Effects of Pedestrians’ Assertiveness on Drivers’ Yielding Behavior at Mid-Block Sections: An Application of Bayesian Structural Equation Modeling

Abstract

Crossing roads at mid-block sections often creates ambiguity about priority between pedestrians and drivers, resulting in conflicts, road crashes, death, and human injury. To share the road space safely, they need to anticipate other user behaviors whilst maintaining and modifying their own habitual and desired maneuvers. This study investigates the effect of pedestrian assertive behaviors and vehicle user characteristics on driver yielding at mid-block sections. Road users’ interactions were observed in a dense mixed land use urban area of Central Auckland, New Zealand. Bayesian structural equation modeling is used to find interrelationships of multivariate data. The result shows that yielding levels decrease when the vehicle speed increases and they are not part of a platoon. Pedestrians’ direct signals (i.e., hand gestures) can increase drivers’ willingness to yield. Conversely, pedestrians, who tend to run or cross heedlessly through the traffic, are less likely to modify driver behavior in a high-speed environment. However, these factors are mediated through vehicle speed-related factors. Women are more likely to be given priority compared to men, especially when they have slow crossing speed. The study offers a better understanding of road users’ interactions outside controlled crossings. It provides evidence why it is important to reduce operating speeds in areas where there is a high demand for sharing between vehicles and vulnerable road users and mid-block crossings. Road users can be better informed to understand more gesture communication combined with appropriate engineering practice, such as traffic calming, and where appropriate re-prioritization of road space to influence drivers’ operating speeds.

Keywords

pedestrian gesture driver yielding behavior mid-block crossing human factors road safety vehicle speed transportation planning

Pedestrian and vehicle interactions in urban traffic environments are complex and inevitable. The result of these interactions can, in some cases, be more complex at mid-block sections than at formal road crossing sections, as drivers expect fewer interactions with pedestrians, and pedestrians can be less visible. Crossing the road at mid-block sections is less controlled, but in many ways, a necessity for people walking in built-up areas and often creates an increased risk of crash involvement and severity of the injury. In New Zealand, about 52% of reported urban pedestrians’ fatalities and serious injuries occur in mid-block locations. The main factors identified in these crashes include a combined effect of pedestrians crossing heedlessly through the traffic and drivers failing to give way and not noticing pedestrians ( 1 ).

To avoid a collision with pedestrians, drivers need to not only detect the pedestrians’ presence but also to recognize and predict whether they aim to cross the road, before reacting appropriately. Without traffic signs and signals, negotiating priority between the two parties largely involves informal and non-verbal cues ( 2 , 3 ). Pedestrians’ assertive behavior, such as walking briskly to the crossing ( 4 ), stepping into the roadway ( 5 , 6 ), and making eye contact or gestures ( 7 – 9 ), can capture driver attention and influence them to give way. However, while drivers need to anticipate and react to pedestrians’ behaviors, they also need to actively maintain their driving tasks and control maneuvers.

Past studies have revealed that speed-related factors are highly associated with driver willingness to yield ( 4 , 6 , 10 , 11 ). Drivers have a relatively short time to respond to unexpected events at mid-block sections even when they are driving at low speed. For congested roads and higher-speed environments, it is even more difficult for drivers to appropriately yield for pedestrians to safely cross. Complex urban street environments can also lead to drivers not seeing or recognizing pedestrians’ desire to cross on the side of the road, as they tend to have a narrower vision and focus on the center of the road ( 11 ). Impact speeds and road user injury are well recognized worldwide. There has been a global focus on low-speed urban street design and a re-prioritization toward active modes (which commonly refers to walking and cycling). In New Zealand, the speed limit of mixed urban center traffic roads and streets has been progressively reduced to “survivable conflict” speeds for pedestrians and cyclists ranging between 30 and 40 km/h, such as in school zones ( 12 ). However, this is not applied to all road types and the majority of urban roads in New Zealand are still dominated by an urban speed limit of 50 km/h. The current design approaches are if there is a high demand for pedestrians and crossings and a high crash risk at multiple mid-block locations, appropriate speed management, and the treatment of mid-block crossings. The considered treatments include the installation of a marked crosswalk (signalized or un-signalized), signage, and other measures (i.e., curb extensions and pedestrian platforms; also known as raised tables) ( 13 ). However, determining appropriate treatments is required to go beyond pedestrians’ demand. One of the ways is to gain more understanding of road user behaviors, which can help complement the current approaches to improve road safety outcomes for pedestrians, other vulnerable road users, and vehicle drivers.

Many studies have explored pedestrian and vehicle interactions. However, few studies have examined pedestrians’ assertive behavior and drivers’ yielding at mid-block sections, and they are mostly preliminary studies under low-speed environments. There is a limited understanding of whether pedestrians’ assertiveness plays a key role in drivers’ yielding when the vehicle speed is relatively high for an urban context. This paper investigates the relationship between pedestrians’ assertiveness and drivers’ yielding behavior at mid-block sections with a speed limit of 50 km/h, which governs the urban roads ( 14 – 16 ). The selected study locations are mid-block sections where pedestrians commonly wish to cross the road. The findings are expected to provide information about driver and pedestrian interaction in higher urban speed environments and possibly help to select appropriate speed zoning afterwards.

The following section provides an overview of key relevant findings from the literature.

Literature Review

Pedestrian Assertiveness and Visibility to the Drivers

Certain pedestrian cues and behaviors can increase drivers’ attention, make drivers aware of their presence, and prepare drivers to appropriately yield. Guéguen et al. ( 8 ) found that when pedestrians show explicit communication, such as making active eye contact with drivers in comparison to looking over their head, they are more likely to be given the priority. Gestures including extending an arm, raising an arm, and waving their hand also influence driver behaviors ( 11 , 17 ). However, establishing eye contact and negotiating priority can be difficult when vehicle speeds are high. A study by Dey and Terken ( 18 ) revealed that pedestrians do not particularly use gestures unless the expected behavior of vehicles is not met, for example, when drivers are expected to slow down but they do not.

Some studies have found that willingness to yield increases when pedestrians wait near the roadway or have already stepped out into the road carriageway ( 4 , 5 , 19 ). The possibility of yielding is even greater if they are crossing the centerline lane in multi-lane crossings rather than near curbside lanes ( 6 ) or are waiting at the median ( 20 ). One of the reasons is that pedestrians are more visible to the drivers and in a vulnerable position when they are far from the curb. Shaon et al. ( 11 ) revealed that the position of pedestrians in the traffic system is correlated to vehicle speed and yielding rate. Faster speeds lead to drivers not recognizing pedestrians waiting to cross behind the curbside. They tend to have a narrower vision and focus on the center of the road. Fast walking or darting into traffic are also found to encourage drivers to slow down or stop for pedestrians ( 4 , 11 ). In addition, drivers are more likely to yield if there are many pedestrians at the crossing ( 19 – 22 ). Large pedestrian groups not only increase pedestrian flows but tend to show more aggressive behavior because of a belief in safety in numbers. As a result, it causes drivers to swerve their driving path more than when a pedestrian is crossing alone ( 21 , 23 ). Considering pedestrian characteristics, some studies observed that drivers are more likely to yield to females, disabled body persons, or the elderly rather than the young, male, or people who seem not to be so vulnerable ( 5 , 23 ). It is suggested that the young and healthy adult pedestrians are usually capable of crossing and have more self-reliance than others. Studies by Goddard et al. ( 24 ) and Coughenour et al. ( 25 ) show that there may be racial bias in driver yielding behavior in the U.S.A., with minority (black) pedestrians experiencing more discrimination than white pedestrians by drivers at crosswalks. Previous studies show that pedestrian behaviors influence drivers’ yielding decisions, and there are specific informal gestures that can modify driver behavior positively or negatively in regard to crash risk. However, most studies have observed behaviors in a low-speed environment (e.g., <30 km/h). It is unclear whether they would react the same way when the urban operating speeds are higher (e.g., 50 km/h).

Vehicle Yielding Behavior

The opportunities for pedestrians to cross the road safely is not only based on their self-behavior but also on that of drivers. This is especially true at unprotected mid-block crossings where the yielding behavior can be negotiated. In many countries, including New Zealand, pedestrians are legally allowed to cross at mid-block sections if they are further than 25 m from protected pedestrian road crossings. There are also no specific rules for drivers to stop for pedestrians who are obviously waiting to cross outside pedestrian crossings ( 26 ). To a great extent, the safety of pedestrians highly depends on vehicular speeds ( 27 – 30 ). Several studies show that the yielding rate reduces significantly when the vehicle speed increases ( 4 , 10 , 19 ).

The position of vehicles in the traffic stream also affects vehicle speed and drivers’ yielding rate. Vehicles in a platoon generally maintain their position and maneuver because of the influence of other vehicles. When there are higher traffic volumes and congested conditions, the speed of platoon vehicles tends to be lower than that of non-platoon vehicles (free-flow speed). As a result, the probability of drivers willing to yield to pedestrians increases ( 9 ). However, other studies argued that the yielding rate reduces when vehicles are in platoons ( 4 ). Himanen and Kulmala ( 19 ) found that when the number of approaching vehicles increases, the probability of the first driver reacting decreases. In fact, a group of vehicles is less likely to yield compared to just one vehicle. Type of vehicle (car, truck, bus, etc.) is also observed to relate to drivers’ yielding rate. Drivers of passenger cars are more likely to yield than drivers of other vehicle types (trucks, vans, SUVs, etc.) ( 31 , 32 ). Willingness to yield is also related to the surrounding traffic environment. An example is when drivers enter courtesy crossings or raised platform crossing at mid-block sections. There is no legal obligation to yield, but they are forced to slow down their approaching speed by the road approach design (i.e., geometry, traffic islands, and lane marking). As a result, they are more likely to yield to pedestrians ( 33 ). Examples include curb extension and refuge islands to slow down approaching vehicles and consequently improve the visibility of users to each other ( 34 , 35 ).

Vehicle speeds determine the severity of crashes. When pedestrians and vehicles collide, pedestrians with no shell protection are far more at risk. The probability of pedestrians being killed significantly increases when impact speeds increase above 30 km/h ( 36 ). A high-speed environment not only gives less time for pedestrians to react but also limits drivers in providing a safe crossing for pedestrians. Increased speed results in a longer reaction time and therefore stopping distances to respond to unexpected events. An increase in the average speed of 1 km/h results in a 3% higher risk of a crash and a 4%–5% increase in fatalities ( 37 ). The protection of vulnerable road users through driver behavioral modification (i.e., speed limit and enforcement) has been reiterated in safe system and vision zero approaches ( 38 – 41 ), such as in Sweden, Switzerland, the U.K., the U.S.A., Canada, Australia, and New Zealand. These policies move toward a sustainable urban street design by prioritizing the safety and accessibility of people around city centers over vehicle mobility, especially for active transport modes. One fundamental principle is understanding that the human body has a limited ability to withstand crash forces. Speed design should therefore fit with the function and level of safety desired of the road. Although speed management can be achieved through design and enforcement, reducing the speed limit might not be applicable on roads with high throughput or those that are prioritized ( 38 ). As the urban form moves toward multimodal transport, understanding the interaction between road users may help advance transport policy and practice to reliably identify the relative risks to benefit the safety of all road users.

Structural Equation Modeling and Bayesian Structural Equation Modeling Applications

Previous studies used similar techniques to model the interaction between pedestrians and drivers. The most common are linear-separable models, such as logistic regression ( 4 , 6 , 8 , 10 , 19 , 22 , 33 ). This technique works well with a probabilistic view of class predictions, such as whether drivers will yield to pedestrians or not. However, it has limits when producing models that can capture the complex reality of pedestrian and driver behavior. Modeling human behavior also has a measurement error issue because an inherent behavior (latent variable) is hard to observe.

Structural equation modeling (SEM) and Bayesian structural equation modeling (B-SEM) are often employed to minimize such errors and capture the relationship of the multi-dimensional variables at the same time ( 42 , 43 ). For example, Sadia et al. ( 44 ) used three model levels to understand driver speed selection through a driving simulator. While the first model covered driver characteristics and speed, the additional model accounted for variables that vary from trip to trip and between road segments. Likewise, Hassan and Abdel-Aty ( 45 ) used SEM to simultaneously model drivers’ responses under reduced visibility conditions. Different scenarios with several visibility levels, traffic conditions, changeable message signs, and variable speed limit signs were designed. These studies show that SEM can handle complex relationships among variables and measurement errors where some variables can be unobserved. However, SEM often suffers from model misspecification to maintain the goodness of fit, especially with small samples. In many cases, some correlations are removed when the goodness of fit is below an acceptable standard. As a result, the models may not always explain the complex nature of the behavior as intended. This is where B-SEM comes in. B-SEM provides easily assessable statistics for goodness of fit and model comparison compared to standard SEM for small samples ( 42 , 43 , 46 ). The Markov chain Monte Carlo (MCMC) algorithms used in the Bayesian framework incorporate existing prior information about model parameters and accommodate the asymmetry of the empirical distribution.

To date, a few drivers’ behavioral studies have adopted B-SEM in an experimental design or questionnaire surveys. For example, Khazaei and Tareq ( 47 ) used B-SEM to determine the factors affecting the adoption of electric vehicles. Jie-Ling and Yuan-Chang ( 48 ) also used this technique to find influential factors in drink-driving behavior. These studies included both measured variables, such as driving experiences, drivers’ characteristics and vehicle type, and subjective factors, such as cultural norms and perceived behavioral control. The models proved practical and accurate to cope with model uncertainty for small and moderate samples and consequently provided valid results. To the authors’ knowledge, there are limited B-SEM studies in a naturalistic observation of the interaction between road users.

Methodology

Conceptual Model of Vehicle Yielding Behavior

The study focuses on an interaction between pedestrians’ assertiveness and drivers’ yielding behavior. Pedestrians are assumed to communicate to the drivers through direct and indirect signals. The causal relationship between the two parties is shown in Figure 1. We hypothesize that under this moderated speed environment, willingness to yield is not directly affected by pedestrians’ behavior but rather is moderated through vehicle speed. Three hypotheses include the following:

pedestrian assertiveness has a low impact on drivers’ yielding behavior under higher speeds;

drivers’ yielding behavior is higher when pedestrians are crossing from the median compared to pedestrians crossing from the curbsides;

the gender of pedestrians significantly affects driver yielding rates.

Figure 1.

Conceptual framework linking pedestrian assertive behavior to drivers’ yielding.

The measurement of pedestrians’ assertiveness and drivers’ yielding behavior are explained as follows.

Pedestrians’ Assertive Behavior

Eight types of pedestrians are identified as being assertive when they perform the following actions.

Run heedlessly through the traffic.

Dart into the traffic without waiting.

Clearly accelerate walking speed.

Use gestures, including extending their arm, raising their arm, and waving their hand.

Do not show hesitation or confusion (body gesture), such as stepping back and forth or changing direction.

Establish eye contact or gaze at oncoming traffic through head orientation.

Step into the roadway while waiting (both at the curbside and the median). Those who wait behind the curbside, regardless of the distance between the curb and their position, were considered to be exhibiting non-assertive behavior.

Are a part of a group.

Drivers’ Yielding Behavior

The dependent variable is whether drivers are willing to yield to pedestrians. Driver yielding is classified based on the studies by Harrell ( 5 ), Schroeder and Rouphail ( 4 ), and Shaon et al. ( 11 ). Drivers are identified as “not yield” (NY) if they do not stop for pedestrians. In the cases when drivers slow down or continue to move slowly but not completely stop, they are identified as “soft yield” (SY). When drivers completely stop before entering the conflict point (crossing area), they are identified as “hard yield” (HY).

Study Locations and Data Collection

In this study, three mid-block locations in Auckland CBD (Central Business District), where pedestrians commonly cross mid-block with no controlled crossing treatments, were selected. The geometry of the roads is relatively similar, such as the number of lanes, speed limit, sidewalk, public transport (PT) access, and land use. The main differences are median presence and type, presence of a bus lane, and parking condition. These differences could affect the pedestrians’ crossing decisions, especially crossing pace, and consequently the findings being discussed. The site characteristics are shown in Table 1. A fieldwork observation took place between June and July 2020 (4 h per site on weekdays: 3–5 p.m.) during the COVID-19 pandemic while New Zealand was at Alert Level 1. Before selecting the time of the day for data collection, the number of PT users at study locations was checked because the study locations are close to transport hubs, such as bus stops and train stations. The evening peak hours were chosen as PT users’ activities were most intense, and therefore various types of pedestrian assertive behavior are expected.

Table 1.

Site Characteristics

Characteristics	Symonds Street (1)	Broadway Road (2)	Park Road (3)
Road classification	Regional road	Arterial road	Arterial road
Road lane	4-Lane road	4-Lane road	4-Lane road
Crossing length	18 m	19.5 m	16 m
Annual average daily traffic	15,934	25,000	17,000
Speed limit	50 km/h^a	50 km/h	50 km/h
Bus lane	Dedicated bus lane	na	Dedicated bus lane
Bus stop	On both sides	On both sides	On both sides
Parking spaces	No parking	On-road parking	No parking
Median	na	Raised median	Flush median
Sidewalks	Wide sidewalks	Wide sidewalks	Wide sidewalks
Adjacent intersections	Barnes Dance crossing	Signalized crossing	Push-button crossing
Obstructions for drivers’ view	Bus stop	Bus stop/on-road parking	Bus stop
Land use	Commercial/high-rise apartments/university	Commercial/retail	University/hospital/housing
Public transport usage	Major bus stops	Bus/train stations	Bus stops

Data is collected when the speed limit was 50 km/h; the speed limit is now 30 km/h ( 14 ).

na = not applicable.

The New Zealand Alert Levels comprise four levels. With regard to transport mobility, Level 1 is almost returned to pre-COVID normal conditions. “Border entry is restricted to minimize risk of importing COVID-19 cases. Schools and workplaces are open but operate safely. There are no restrictions on personal movement and on gatherings” ( 49 ). On average, vehicle mobility at this time (June and July 2020) was about 10% lower than pre-COVID levels. Walking was also approximately 10% lower compared to January 2020, before the COVID-19 pandemic was announced ( 50 ).

A total of 1330 interactions between drivers and pedestrians were observed using two GoPro cameras. One camera was used to observe interactions (i.e., vehicle’s motion) from higher angles and views, while the other camera was used to capture pedestrians’ behaviors in detail (i.e., gesture, pedestrian inattentive, crossing heedlessly). Behaviors of interest were extracted manually from the video footage, including categorical (binary, discrete) and continuous data. Details of the variables are shown in Table 2. Continuous variables, such as vehicle speed, were extracted with an accuracy of 30 frames per second. Pedestrians’ general assumed characteristics included age category and gender. Gender was estimated. With regard to age group, previous observational studies have estimated pedestrians’ age classification based on their general appearance, including facial textures and body figures ( 33 , 51 ). Therefore, it is accepted that this is not necessarily an accurate categorization. In this study, we differentiated pedestrians into four age groups. Secondary school students (aged 15–19) who wore school uniforms were identified as adolescents, whilst adults were coded based on general appearance. The under 15s were excluded in this study because of the small sample size in the observed locations. Young adults referred to those aged 18–24, middle-aged adults referred to those aged 25–64, and senior adults referred to those aged 65 and older.

Table 2.

Potential Variables Associated With Driver Yielding

Variables	Description (codes)
Pedestrian characteristics
Gender	Male (0)/Female (1)
Age	Adolescent (secondary school students wearing uniform) (0), young adult (1), middle-aged adult (2), senior adult (3)
Pedestrian’s assertive behavior (AST)
1. Pedestrian’s crossing pace (PCP)
- Run (PR)	Pedestrians run heedlessly through traffic (0), no (1)
- Darting into the road (PD)	Pedestrians straight to cross without waiting (0), no (1)
- Acceleration (PA)	Pedestrians appear to increase walking speed (0), no (1)
2. Pedestrian’s gesture (PGT)
- Body gesture (BG)	Pedestrians do not show hesitation or confusion before crossing (i.e., changing the direction of travel or stepping back and forth before crossing) (0), pedestrians do show hesitation or confusion before crossing (1)
- Hand gesture (HG)	Waving hand to signal an intention to cross to the driver (0), no (1)
3. Gazing (GZ)	Pedestrians keep looking at the oncoming traffic (0), no (1)
4. Waiting position (PW)	Stepping into the roadway (0), waiting behind a curb edge (1)
5. Number of pedestrian present (NIG)	1–2 people (0), 3–5 people (1), ≥6 people (2)
6. Crossing position (PP)	Crossing from curbside (0), median (1)
Vehicle characteristics (VC)
1. Speed-related factors (VS)
- Speed (SPD)	Average speed by the time pedestrian start to cross, measured as a continuous variable (km/h)
- Part of a queue (QUE)	Approaching vehicle is a part of the platoon (0), no (1)
- The vehicle has a close follower (FOL)	The vehicle has a close follower by less than 3 s (0), no (1)
2. Type of vehicle (TYP)	Bus (0), bicycle/roller (1), car/pickup truck/van (2), motorcycle/mop (3), small–medium truck (4), otherwise (5)
Driver yielding behavior (DYB)	Driver does not yield to pedestrians (0), driver slows down but does not completely stop, soft yield (1), driver slows down and completely stops, hard yield (2)

An interaction between pedestrians and vehicles on the road was observed when pedestrians accepted an available gap in the traffic stream and started to cross. Since pedestrians cross through several gaps at a multi-lane road crossing, only the minimum accepted gap of all directions and lanes for each pedestrian were included in the analysis. An exception is for hypothesis 2: “drivers yielding rate is higher when pedestrians are waiting at the median than waiting to cross on the curbsides.” The comparison was examined based on the first lane (near lane) when pedestrians start to cross for each direction, as shown in Figure 2. “Average speed” and “The vehicle has a close follower” were extracted manually from video footage with the frame rate (30 fps) in seconds.

Figure 2.

Observation lane for comparing the effect of the crossing position.

Statistical Analysis

This study uses B-SEM to infer a causal relationship between pedestrians’ assertiveness and drivers’ yielding. B-SEM is appropriate to examine the interrelationship of multivariate data among observed and latent variables. It can analyze multiple layers of factors simultaneously when the observed variables are mixed with categorical, ordered, and continuous data with the nonlinear distribution while obtaining the goodness of fit thorough Bayesian framework.

The concept of latent variables has been widely applied to measure behaviors that are not directly observed. Although factors in this study are measurable with naturalistic observation, they are related to human behavior. As such, some of the characteristics are hidden and observed values may not perfectly match with the true behavior. Also, given that pedestrian and vehicle interactions are dynamic events, a measurement error may exist in observed variables ( 52 ). Therefore, some variables in this study are explained with regard to latent variables. This study used the posterior predictive (PP) p-value for testing the goodness of fit for both confirmatory factor analysis (CFA) and SEM. A hypothesized model is considered as plausible when PP p-values are close to 0.5 ( 43 ).

In addition, to make coefficients comparable (which independent variables have more impact compared to others), standardization of the coefficients is used. Kim and Mueller ( 53 ) indicated that “the standardized coefficients are contaminated by differences in the variances of the variables across the populations.” In contrast, to compare causal relationships across the population, unstandardized coefficients are applied. According to Grace and Bollen ( 54 ), since unstandardized parameters are generally expressed in the original units of the independent and dependent variables, the coefficient will describe the association between one variable and a one-unit change in the other variable. Therefore, the original units of the unstandardized coefficient are various. To make coefficients comparable and more interpretable from one variable to another, standardized coefficients that are in standard deviation units are preferable. In this study, we rescale the variables (by making mean = 0 and standard deviation = 1) and rank independent variables by the absolute value of standardized coefficients. SPSS and AMOS Version 26 software were employed to construct this model.

As shown in Table 2, this study assumes DYB to be influenced by AST and VC. Based on the prior studies ( 4 , 5 , 11 ), data from observed variables {PR, PD, PA} were collected to measure the latent variable “PCP.” Here, BG and HG were collected to form “PGT.” Likewise, VS was formed by combining observed SPD, QUE, and FOL. The measurement equations are shown as follows:

PCP = α_{1} + α_{2} PR + α_{3} PD + α_{4} PA + e

(1)

PGT = β_{1} + β_{2} BG + β_{3} HG + e

(2)

VS = δ_{1} + δ_{2} SPD + δ_{3} QUE + δ_{4} FOL + e

(3)

where the parameters α, β, δ are unknown coefficients that represent the effects of observed variables, and e is the residual error.

After the highly correlated observed variables were grouped as latent variables, they were regressed into explanatory variables to the outcome variable “DYB.” It is important to note that although “DYB” can be measured from the fieldwork, it can be unclear such that this factor itself is also considered as a latent variable. Fixed covariates (observed values) (GZ, PW, NIG, and TYP) were also incorporated into the structural equation as follows:

DYB = γ_{1} + γ_{2} PCP + γ_{3} PGT + γ_{4} PW + γ_{5} NIG + γ_{6} VS + γ_{7} TYP + e

(4)

where γ₁, γ₂, γ₃, γ₄, γ₅, γ₆, and γ₇ are unknown regression coefficients.

Results

Descriptive Analysis

Of 1330 interactions, 55% of pedestrians were male and 45% were female. About 67% of observed pedestrians were under the age of 30. While 28% were observed running, 32% accelerated walking speed while crossing. Pedestrians using gestures was relatively low, with about 12% using a body gesture and 3% using a hand gesture. The majority of the pedestrians waited behind the curbside (73%).

Driver yielding behavior (both hard yield and soft yield) substantially increases when the vehicle is a part of a queue (average speed of 15 km/h). There is a small difference in gender concerning driver yielding. Drivers tend to yield to older adults when they are in the queue but there is a similar yielding level between ages when they are not a part of the queue. Pedestrians showing hand gestures indicating their crossing intention seems to have a great effect on the driver yielding rate. However, the rate of hard yield considerably decreases by nearly 30% when vehicles are not a part of a queue compared to when they are a part of the queue. The same appears in pedestrian gazing or keeping looking throughout the crossing. It has an effect on drivers’ yielding mostly when they are a part of a platoon. About 80% of drivers yield to pedestrians who run heedlessly across the traffic when they are a part of a platoon, while only 18% do so when they are not a part of the queue. A similar figure is shown in pedestrians who accelerate their walking speed. About 60% of drivers who are a part of the queue yield to pedestrians crossing from either a curbside or a median. The rate, however, drops significantly when vehicles are not a part of the platoon (22% from a median and 18% from a curbside). Unexpectedly, only 9% of vehicles that are a part of the queue exhibit a hard yield to a group of three to five people crossing together, while 34% exhibit a hard yield to an individual or a pair of pedestrians. Considering the waiting position before crossing, about 19% of drivers give a hard yield to pedestrians who step in the roadway while waiting, whereas 48% yield to pedestrians who wait behind the curbside. The sample size and details are shown in Table 3.

Table 3.

Driver Yielding Rate (%) Based on Pedestrian Characteristics (1330 Interactions)

Category	Sample size (%)	Vehicle is a part of the queue			Vehicle is not a part of the queue
		(Avg. speed 15 km/h)			(Avg. speed 34 km/h)
		NY	SY	HY	NY	SY	HY
Gender: Male	55	20	59	21	81	11	8
Female	45	13	35	52	80	15	5
Age: Adolescent (12–18)	29	23	59	18	72	15	13
Young adult (19–30)	38	21	49	30	85	11	4
Middle-aged adult (30–60)	24	8	28	64	83	13	4
Senior adult (60+)	9	0	28	72	80	14	6
PR	28	19	41	40	82	13	5
PA	32	19	39	42	77	12	11
BG (Do not showing hesitation)	12	15	46	39	82	12	6
HG	3	^a	38	62	28	39	33
GZ	60	14	45	41	81	12	7
PW (step into the roadway while waiting)	27	31	50	19	80	11	9
PW (waiting behind curbside)	73	10	42	48	81	14	5
Group crossings: ≤2	48	7	59	34	81	15	4
3–5	38	39	52	9	71	18	11
≥6	14	^a	^a	^a	79	3	18
PP (crossing from curbside)	62	16	43	41	82	9	9
PP (crossing from median)	38	16	45	39	78	19	3

Note: Avg. = average; NY = not yield; SY = soft yield; HY = hard yield; PR = Run; PA = Acceleration; HG = Hand gesture; GZ = Gazing; BG = Body gesture; PW = Waiting position; PP = Crossing position.

Zero frequencies.

Hypothesis 1: The Effect of Pedestrian Assertiveness

To compare the effect size of variables, Bayesian standardized estimates were used. As explained in the Statistical analysis section, the initial model assumes DYB to be influenced by AST and VC, based on prior studies. After running three different forms of relationship between variables, by including and excluding the potential variables, a model has been determined (refer Equation 5) that reaches the most statistically significant value (PP p-value = 0.5). A path diagram of the final model is shown in Figure 3. The estimates are conducted with 57,000 simulated observations after 1000 burn-in iterations. The result shows a strong relationship between latent variables and the corresponding indicators (PP p-values = 0.5). B-SEM predicted 66% of the variance in driver yielding behavior, while VS has the greatest effect on DYB with a factor loading of −0.80. The model allows PGT, PCP, and PW to exert an indirect effect on DYB that is mediated by VS. The indirect (mediated) effect of PGT on DYB is −0.73, whereas the indirect (mediated) effect of PCP on DYB is 0.25. This is in addition to any direct (unmediated) effect that PGT and PCP have on DYB. The total effect of PW (indirect effect and direct effect) on DYB is 0.06. Here, TYP, FOL, GZ, and PD are not significantly correlated to DYB. Therefore, they are excluded from the final model.

Figure 3.

Structural equation modeling illustrating the relationship between variables (standardized estimated).

To investigate the amount of change for a dependent variable caused by the change of independent variables, unstandardized coefficients were used. The final estimated structural equation (unstandardized regression weight) is shown below:

DYB = - 2.75 VS + 0.08 PW + 0.12 NIG - 5.19 PGT + 0.27 PCP + e

(5)

From Equation 5 it can be interpreted that when VS goes up by 1, DYB goes down by 2.75. In other words, when vehicle speed increases, vehicles are not a part of platoons, or both, driver yielding decreases. Conversely, when NIG increases by 1, DYB goes up by 0.17. Here, PGT and PCP have an indirect effect on DYB. This shows that when PGT goes up by 1 (0 = showing gesture, 1 = not showing gesture), DYB goes down by 5.19. This indicates that when there is no hand gesture, the possibility of not yielding increases. In contrast, when PCP goes up by 1, DYB goes up by 0.27. This means when pedestrians exhibit fast walking, drivers are not likely to yield. However, it is important to note that PGT and PCP indirectly affect DYB through VS.

Hypothesis 2: The Effect of Crossing Position

To investigate the effect of crossing position (PP), whether a driver is more likely to yield to pedestrians waiting to cross at the median than the curbside, a multi-group analysis was performed. Unstandardized coefficients are used to compare causal relationships between crossing from the median and crossing the curbside. The comparison is examined only in the first lane (near lane) when pedestrians start to cross, as shown in Figure 1. The result shows that drivers respond to pedestrians differently when pedestrians cross from the median and the curbside. B-SEM predicted 73% of the variance in driver yielding behavior for crossing from the median and 63% crossing from the curbside (PP p-values = 0.51). The effect of crossing position is shown in Table 4.

Table 4.

Unstandardized Regression Weight Between Pedestrians Waiting at Median and Curbside

Regression weights	Crossing from median				Crossing from curbside
Regression weights	Mean	SD	SE	95% CI	Mean	SD	SE	95% CI
Direct effect
DYB←VS	−1.93	0.15	0.01	−2.23, −1.65	−4.05	0.38	0.03	−4.83, −3.40
DYB←NIG	0.07	0.06	0.00	−0.04, 0.17	0.13	0.02	0.00	0.08, 0.17
DYB←PW	0.26	0.11	0.01	0.06, 0.45	0.23	0.05	0.00	0.14, 0.33
Indirect effect
DYB←PGT	−4.77	0.76	0.09	−6.40, −3.56	−3.84	1.05	0.12	−6.93, −2.38
DYB←PCP	0.31	0.09	0.01	0.15, 0.50	0.17	0.05	0.00	0.07, 0.28
DYB←PW	−0.30	0.10	0.01	−0.50, −0.09	−0.16	0.05	0.00	−0.27, −0.06
Total effect
DYB←PW	−0.04	0.10	0.01	−0.24, 0.17	0.07	0.05	0.00	−0.03, 0.17

Note: p-value is <.00001. SE = standard error; SD = standard deviation; CI = confidence interval.

Here, VS has a much more negative effect on DYB for pedestrians crossing from the curbside (nearest lane) than for those crossing from the median (nearest lane). When VS goes up by 1, DYB goes down by 1.93 for pedestrians crossing from the median and 4.05 for pedestrians crossing from the curbside; PGT and PCP at the median have more impact on DYB than at the curbside. This total effect of PGT and PCP on DYB is caused by indirect (mediated) effects. Here, NIG and PW (stepping in the roadway or waiting behind the curbside) at the curbside and the median have a similar impact on DYB. The total effect of PW is also relatively small on DYB, regardless of the crossing position.

In many cases, parked vehicles can put pedestrians in a low conspicuousness situation. Such situations can potentially reduce drivers’ willingness to yield. The multi-group analysis was performed to investigate the relationship between PP and DYB (with/without parking). B-SEM predicted 82% of the variance in DYB with parking present and 44% without parking present (PP p-values of 0.49). Here, VS has an almost twice-negative effect on DYB for pedestrians crossing when there is parking on-site compared to no parking. When VS goes up by 1, DYB goes down by 4.22 for pedestrians crossing in the presence of parking and 2.8 for pedestrians crossing with no parking. An indirect effect of PGT shows that when this factor goes up by 1 (moving from using gestures [0] to no gestures [1]), DYB goes down by 6.47 with parking present and 2.65 without parking. The result implies that when pedestrians do not use hand gestures and are waiting with parking present, the possibility that the driver yields to them is lower than with no parking. The effect of parking is shown in Table 5.

Table 5.

Unstandardized Regression Weight for Curbside Crossing Between With/Without Parking Present

Regression weights	Curbside crossing (parking present)				Curbside crossing (no parking present)
Regression weights	Mean	SD	SE	95% CI	Mean	SD	SE	95% CI
Direct effect
DYB←VS	−4.22	0.08	0.49	−5.36, −3.40	−2.80	0.06	0.44	−3.66, −2.01
DYB←NIG	0.13	0.01	0.03	0.07, 0.02	0.16	0.01	0.06	0.03, 0.27
DYB←PW	0.05	0.01	0.07	−0.09, 0.18	0.31	0.01	0.06	0.20, 0.45
Indirect effect
DYB←PGT	−6.47	0.55	2.547	−11.25, −3.04	−2.65	0.23	1.11	−4.83, −1.05
DYB←PCP	0.32	0.02	0.1	0.16, 0.54	−0.061	0.01	0.04	−0.51, 0.02
DYB←PW	−0.01	0.01	0.09	−0.17, 0.15	−0.238	0.01	0.05	−0.34, −0.15
Total effect
DYB←PW	0.05	0.01	0.08	−0.10, 0.20	0.08	0.01	0.05	−0.01, 0.18

Note: p-value is <.00001. SE = standard error; SD = standard deviation; CI = confidence interval.

Hypothesis 3: Role of Gender

Here, VS has more negative effects on DYB for males than for females. When VS goes up by 1, DYB goes down by 3.83 for male pedestrians and 2.15 for female pedestrians. An indirect effect of PGT shows that when this factor goes up by 1 (moving from using gestures [0] to no gesture [1]), DYB goes down by 5.86 for male pedestrians and 4.34 for female pedestrians. This implies that when males do not use hand gestures, the possibility that the driver yields to them is lower than for females using hand gestures. Conversely, when females do not have an assertive fast crossing pace (PCP) (regression weight = 0.32), DYB increases to almost double than that for males who exhibit a similar PCP. B-SEM predicted 65% of the variance in DYB with PP p-values of 0.50. The effect of gender on DYB is shown in Table 6. The total effect of PW on DYB is relatively similar between gender but somewhat smaller for males. For an age comparison, the results show that there are no significant differences between pedestrian ages in relation to the driver yielding behavior.

Table 6.

Unstandardized Regression Weight Between Male and Female

Regression weights	Male				Female
Regression weights	Mean	SD	SE	95% CI	Mean	SD	SE	95% CI
Direct effect
DYB←VS	−3.83	0.41	0.01	−4.74, −3.12	−2.15	0.16	0.00	−2.47, −1.85
DYB←NIG	0.16	0.02	0.00	0.11, 0.20	0.00	0.06	0.00	−0.12, 0.11
DYB←PW	0.16	0.05	0.00	0.07, 0.26	0.19	0.06	0.00	0.07, 0.32
Indirect effect
DYB←PGT	−5.86	1.82	0.09	−10.29, −3.06	−4.34	1.02	0.06	−6.81, −2.72
DYB←PCP	0.18	0.09	0.01	0.04, 0.40	0.32	0.10	0.00	0.16, 0.53
DYB←PW	−0.13	0.05	0.00	−0.23, −0.03	−0.07	0.07	0.00	−0.20, 0.06
Total effect
DYB←PW	0.04	0.05	0.00	−0.07, 0.15	0.12	0.07	0.00	−0.01, 0.26

Note: p-value is <.00001. SE = standard error; SD = standard deviation; CI = confidence interval.

Discussion

The findings of this research in the context of Auckland, New Zealand, show that pedestrians’ behaviors have a relatively low impact on drivers’ yielding compared under a moderate speed environment (50 km/h speed limit). Overall, drivers are less likely to yield to pedestrians as speed increases. The position of the vehicle in the traffic is also a significant factor for drivers’ yielding behaviors. When vehicles are in a platoon, their speed tends to be low, and this consequently increases the yielding rate. Pedestrians who use a direct signal (i.e., hand gesture) seem to increase drivers’ yielding rates, whereas those running or accelerating their walking speed are less likely to be given priority. It is possible that hand gestures can alert drivers that pedestrians would like to cross and promote courtesy between the road users ( 17 ). In contrast, running or fast walking is not an explicit act of negotiating priority, and probably more difficult for drivers to read than hand gestures. Drivers may interpret it as an intention to minimize the exposure of crash risks. If available gaps seem to be safe for pedestrians, drivers can assume that they do not need to yield. Notably, these behaviors do not directly affect drivers but are mediated through speed-related factors. The moderated impact implies that drivers may not always yield to assertive pedestrians unless they have adequate reaction time to safely change their speed.

The number of pedestrians waiting to cross and waiting positions (stepping on to the road or waiting behind the curbside) increase the likelihood of yielding, but it is relatively small. Waiting behind the curbside or stepping into the roadway show similar results. This finding is not surprising because, in an urban area, drivers’ views can be blocked by the surrounding environment so that pedestrians waiting to cross may be less visible to drivers. The difference between stepping into the road or waiting behind the curbside are even less obvious when pedestrians are in a less conspicuous position to the drivers, for example, when they wait to cross nearby parked vehicles. Waiting position also indirectly affects yielding rate through vehicle speed. It indicates that when drivers approach with a higher speed, they may be less likely to notice pedestrians and provide priority. However, pedestrians crossing from the median attract more attention from drivers than from the curbside. When vehicle speed increases, the yielding rate goes down more for the curbside than the median. This result is in line with previous studies ( 11 ) suggesting that faster speeds lead drivers to focus more on the center of the road. Note that, although waiting at the median can make pedestrians more visible, it does not always imply an intention to cross. When pedestrians make an assertive move, such as using hand or body gestures, the yielding rate is even higher at the median compared to the curbside.

Considering pedestrians’ gender, findings show that drivers are more likely to yield to females than males, especially for those who have a slow walking pace. It is possible that males negotiate the traffic environment faster in higher risk crossing conditions and may be perceived to be independently confident. Females, in contrast, are often defined as pedestrians needing help more than males ( 5 , 55 ). However, males using gestures affect drivers more than females. It is unclear why drivers yield to males more than females in this situation. One possible reason is that males tend to use decisive and big gestures in general ( 56 ), and this may give clear signals to the driver that they will decisively cross the road.

The findings provide a better understanding of how road users interact with each other outside controlled crossings and evidence for reduced mid-block operating speeds where there is a high pedestrian crossing demand. They could also help to apply proper strategies to ensure the safety of all road users that are not yet fully explored. Based on the findings, some recommendations are made in relation to the application of mid-block road crossings.

Negotiating priority at mid-block sections can be ambiguous and difficult. Pedestrians’ explicit communication, such as hand gestures, tend to influence drivers to yield. This gesture communication can be added to recommended pedestrian behavior and driver education courses ( 17 ). Ongoing education should be in combination with other public awareness schemes. For example, programs should emphasize information that helps both groups understand their right of way, responsibilities, and how to behave according to the law and in the best interest of pedestrian safety.

Notably, although these cues effectively alert drivers to pay extra care at the mid-block section, it works well when the operating speed is relatively low. Vehicles traveling under higher-speed environments gives less time for both parties to effectively communicate or connect, such as establishing eye contact. It also narrows the drivers’ vision and increases their response time to stop or avoid a crash ( 11 , 37 ). This reason may, in part, discourage some drivers from slowing down for pedestrians. Enforcement of appropriate speed zones should provide greater support of policy and regulations to improve pedestrian safety. Pedestrian demand and desire crossing lines are essential to set appropriate “sharing” and identify speed zones and adjacent land use. Typically, setting operating speeds closer to a maximum of 30 km/h, where there is a high crossing demand, allows drivers to manage their maneuver to slow down and increase pedestrians’ survivability ( 36 ). However, pedestrian behaviors are complex and depend on multiple human factors. Their vulnerability and abilities also differ significantly between ages. Exceptions should also be considered where pedestrian users include high proportions of children or the elderly, as they tend to have a lower tolerance to withstand impacts, cognitive abilities are still forming in children, and reaction times are generally longer for elderly pedestrians. Traffic environments dominated by these groups need to be more careful with determining appropriate speed zones and management. Taking these factors into account should elevate the validity of developing appropriate lower-speed management programs in urban areas.

In many cities, speed limits have been reduced from 50 to 30 km/h to make speeds survivable in the case of crashes. However, one of many issues is that lowering the speed limit cannot be easily implemented on all road types, especially arterial and collector roads when high through movement is prioritized and mid-block pedestrian crossing demand is low ( 38 ). Under moderated speed environments, drivers’ decisions to yield or not highly depends on their maneuver and alertness. When pedestrian-controlled crossings are not applicable, increasing the inherent safety of the road infrastructure is advised ( 57 ). Various forms of traffic engineering practices, such as warning textiles, bulb-outs, and speed tables, may help to alert drivers of pedestrians’ desired crossing lines. On multi-lane roads where speed and traffic volume are relatively high, making a one-stage crossing can be unsafe. Refuge islands make crossings easier by breaking the crossing into two stages and safer for pedestrians while increasing their visibility to drivers. Other in-vehicle measures can also influence traffic speeds. Visual and sensory inputs, for example, can notify drivers before entering an interactive or multimodal space ( 58 ). Drivers should be warned that they are approaching an area of high pedestrian crossing activity in good time to reduce their approach speed. If this technique is appropriately and consistently used, it should balance the traffic flow and safety of all road users and lead to reduced crash rates. If both reducing the speed limit and increasing the safety of the road environment are not currently possible or feasible, it is important to discourage uncontrolled pedestrians crossing mid-block via alternative interventions. Pedestrians often perceive this risk-taking behavior as an acceptable act by society ( 59 ). For this reason, promoting safety awareness and information on associated risks may gradually change user behavior over time. All traffic users (pedestrians, drivers, and other users) need to better understand that it is not a low-risk activity and need to be made aware of their own vulnerability. Community engagement is crucial to achieve wider public acceptance.

The main challenges to applying these recommendations are the commitment and involvement of multiple stakeholders, including municipalities, vehicle manufacturers, and education centers. For example, improving infrastructure for local authorities may rely on central governments’ funding allocation, which often has a standard safety intervention to follow. Many countermeasures also need to be compromised between economic appraisal and expected outcomes ( 13 ). Increasing the inherent safety of the existing urban road function is another limitation, as spaces are unavailable to achieve the desired standard ( 60 ).

This study has some limitations. Firstly, the observation may have an observer bias caused by subjective judgments, such as age and gender. To minimize this bias, a preliminary investigation of a smaller test group was conducted, where the detail and criteria for rating the variables were clearly defined. Secondly, this study collected data during the COVID-19 pandemic, where vehicle and pedestrian mobility was approximately 10% lower than in pre-COVID conditions. This may affect vehicle speed and consequently pedestrians’ behavior and drivers’ alertness toward pedestrians. These factors caused by this event are not examined. However, since very few drivers exceed the speed limit of the roads, behavioral changes in driving are likely comparable to pre-pandemic behavior. Thirdly, there are small numbers of pedestrians using hand gestures and a small number of senior adults. The differences in some road elements across the study locations were also not examined. These factors could affect the pedestrians’ crossing decisions and the hypotheses being discussed. Finally, information such as driver characteristics (i.e., age, gender), which is also an important element of driver decision making, was not observed because of limitations in camera settings. Since the first camera was set to view entire road user interactions from a high angle, and the second camera was set at a close-up shot to capture pedestrians’ behaviors in detail, they were inapplicable to capture inside vehicles.

Conclusions

The present study has examined the relationship between pedestrians’ assertiveness and drivers’ yielding behavior at mid-block road sections in Auckland, New Zealand. A total of 1330 interactions between drivers and pedestrians were observed using fixed cameras. B-SEM was employed to understand the relationship between variables. The study contributes by focusing on informal communication between road users under a moderated speed environment of 50 km/h. With this speed condition, the findings suggest the following.

Drivers modify their yield behavior less in higher-speed operating environments. This is possibly affected by the driver having less time to safely see, perceive, react, and modify their maneuvers at higher operating speeds. The consequence of conflicts at such higher speeds could be more severe for pedestrians in the event of crashes. Where there is a high demand for pedestrian mid-block crossing in dense urban environments, speed limits and associated traffic environments should be modified to survivable impact speeds (i.e., less than 30 km/h).

Pedestrian assertiveness has a low impact on drivers’ yielding behavior. Although a direct signal, particularly hand gestures, increases drivers’ willingness to yield, it is moderated through speed-related factors.

Drivers’ yielding level is higher when pedestrians cross from the median than from the curbside.

The number of pedestrians waiting to cross and waiting positions have low impact on drivers’ willingness to yield.

The gender of pedestrians significantly affects driver yielding rates. Drivers yield to females more than males in general, but when males use gestures, drivers are more likely to give them priority than females.

The interaction between road users at mid-block sections is a complex event as it relies on informal behavioral and societal rules, the information available, and a connection with the vehicle driver. When autonomous vehicle traffic environments become a reality, pedestrian safety issues could be intensified as a “connection” with the vehicle, and visual and behavioral cues that do not include a human driver will be very different to the current societal norm; this and its implications will need to be understood. Similarly, with electric scooters and electric vehicles becoming more popular, further research is required to understand their impact for pedestrian safety. Electric scooters can dart in and out between footpaths and roads, which makes it difficult for pedestrians to predict their behavior and move safely around them. It is, therefore, unavoidable for pedestrians to be more exposed to crash risks in shared paths and zones. Electric vehicles were also reported to increase pedestrians risks because of their lower engine noise ( 61 ). As such, pedestrians are unable to detect their approaching, especially visually impaired people. These are new challenges for road practitioners to ensure the safety for all road users.

Footnotes

Acknowledgements

The authors would like to thank Rahul Kadam and Dipendra Magaju for the help in data collection, Sujith Padiyara for obtaining instruments and approval of field-based research activity, and Waka Kotahi NZTA for providing CAS access.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: A. Soathong, D. Wilson, P. Ranjitkar and S. Chowdhury; data collection: A. Soathong; analysis and interpretation of results: A. Soathong; draft manuscript preparation: A. Soathong. A. Soathong, D. Wilson, P. Ranjitkar and S. Chowdhury reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Ajjima Soathong

Douglas Wilson

Subeh Chowdhury

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