrence of the same event given the exposure not existing (Szumilas, 2010). Although the OR is a good measure of association between an exposure and an event, it is highly skewed, and it is difficult to compare the association within 0 b OR b 1 and OR N 1. The logarithm of the odds ratio (logOR) that converts the scale into negative and positive is preferred (Kim & Wang, 2016). Its interpretation is straightforward: if the logOR is greater than zero, then having a given scenario is associated with the event, while the logOR less than zero implies that having that scenario translates into a less likely occurrence of that event. The logarithms of odds ratios for various scenarios were computed and

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No incoming vehicle Pedestrian

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Push button pressing Yielding compliance

First to arrive Approaching from far side Comparable scenarios

CRFB & RRFB RRFB OFB Pressed button Three or more people crossing Two people crossing One person crossing Green lights at the intersection Already flashing Cross between yield line and APCS Cross between strip and yield line Within marked strip -4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

Log of odds raio Fig. 4. Logarithm of odds ratios for yielding and pushing button.

presented in Fig. 4. It can be observed that crossing between the yield line and APCS has the highest negative logOR for yielding compliance, which means that drivers are far less likely to yield to people crossing in this zone. By comparison, crossing within the marked stripes (1.34) and active flashing (1.35) have relatively equal logOR and are highly associated with yielding compliance. Other notable exposures that are shown to have positive impact on yielding are the combined CRFB & RRFB treatment and pushbutton pressing. Conversely, in the order of decreasing magnitude of positive impact, crossing within strip, first to arrive, and pedestrian as a type of user are associated with increase in yielding; whereas, crossing between the strip and yield line, absence of incoming vehicular traffic, approaching from far side of a pushbutton, arriving while flashes already flashing, and crossing between yield line and APCS have shown not to favor the pressing of a pushbutton. 5. Conclusion and recommendations This study presented the probabilistic prediction inference of driver yielding compliance and pedestrian tendency of pressing a pushbutton at a mid-block signalized crosswalk. The study applied the Bayesian Networks analysis on the observational survey data collected for a period of 33 days from five Danish offset crosswalks located in Las Vegas, Nevada. The descriptive analysis was first performed, which revealed that the average yielding compliance for drivers in the five crosswalks was 64.6%, while 56% of the pedestrians and bicyclists pressed a pushbutton to activate the warning lights. The Bayesian Networks analysis was then applied to estimate/determine the relationship between the variables. The BN structure was learnt from the data by application of three score function criteria; AIC, BIC, and K2, with a 5% rejection significance level. The BIC-based network was found to be the best network structure by considering the prediction accuracy and the AUC. The parameter learning was performed followed by prediction inferences, which involved the parent nodes that are directly linked to the child node of interest. The prediction inference results revealed that active warning lights was the single main scenario that would result in the highest predicted probability of drivers to yield. The predicted yielding probability, given that the flashes were active when the driver arrived at the crosswalk, was found to be 81.1%. Other notable scenarios with their

accompanying predicted probabilities are: the presence of CRFB & RRFB treatment type (75%); when pedestrians pressed a pushbutton while the lights were inactive (72%); and pedestrians and bicyclists crossing in the marked stripes (70.6%). Further, the sensitivity of yielding predicted probabilities shows that the highest drop (47.2%) in predicted yielding probability is observed when two crossing zones (crossing within marked stripes, and between the yield line and advanced pedestrian crossing sign) scenarios are compared. About a 26% increase in predicted yielding probability was observed when the flashing lights were active when a driver arrived at the crosswalk compared to when they were inactive. Also, about a 21% increase in yielding compliance was observed when pedestrians or bicyclists activated the warning light if they arrived while lights were inactive. Overall, the maximum attainable yielding compliance for a given set of combination scenarios was found to be 96.3%. Furthermore, the logarithm of the odds ratio results shows that the log odds of drivers to yield when the lights are active is 1.35, while the one for the crosswalk users crossing through the marked stripes is 1.34. Contrary to that, the logOR for a driver to yield when pedestrians are crossing between the yield line and advanced pedestrian crossing sign is −1.59. On the other hand, four scenarios resulted in relatively high predicted probabilities for pedestrians to press the pushbutton. These scenarios are; crossing within marked stripes (67.8%); approaching the crosswalk from the near side of the pushbutton pole (63.8%); inactive flashing lights (63.7%); and the being first to arrive at the crosswalk (63.0%). The sensitivity analysis for this case revealed that the difference between the pedestrian crossing in two zones (within marked stripes and between the yield line and advanced pedestrian crossing sign) to be as high as 65%. Others worth mentioning include: the difference in arrival sequence (first to arrive and not first to arrive) (45%); crossing within marked stripes and between the yield line and marked stripes (36%); active and inactive flashes (35.3%); and the approaching side of the pushbutton pole (27.4%). The maximum achievable predicted probability given a combination of the scenarios was 87.5%. The crossing zone was shown to play very important role, as shown by the log of odds ratio. It was found that as high as a −3.5 log of odds ratio was observed when crosswalk users who crossed between the yield line and other crossing zones were compared. Contrarily, a 2.3 log of odds ratio was observed when the crosswalk users who crossed through the marked stripes were compared to the other zones.

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The findings from this study are important to practitioners as well as to the body of literature. This study provides another way of assessing behavior analyses of drivers and pedestrians at crosswalks and other similar locations that involve the interaction between pedestrians and drivers. Through linking the prevailing conditions at the location, the probabilities of an action to occur given the prevailing conditions can be deduced. The reversal action can also be performed; this is, given an action is observed, the chance that a certain scenario is the cause can also be deduced. Through this study, the quantified impact of locating the pushbutton on the side that is not as accessible to the pedestrians provides the practitioners an opportunity to perform a thorough pedestrian flow study before deciding where to locate the pushbutton. 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Network or Regression-Based Methods for Disease Discrimination: A Comparison Study. https://bmcmedresmethodol.biomedcentral.com/track/ pdf/10.1186/s12874-016-0207-2 (November 17, 2018). Boniphace Kutela is a graduate student in the Department of Civil and Environmental Engineering and Construction at University of Nevada Las Vegas (UNLV). He obtained his master's degree in Civil Engineering from Tennessee State University (TSU), and his bachelor's degree in Civil and Structural Engineering from the University of Dar es Salaam (UDSM) in Tanzania. His research interests are traffic safety and operations, human behavior in transportation engineering, shared mobility, application of machine learning and artificial intelligence in transportation engineering, connected and autonomous vehicles safety, and railroad network analysis. In addition, he has authored technical papers that have been published in professional journals and presented research at conferences. Hualiang Teng, a professor in Transportation Engineering at University of Nevada Las Vegas (UNLV), has about 30 years of research and education experience in Transportation Engineering and Management. He graduated from China's Beijing Jiaotong University with his BS and MS degrees in railroad engineering and management. He has a second MS

B. Kutela, H. Teng / Journal of Safety Research 69 (2019) 75–83 degree in railroad operations from West Virginia University, and a PhD in civil engineering from Purdue University. He is a Commissioner of Nevada High Speed Rail Authority, Director of U.S. DOT Railroad University Transportation Center, and Director of Railroad, High Speed Rail and Transit Initiative. Dr. Teng initiated and leads UNLV's railroad program, and he developed its railroad curriculum and certificate program. He oversees U.S. DOT Railroad University Transportation Center, for which he has been involved in research with federal and local agencies and organized distinguished seminars and conferences. In addition, he is the advisor for the university's American Railway Engineering and Maintenance-of-Way Association (AREMA) student chapter at UNLV. Dr. Teng, who is active in

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railroad professional activities, also is interested in intelligent transportation systems, infrastructure maintenance, air quality analysis, freight transportation, safety, and demand forecasting. In addition to UNLV, he has taught at Beijing Jiaotong University, Polytechnic University of New York (currently New York University) and the University of Virginia (UVA), and he served as associate director for the Center for Transportation Studies at UVA. So far, he has published about 40 peer reviewed technical papers in various international journals.