Pedestrian Safety: Drivers’ Stopping Behavior at Crosswalks

Abstract

The safety of a pedestrian crossing may depend on infrastructure, vehicular and pedestrian traffic characteristics. This academic research typically portrays the safety challenges knowingly caused by vehicles on crosswalks in the city of Kigali. Through carefully observing the stopping of local drivers in pedestrian crossing events, the study aims to objectively evaluate drivers’ questionable behavior against traffic flow parameters. Ten collection sites were ultimately selected purposefully and randomly to suit observations for data recording. A grand total of 10,259 crossing events were properly recorded within 280 h. Statistical analyses, practical tests and binary logistic regression models were promptly used to adequately evaluate the specific behaviors. Woefully, 82.4% of drivers violate crosswalks, endangering crossing pedestrians. Motorcyclists typically exhibit the most aggressive behavior. Car drivers are relatively less aggressive, whereby 60% managed to brake in the events. Local buses and authorized bicycles enthusiastically shared a negligible collective percentage of 2%, being aggressive and not stopping. In general, cars are 10.389 times more likely to voluntarily and justly stop compared to bicycles. Maintaining more vehicles in a row is safer for a pedestrian to cross, as for each unit increase on the vehicle density scale, there were 1.956 more chances that every driver would stop. In brief, 13% to 21% of traffic variables positively predict the considerable variance in the stopping behavior model.

1. Introduction

The assured safety of a pedestrian facility may naturally depend on various key factors. According to [1], it mainly depends on its features and on how it is used, in other words, crossing infrastructure details and traffic characteristics. Models existing in the literature are based both on traffic and pedestrian volume information and on pedestrian crossing features, but in many cases, traffic data are unavailable. This academic research properly focuses on the possible safety of a pedestrian crossing, adequately taking into account the existing traffic composition and apparent volumes.

According to police data, road accidents that happen in the city of Kigali involve many pedestrians and motorcycles. For instance, in the year of 2017 alone, 71% of the total registered road accidents involved motorcycles (moto-taxis), pedestrians and bicycles. The KN 7 road, the KN 5 road and city circle junctions remain hotspots for fatal accidents in Kigali, as determined by a study presented in the police database [2].

Since the study area for this research was instantly under the geographical scope of the capital city of Kigali, non-probability purposive sampling was intentionally used to unanimously select pedestrian crossings.

A separate study conducted on the roads (RN1 and RN3) in the same study area of the city of Kigali by [3], in describing the traffic characteristics, counted motorcycles as being the most significant number of moving vehicles, and this has also been confirmed by the results of this study. From the key findings, it was recognized that the traffic flow rates for buses, bicycles, cars and motorcycles were on average 68, 113, 1943 and 4955 vehicles per hour, respectively, when studying crosswalk sites; this informs us that the motorcycle vehicle type is very important in traffic flow characteristics and will be the most common traffic scenario to impact on pedestrian crossings as far as drivers’ stopping behavior is concerned.

The independent survey unambiguously identified four specific types of vehicles. These include big ones, on four wheels or more (cars and buses), and two-wheeled ones (motorcycles and bicycles). In terms of frequency, it is very clear that motorcycles are the most present vehicles on the surveyed roads, with a prominence of 14,865 counts (67.4% of all surveyed vehicles). Cars come second, with about a quarter prominence, while bicycles and buses are rare, with collective negligible percentages of about 1.5% and 0.9%, respectively. Vehicle density and types are very important independent variable characteristics that affect the drivers’ behavior greatly in giving access to pedestrians to cross, and research has proven this in a model by displaying the odds ratios that are greater than one.

Figure 1 is a flowchart that describes the process through which this study was conducted. It starts by reviewing the literature related to driver and pedestrian characteristics at a crosswalk; it discusses a site visit tour to study pedestrian challenges in the city of Kigali; it makes a critical selection of data collection sites; it sets up observational protocols; it extracts data from recorded videos; it carefully performs data cleaning and it uses and applies logistic regression models to deduct concluding remarks.

Therefore, further research is enthusiastically encouraged to uncover other relevant parameters that would positively influence a driver to stop or not to stop; these may undoubtedly include external factors like unique infrastructure characteristics or internal factors that may be unique for each local driver.

1.1. Literature Review

1.1.1. Traffic Safety on Pedestrian Crossings

Pedestrian safety is justly regarded as one of the most challenging problems in urban transport [4]; hence, it should be jointly considered with the motorized transport system that occupies a central role in most societies. In many notable instances, commercial goods needed for everyday life are efficiently transported via local roads. In notable addition to this, local residents of various places use motorized travel to fortunately reach their personal workplace or leisure destinations. While this advantage has been achieved, high levels of motorization contribute to catastrophic consequences such as human and economic losses owed to road accidents [4]. With this in mind, pedestrian safety has recently been recognized as a public health challenge worldwide [5]. According to the insightful report of [6] on transportation considerations for the 2030 sustainable development goals, road safety remains an important development issue. In many instances, commercial goods needed for everyday life are transported via roads. Ref. [7] shows that pedestrian characteristics are one of the factors that affect pedestrian crossing safety. Pedestrian accidents also frequently result from infrastructure-related factors of crosswalks [8].

In direct contrast to the declining number of confirmed fatalities due to train–vehicle collisions at highway–railway crossings, the considerable number of pedestrians and bicycle fatalities at highway– and pathway–railway crossings has progressively increased in the last dozen years [9]. A large number of deaths and injuries occur annually as a result of road crashes among pedestrians, especially in low-income countries, and unsafe crossing behaviors still exist [7]. Globally, about 400,000 pedestrians are killed due to road traffic accidents [10]. Ref. [8] shows that around 35% of all pedestrian fatalities happen at crosswalks, and this requires improvement.

To combat the issue of pedestrian deaths and injuries, engineers have come up with various ingenuities to address the issue. Ref. [11] has also suggested that education and training on safe crossing behavior in traffic can be a pedestrian protection measure. One of the most used pedestrian crossing types, a zebra crossing, was first designed and efficiently implemented in Slough, the United Kingdom, in 1951 [12]. Likewise, it is assuredly the most popular pedestrian crossing in Rwanda.

1.1.2. Pedestrian Mobility in the city of Kigali

According to the 2018 Transport Master Plan, the population of Kigali stood at approximately 1.5 million. It was accurately forecasted to typically grow to approximately 3.8 million in 2050. This is something that may increase pressure on existing transport infrastructure, and hence on traffic safety measures that have been put in place [13].

According to this similar survey, on average, the majority of active citizens live within two kilometers from their place of work. When carefully comparing the used mode of transport employed to typically travel to work and the average monthly combined income, it has been made clear that the areas where people earn a higher income are also the areas where the usage of private car travel is more common. Since most urban citizens do not fall into this distinct category, it has then been concluded that the overwhelming majority of employed citizens use walking as a mode of transport to get to their place of work [14]. The homeward journey study began by surveying Kigali major road networks, in terms of its main corridors. Significant traffic and low traffic areas were purposefully sampled. Safety risk is hypothetically present in either situation.

The Inspectorate General of the Police Office set a tariff for violation of pedestrian crosswalks by drivers, excluding bike riders, to an amount of USD 25 in 2015 under serial number 24 [15]. In notable addition to this, an annual “arrives safely/Gerayo Amahoro” weekly campaign was meticulously organized by the Rwanda National Police (RNP) together with the Ministry of Infrastructure in the Republic of Rwanda to alert drivers to drive carefully and give access to pedestrians for crossing at designated facilities. According to reliable RNP data, road crash rates in Rwanda decreased by 17% [16].

This study was conducted as a measuring tool to cross check drivers’ stopping behavior in order to investigate the prevailing situation in the city of Kigali and found that there is still a gap to fill as far as pedestrian safety is concerned at the crosswalk, based on the research output.

Moreover, in terms of schooling and other motives of people’s movements, it has been noted that walking remains the most prevailing mode of transport for students traveling to school [14]. In addition to this, the time of day that people will most likely travel to work in Kigali in general is between 06:00 and 09:00 in the morning [3].

Population concentration and potential mobility density are purportedly shown in Figure 2 for the city of Kigali. They are very high in Nyarugenge, followed by Gasabo, and deep concentration is allegedly experienced in Kicukiro.

1.1.3. Zebra Characteristics and Traffic Regulations

Pavement markings are a vital means of traffic control on streets and roads. In some cases, pavement markings are used to supplement general traffic regulations or regulations and warnings issued by signs and signals. In other cases, markings can be implemented without being supplemented by other devices [17]. The principal advantage of road markings is that they convey guidance or information to the driver without diverting attention from the roadway. Road crashes lead to considerable social and economic losses and occur frequently as a result of unsafe road design and characteristics [18]. In bad weather conditions, this may, in general, be of vital importance to road safety [19]. Pavement markings should therefore be given meticulous attention with respect to both application and maintenance [17].

The same philosophy is used to convey guidance toward pedestrian crossing roads, and it is very well known that the most crucial factors in road construction are the safety of road users. Various markings, as presented later in this report, are drawn to guide drivers and pedestrians. At some exceptional intersections, traffic lights are used to guide both drivers and pedestrians, while in most places, only road markings are used. In Rwanda, it is a traffic offense to violate pedestrian crossings like a zebra crossing.

Since 2019, when the Government of Rwanda launched the safety week, it is in this regard the best practice that the pedestrian has right of way over a vehicle when the pedestrian reaches the crossing first [20]. In such cases, the vehicle is supposed to stop, preferably somewhere in the deceleration zone, before the stop line marking.

The government has continued to implement safer road programs through other government institutions to educate road users on effective and safe usage of the road. In 2017, the government reviewed the laws on road safety to toughen penalties against traffic offenders. They have also committed to implementing all possible strategies to enhance road safety measures, as evidenced through a campaign launched by the Rwanda National Police (RNP) and Ministry of Infrastructure (MININFRA) in 2017 to curb road accidents and promote road user respect so as to abide by road safety standards [21]. The vulnerable road user population, mainly pedestrian users [22], need a strong government road safety program for the safe usage of roads.

2. Materials and Methods

2.1. Methodology

The studies used both quantitative and qualitative methods to analyze the safety and zebra crossing topics, as in [1,18,23]. In addition, other qualitative techniques were commonly used in terms of graphical analysis, importantly, photography based on time-lapse photos [24] and the mapping of data through the overlaying of graphical features [25]. The quantitative methods and techniques applied structured observation to study the behavioral patterns of the users [14,26]; on the other hand, the quantitative methods used statistical data to sort the data out based on software analysis [3,4,27]. Particularly, chi-square and regression tests were applied to measure two independent variables due to the verification of the hypothesis through statistical tests [28,29,30].

2.2. Aims, Sampling and Scope

To assess and portray the safety challenges on pedestrian crossings, a survey was designed on various crossing facilities in the city of Kigali. It was properly designed in an observatory manner to critically assess how drivers abide by pedestrian crossing markings. It is additionally noted that pedestrian interaction with any type of vehicle (two- or four-wheeled types) generates a severe conflict on roads while crossing at crosswalks [31].

2.3. Research Design

There are many pedestrian crossing facilities that typically exist and this research is limited to crossings that fall in the category of white stripes on black road. They are repeatedly referred to as zebra crossings. In the first place, the main research team took a tour of Kigali and identified more than 50 zebra crossings in the three districts that make up Kigali. Nyarugenge is the most densely populated, second to Gasabo and Kicukiro. For remarkable uniformity in the data collection process, observation sites were reduced to the number of fifteen.

The following criteria were employed to reduce the number of sites from 50 to 15. The selected crossings were those limited to the following factors:

• Existence of relatively high pedestrian mobility (hospital, market, school, church);
• Existence of stop lines (white lines that mark the beginning of a zebra crossing);
• No existence of traffic police or traffic cameras;
• No road humps before or after the crossing;
• No intersection around the crossing;
• No roundabout around the crossing;
• Only for 1 carriage way with 2-way traffic.

For site randomization purposes, data collection sites were reduced from 15 to 10 using random probability sampling. This gave sampling an edge of statistical reliability and reduced purposive bias.

2.4. Observation Protocol

Data were collected using handheld cameras fixed on tripods. These cameras were strategically positioned in a proper angle that could promptly capture all pedestrian crossing events. Cameras were mounted on tripods, in hidden locations, to allow for almost purely anonymous observation. The local traffic safety law enforcement institution was informed of the intended survey for research ethics purposes. In addition, a clearance letter from the University of Rwanda was passed to the City Council to reiterate the same.

Collectively, there were 10 data collectors deployed to 10 data collection sites each. Necessary data were collected for one week (7 days) during peak hours (6–8 A.M. and 5–8 P.M.). This research was therefore cross-sectional in nature. In brief, the total observation time amounted to 280 h, that is, 4 h of recording per day, per site, for seven days at 10 sites. Mathematically, it can be shown as follows:

$$\begin{gathered} \mathrm{Total}\mathrm{Hours}=\left(\mathrm{Morning}+\mathrm{Evening}\right)\mathrm{x}\mathrm{Days}\mathrm{x}\mathrm{Sites} \\ \mathrm{Total}\mathrm{Hours}=\left(2+2\right)\mathrm{x}7\mathrm{x}10=280\mathrm{H} \end{gathered}$$

Every video was timestamped for further analysis. Geographical meta data like altitude, wind speed, Global Positioning System (GPS) coordinates, micro maps and live location were appended to videos as well. These were employed to help with data quality, reliability and intended research. All data were digitally archived on mass and are in cloud storage repositories.

2.5. Data Analysis

Using online questionnaire tools to capture pedestrian crossing events, basic observation and the replay of videos helped with spotting and noting down various traffic flow variables. These included, but were not limited to, the type of vehicles, crossing times, stopping times, stopping distances, count of vehicles per crossing event and more. Zebra characteristics, mostly geometric, were also captured in a separate questionnaire. Tape measures, to the precision of 1 cm, were used to measure road marking characteristics, including, but not limited to, carriage way width, zebra line lengths, distance between center lines and stopping lines, etc.

Having carefully collected an overwhelmingly immense amount of data, this study will only seek to evaluate drivers’ stopping behavior with respect to various traffic flow characteristics.

2.6. Statistical Tests

Cross tabulations and Pearson chi-square tests were used to evaluate the probable dependencies of subject variables. Using spatial dimensions attached to each entry, spatial analysis was conducted. Using Tableau (version 2021.4), spatial visualizations were created to compare population densities, traffic densities and pedestrian crossing compliance at each surveyed site. Descriptive statistics were used to portray the safety challenges caused by vehicles.

Cross tabulations and Pearson chi-square tests were used to evaluate the probable dependencies of subject variables. To conclude the analysis part, binary logistic regression models were powerfully built and used to carefully evaluate drivers’ stopping behavior against traffic flow characteristics.

2.6.1. Chi-Square

Chi-square tests of independence test whether two qualitative variables are independent, that is, whether there exists a relationship between two categorical variables [29]. If the test shows no association between the two variables (i.e., the variables are independent), it means that knowing the value of one variable gives no information about the value of the other variable [28].

The chi-square test of independence is a hypothesis test; so, it has a null (H₀) and an alternative hypothesis (H₁):

H₀: 

The variables are independent, and there is no relationship between the two categorical variables. Knowing the value of one variable does not help to predict the value of the other variable.

H₁: 

The variables are dependent, and there is a relationship between the two categorical variables. Knowing the value of one variable helps to predict the value of the other variable.

The calculation aspects of this test stem from the logic of mathematical probability. For two independent events A and B, the following probability equation should always hold true:

$$P\left(A\cap B\right)=P\left(A\right)\ast P\left(B\right)$$

Therefore, the chi-square test of independence works by comparing the observed frequencies (so, the frequencies observed in our sample) with the expected frequencies, if there is no relationship between the two categorical variables (so, the expected frequencies if the null hypothesis is true). This difference, referred to as the test statistic (or t-stat) and denoted by χ2, is computed as follows:

$$\mathsf{\chi }2={\displaystyle \sum }_{\mathrm{i},\mathrm{j}}^{ }\frac{{\left({\mathrm{O}}_{\mathrm{ij}}-{\mathrm{E}}_{\mathrm{ij}}\right)}^2}{{\mathrm{E}}_{\mathrm{ij}}}$$

O represents the observed frequencies and E represents the expected frequencies.

The statistical test alone is not enough to draw conclusions regarding independence or dependence between the two variables. As previously mentioned, this test statistic (which in some sense is the difference between the observed and expected frequencies) must be compared to a critical value to determine whether the difference is large or small.

The critical value can be found in the statistical table of the chi-square distribution and depends on the significance level, denoted by α, and the degrees of freedom, denoted by $df=\left(rows-1\right)\left(columns-1\right)$. The significance level is usually set equal to 5%.

Like for many other statistical tests, when the test statistic is larger than the critical value, the null hypothesis is rejected at the specified significance level. Figure 3 illustrates the chi-square distribution in a dataset.

2.6.2. Binary Logistic Regression

Collected data were also analyzed using binary logistic regression. This one can predict the probability (P) of a specific event when the dependent variable is dichotomous [32]. In this study, the occurrence of a specific stopping behavior can be considered as a binary response variable. The driver will either stop or continue driving during a pedestrian crossing event. The log odds (logit) of P equal the natural logarithm of P/(1 − P). Therefore, binary logistic regression estimates the log odds of the independent variables as a linear combination, as shown in the equation below:

$$\mathrm{Logit}\left(\mathrm{P}\right)=\mathrm{Ln}\left(\frac{\mathrm{P}}{1-\mathrm{P}}\right)={\mathsf{\beta }}_0+{\mathsf{\beta }}_1{\mathrm{X}}_1+{\mathsf{\beta }}_2{\mathrm{X}}_2+\dots {\mathsf{\beta }}_{\mathrm{n}}{\mathrm{X}}_{\mathrm{n}}$$

In this equation, P is the probability of the behavior’s occurrence, X_n is the independent variable and β_n is the logistic regression coefficient. For each research question, the significance value of 0.05 was accepted as an influential predictor variable. For each model, the odds ratio was calculated to determine whether there was an increase (>1) or decrease (0–1) in the probability of the behavior when the independent variables increased with one unit [33]. The Cox and Snell R squared and Nagelkerke R squared tests were used to assess each model’s goodness of fit. The test determines the percentage of variance caused by independent variables in the equation [30]. SPSS 25.0 was used for all statistical computations.

3. Results

3.1. Zebra Characteristics

According to Figure 4, using satellite imagery, it is straightforward to track zebra crossings. Using remote sensing on the 6 m scale precise coordinates, it was possible to estimate the zebra crossing characteristics and track asymmetries. Generally, in road design, it is standard to obtain non-uniform dimensions depending on the nature of the terrain. The focus of this research is on investigating the relationship between zebra characteristics and vehicles’ un-stopping behaviors. The stopping behaviors of vehicles are subject to pedestrian safety.

The letters shown on the far right end in Figure 4 indicate various dimensional parameters of the crosswalk (zebra stripes) as follows:

A: Left stop line length;

B: Left stop line width;

C: Right walkway width;

D: Carriage way width;

E: Left walkway width;

F: Left walkway width;

G: Zebra line width;

H: Zebra line distancing;

I: Left stop line distance to zebra;

J: Right stop line distance to zebra;

K: Right stop line width;

L: Right stop line length.

A pedestrian crossing can be characterized by various aspects. Some are inherently due to the way that the road infrastructure has been set up. Other factors may depend on how the markings have been drawn. In both cases, the data collectors collected important information using tape measures.

While the sites were trimmed down to granular uniformity details, the recorded measurements still show that there are clear inconsistencies in zebra characteristics in the city of Kigali. For instance, one site (Site 9) did not have a stop line on one side of the lane. Zebra line lengths also greatly vary in measurement, with μ = 3.7 m (mean) and σ = 0.96 m (standard deviation). Zebra line lengths are arguably designed depending on the pedestrian traffic at both ends of the road facility (Figure 5).

One other major characteristic with variability is the distance between stopping lines and zebra lines themselves. They were measured on both lanes with maximum μ = 2.9 m and σ = 1.25 m. Zebra line markings vary from country to country. Like all other road markings, there is no fixed or correct length. Most markings are adapted to the traffic situation, to address factors like overtaking possibility, speed design and more. Therefore, design standards suggest acceptable ranges. Nonetheless, it is of great interest to investigate whether zebra characteristics have any, or whether they are in anyway associated with drivers’ stopping behavior in cases of pedestrian crossings. According to our observations, most measurements fell into acceptable ranges, with some exceptions. This was partly due to the fact that data collection sites were hand-picked based upon various factors.

Pedestrian walkways may affect pedestrian safety at pedestrian crossings. According to the collected data, at least 3 out of 10 sites did not have a pedestrian walkway on either of its lanes. It is unknown whether this characteristic influences a positive or negative stopping behavior by drivers, but it is arguably a non-ignorable safety risk for pedestrians. In most cases, when pedestrians are crossing, they tend to feel safer when the crossing destination is safer. The lack of pedestrian walkways on some roads therefore poses a significant hazard for pedestrian safety. In the worst cases, the lack of walkways was associated with the existence of non-covered water canals and drenches. It is therefore undeniably risky to cross over such a facility.

3.2. Spatial Analysis

This study was carried out in the capital city of Kigali, Rwanda. This analysis aims to visualize traffic flow on zebra crossings across the capital. Data collection sites were purposefully distanced.

The spatial analysis data almost corresponded to the population density map portrayed earlier in Figure 2. Transport by foot being the most used mode of transport to reach workplaces and schools is shown in Figure 6. For relatively dense areas, there will be a lot of pedestrian traffic, thus prompting multiple vehicles to stop for crossing occasions. This is particularly true for Sites 2 and 4.

Upon a second glance, it is almost noticeable that buses and bicycles are rarely spotted, and motorcycles and cars are in abundance. For dense areas, motorcycles greatly outnumber cars. One of the reasons for this is arguably due to the economic profile of densely populated households. In places where there are a few residents, for instance, Sites 9 and 6, there will be relatively more cars, since residents are more affluent.

3.3. Descriptive Analysis

The collection of data was long and interesting, as indicated in

Table 1. Cross tabulation of major frequencies.

Variable Name	Evening		Morning		Totals
	N	%	N	%	N	%
	11,354	(51.5)	10,704	(48.5)	22,058	(100)
Did the vehicle stop?
No	9124	(41.4)	9049	(41.0)	18,173	(82.4)
Yes	2230	(10.1)	1655	(7.5)	3885	(17.6)
Vehicle Type
Bicycle	95	(0.4)	245	(1.1)	340	(1.5)
Motorbike	7499	(34.0)	7366	(33.4)	14,865	(67.4)
Bus	89	(0.4)	116	(0.5)	205	(0.9)
Car	3428	(15.5)	2401	(10.9)	5829	(26.4)
Stopping Distance
Breached	9124	(41.4)	9049	(41.0)	18,173	(82.4)
<0.5 m	142	(0.6)	109	(0.5)	251	(1.1)
<1.0 m	120	(0.5)	48	(0.2)	168	(0.8)
<1.5 m	147	(0.7)	110	(0.5)	257	(1.2)
<2.0 m	344	(1.6)	148	(0.7)	492	(2.2)
<2.5 m	296	(1.3)	162	(0.7)	458	(2.1)
<3.0 m	429	(1.9)	299	(1.4)	728	(3.3)
<3.5 m	265	(1.2)	370	(1.7)	635	(2.9)
Greater than 4 m	487	(2.2)	409	(1.9)	896	(4.1)
Weekday
Monday	1230	(5.6)	1175	(5.3)	2405	(10.9)
Tuesday	1400	(6.3)	1690	(7.7)	3090	(14.0)
Wednesday	1536	(7.0)	2064	(9.4)	3600	(16.3)
Thursday	2020	(9.2)	1937	(8.8)	3957	(17.9)
Friday	1327	(6.0)	1863	(8.4)	3190	(14.5)
Saturday	2241	(10.2)	1224	(5.5)	3465	(15.7)
Sunday	1600	(7.3)	751	(3.4)	2351	(10.7)

. Over 22,000 vehicles were identified in 10,259 stopping occasions. Across 10 sites, the drivers, vehicles, pedestrians and road characteristics were different. This variety of situations resulted in interesting findings, summarized as follows:

At a glance, zebra crossing compliance is arguably in a bad shape and safety at pedestrian crossings is not the best. In all observed occasions, from Monday to Sunday, in morning and evening peak hours, only 17.6% of drivers stopped to allow pedestrians to cross. Everyone else just continued to drive while pedestrians were crossing, not to mention that those who stopped did not necessarily stop far away from pedestrians. According to the recorded observations, only 896 vehicles (4.1%) stopped at least 4 m away from the zebra center line.

In this study, the researchers tried to visualize four variables of traffic flow and pedestrian crossing events in one graph. These included vehicle types, days of the week, peak hour periods (hours, minutes and seconds) and stopping distances. Advanced statistical and data computational tools were used to come up with such graphs.

Figure 7, as shown above, is a clear and integral visualization of pedestrian safety on zebra crossings in Kigali. From the left, on the upper axis, there are consecutive days of the week when the survey was carried out. On the bottom x-axis, there are stopping distances per zebra crossing. Distance 0 is recorded for every vehicle that crossed the center line of the zebra crossing, hence breaching safety regulations and putting pedestrians’ lives at risk.

On the y-axis, the graph portrays traffic peak hours in a continuous fashion. By trimming outliers and other edge observations, the graph shows data from the morning at 6:00 A.M. until 7:00 P.M. in the evening. A four-tiered semi-transparent color legend variable was used to portray vehicle type, while circle radii were used to showcase the density of the same.

On a granular level, there are obvious observations that can be noted. For instance, regarding the traffic flow aspect, there are a few vehicles on weekend mornings. The same goes for a Wednesday evening; nevertheless, this could have been an anomaly since it rained heavily that evening, halting pedestrian mobility and data collection altogether.

In addition, on the first day of recording data, observers and data analysts were at first agnostic regarding vehicle type, until they realized that vehicles behave differently with various crossing events. As shown in the videos, two-wheeled vehicles are likely to continue moving while pedestrians are crossing, even when four-wheeled (or more) ones have stopped to allow the safe passage of pedestrians. From this point forward, vehicle types were recorded as part of the survey.

3.4. Stopping Behaviors

To compute various equation elements of the chi-square, the following table was created (

Table 2. Cross tabulation and chi-square values (expected values in bold).

Did the Vehicle Stop?	No			Yes			Totals
	N	%		N	%		N	%
	18,173	(82.4)		3885	(17.6)		22,058	(100.0)
1. Peak Hour Period—X2 (1) = 66.3, p < 0.001
Evening	9124	(41.4)	(42.4)	2230	(10.1)	(9.1)	11,354	(51.5)
Morning	9049	(41.0)	(40.0)	1655	(7.5)	(8.5)	10,704	(48.5)
2. Vehicle Type—X2 (4) = 2774, p < 0.001
Bicycles	323	(1.5)	(1.3)	17	(0.1)	(0.3)	340	(1.5)
Motorcycles	13,519	(61.3)	(55.5)	1346	(6.1)	(11.9)	14,865	(67.4)
Buses	131	(0.6)	(0.8)	74	(0.3)	(0.2)	205	(0.9)
Cars	3522	(16.0)	(21.8)	2307	(10.5)	(4.7)	5829	(26.4)
Null	678	(3.1)	(3.1)	141	(0.6)	(0.7)	819	(3.7)
3. Day of the Week—X2 (6) = 259.2, p < 0.001
Monday	1897	(8.6)	(9.0)	508	(2.3)	(1.9)	2405	(10.9)
Tuesday	2391	(10.8)	(11.5)	699	(3.2)	(2.5)	3090	(14.0)
Wednesday	2898	(13.1)	(13.4)	702	(3.2)	(2.9)	3600	(16.3)
Thursday	3197	(14.5)	(14.8)	760	(3.4)	(3.2)	3957	(17.9)
Friday	2625	(11.9)	(11.9)	565	(2.6)	(2.5)	3190	(14.5)
Saturday	3107	(14.1)	(12.9)	358	(1.6)	(2.8)	3465	(15.7)
Sunday	2058	(9.3)	(8.8)	293	(1.3)	(1.9)	2351	(10.7)
4. Vehicle Density—X2 (2) = 181.3, p < 0.001
Low	3039	(13.8)	(14.3)	788	(3.6)	(3.1)	3827	(17.3)
Medium	4426	(20.1)	(18.6)	564	(2.6)	(4.0)	4990	(22.6)
High	10708	(48.5)	(49.5)	2533	(11.5)	(10.6)	13,241	(60.0)
5. Pedestrian Density—X2 (3) = 138.4, p < 0.001
Less Dense	6327	(28.7)	(27.6)	1061	(4.8)	(5.9)	7388	(33.5)
Dense	1138	(5.2)	(5.3)	291	(1.3)	(1.1)	1429	(6.5)
Very Dense	4863	(22.0)	(23.2)	1353	(6.1)	(5.0)	6216	(28.2)
Extremely Dense	5845	(26.5)	(26.2)	1180	(5.3)	(5.6)	7025	(31.8)

):

Model Fit

A logistic regression was conducted to determine whether five traffic flow variables (vehicle type, peak hour period, day of the week, vehicle density and pedestrian density) were able to predict the stopping behaviors of drivers to allow safe pedestrian use of zebra crossings. The results of the logistic regression were highly statistically significant, with X² (13) = 2954.6 and p < 0.001, using the omnibus test.

Effect size

The variance in drivers’ stopping behavior predicted by traffic flow variables in the model ranges from 12.5% to 20.7% based on the Cox and Snell R square or Nagelkerke R², respectively.

Classification Table

Without any predictor, the model would have predicted 82.4% of the stopping behavior correctly. On the flipside, with independent variables included, this number increased slightly with 0.50 basis points to 82.9%. Some statisticians refer to this percentage accuracy (PAC) in classification too.

Sensitivity

This refers to the percentage of cases in which stopping at a zebra crossing was observed (“yes”) and was correctly predicted by the model. A total of 9.5% of drivers who stopped were predicted by the model to have stopped. The positive predictive value is the percentage of correctly predicted cases with the observed characteristic (those who stopped) compared to the total number of cases that were predicted to stop. That is, of all cases predicted to stop, 93.7% were correctly predicted.

Specificity

This refers to the percentage of cases in which stopping at a zebra crossing was observed (“no”) and was correctly predicted by the model. A total of 98.6% of drivers who breached the zebra crossing were predicted by the model to have violated it. The negative predictive value is the percentage of correctly predicted cases with the observed characteristic (those who breached it) compared to the total number of cases that were predicted to breach it. That is, of all cases predicted to violate it, 99.9% were correctly predicted.

Model Summary

The model (traffic variables) explained between 12.5% (Cox and Snell R²) and 20.7% (Nagelkerke R²) of the variance in drivers’ stopping behavior and correctly classified 82.9% of cases. The sensitivity was 9.5% and specificity was 98.6%. The positive predictive value was 93.7%, and the negative predictive value was 99.9%.

4. Discussion

This discussion will be based on the results of the Nagelkerke R² as an adjusted version of the Cox and Snell R2 to adjust the scale of the statistic to cover the full range from 0 to 1. The value of around 21% change in the dependent variables (drivers stopped or drivers did not stop) can be attributed to the independent variables in the model. Only about 13% to 21% of the recorded traffic variables were able to predict the variance in the stopping behavior model, according to the Cox and Snell and Nagelkerke R² values, respectively.

The model sensitivity, also called the true positive rate, of 9.5% here represents the percentage of the observed cases to fall under the category of drivers who stopped (target group). In brief, the drivers’ predicted rate of stopping at zebra crossings to let pedestrians cross was 9.5%.

The model specificity, also known as the true negative rate, of 98.6% standing for the percentage of the observed behavior of the driver not to stop but to breach traffic rules shows that which was included in the non-target category. The drivers’ predicted behavior of not stopping but breaching traffic rules, i.e., preventing the pedestrian’s rights to cross, was at a rate of 98.6%.

4.1. Effect of Peak Hour Period

As per the raw statistical data in Table 2, the peak hour period plays a minor role under descriptive statistics. Drivers’ behavior to give access to pedestrians to cross is better and more frequent during evening times than mornings. This may be due to the fact that in the evening period, people are no longer stressed about being late for work but are instead going home. Still, the probability of giving access to pedestrians is below 1, as per the odds ratio of 0.733 from

Table 3. Logistic regression equation variables and their statistical significance.

							Lower	Upper
Variable	B	S.E.	Wald	df	Sig.	Exp(B)	95% C.I.—Exp(B)
Intercept	−3.390	0.266	162.468	1	0.000	0.034
1. Peak Hour Period	−0.311	0.040	59.095	1	0.000	0.733	0.677	0.793
2. Vehicle Type
Bicycle (1)			2289.644	4	0.000
Moto	0.415	0.252	2.704	1	0.100	1.514	0.924	2.481
Bus	2.208	0.290	57.838	1	0.000	9.094	5.148	16.064
Car	2.341	0.252	86.486	1	0.000	10.389	6.343	17.014
Null	0.992	0.273	13.157	1	0.000	2.696	1.578	4.609
3. Day of the Week
Monday (1)			168.105	6	0.000
Tuesday	−0.078	0.081	0.923	1	0.337	0.925	0.789	1.085
Wednesday	−0.162	0.080	4.061	1	0.044	0.851	0.727	0.996
Thursday	−0.269	0.079	11.601	1	0.001	0.764	0.655	0.892
Friday	−0.276	0.083	10.936	1	0.001	0.759	0.645	0.894
Saturday	−0.884	0.088	100.973	1	0.000	0.413	0.348	0.491
Sunday	−0.599	0.093	41.426	1	0.000	0.549	0.458	0.659
4. Vehicle Density	0.671	0.044	233.313	1	0.000	1.956	1.795	2.132
5. Pedestrian Density	−0.494	0.056	77.360	1	0.000	0.610	0.547	0.681

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4.2. Effect of Vehicle Type

Under this research, vehicles were classified under two broad categories of four-wheeled vehicles (cars and buses) and two-wheeled vehicles (motorcycles and bicycles). Statistically, motorcycles represent 67.4%, buses cover less than 1%, bicycles have 1.5% and cars account for 26.4% of the vehicle population, and all have a different impact on the traffic flow characteristics, specifically for motorcycles and cars, based on their volume and effect on the predicted driver behavior model.

Cars, buses and motorcycles (moto) have respective odds ratios of 10.389, 9.094 and 1.514, respectively, which are greater than 1; hence, the probability of falling into the target group to give access to crossing pedestrians is greater. Vehicle type has a considerable effect on drivers’ behavior in the model to give access to crossing pedestrians.

4.3. Effect of Weekdays

Considering weekdays and their effect on the driver’s behavior, the model shows that the odds ratio varies between 0.413 and 0.925 and still is less than 1. This is one reason why the probability of falling into the target group of stopping and giving access to pedestrians is much less and limited regardless of any day of the week. It can be noted that vehicle flow number during the week was found to be almost uniformly distributed from Tuesdays to Saturdays and presented an abrupt fall of around 3% on Sundays, as per Table 2. This may be related to weekend breaks/being off work for activities.

4.4. Effect of Vehicle Density

Vehicle density is expressed in terms of the number of vehicles per kilometer length of a roadway. Referring to Table 2 and considering high vehicle densities inform us that individual vehicles are very close to each other, while low densities indicate that greater distances between vehicles are experienced. In general practice, high-density vehicles will move slowly with a great chance of stopping at any time, giving the right to pedestrians to cross (10.6%), but a low vehicle density implies that vehicles are more spaced out and tend to move at a high speed, with little chance of stopping (3.1%) and giving access. As per our research outcomes, it is realized that the odds ratio of this independent variable is 1.956, that is, greater than 1, making the probability of falling under the target group of stopping and giving access to crossing pedestrians greater; hence, the vehicle density being low, medium or high affects the drivers’ behavior.

4.5. Effect of Pedestrian Density

The pedestrian density was estimated based on the counting of the number of people crossing a particular road width in a crossing event, and classified as less dense, dense, very dense and extremely dense. As per this research, the odds ratio for the pedestrian density variable is 0.610, i.e., less than 1, and indicates that the probability of drivers stopping is minimal/less.

5. Conclusions

The objective analysis of the alleged relationship between the dependent variables of drivers’ behavior of “stopping” and “not stopping” to give access to pedestrians to cross based on the independent variables traffic characteristics of peak hour period, vehicle type, day of the week, vehicle density and pedestrian density in the city of Kigali was analyzed with the help of a binary logistic regression model.

Based on the findings, lamentably, 82.4% of drivers violated crossing regulations, putting pedestrian safety at risk. Motorcyclists exhibited the most aggressive behavior toward pedestrians. About three quarters of all of the surveyed motorcyclists did not stop. On the flipside, car drivers were relatively less aggressive, where 60% managed to brake during pedestrian crossing events. While buses and bicycles share a negligible share of traffic with a collective percentage of 2%, they are likewise aggressive and would not always stop.

For instance, in a crossing event, cars were 10.389 times more likely to stop compared to bicycles. Moreover, it seemed that having multiple vehicles in a row meant it was safer to cross, where for each unit increase on the vehicle density scale, there were 1.956 more chances that every driver would stop to give right of way to pedestrians. This may be owed to an induction effect in traffic. In terms of real-world application, this study warns pedestrians crossing in the city of Kigali to pay much attention to two-wheeled vehicles as they are much more involved in non-stopping behavior than four-wheeled vehicles. Pedestrian safety at crosswalks is greatly affected by the vehicle density and type, as the main traffic flow characteristics that influence drivers to give access to pedestrians who are crossing. While most multiple tests were statistically significant—owing to a large sample size—traffic flow characteristics alone did not manage to predict where the variance in stopping behaviors originated from.

Only about 13% to 21% of the recorded traffic variables were able to predict the variance in the stopping behavior model, according to the Cox and Snell and Nagelkerke R² values, respectively.

Therefore, further research is encouraged to uncover other relevant parameters that would influence a driver to stop. These may include external factors like infrastructure characteristics or internal factors that may be unique for each driver.