Evaluating the Relationship between Surrogate Safety Measures and Traffic Event Severity in Terms of Human Perception of Danger: A Perspective under Indian Traffic Conditions

Abstract

The current study aimed to develop a relationship between surrogate safety indicators and human judgement of severity. It has been demonstrated that human observers frequently display excellent agreement when asked to assess traffic incidents by their level of danger. Therefore, this research examines, in depth, how surrogate safety indicators might be used to represent human judgement of the severity of traffic incidents. This study analyzed 1141 traffic incidences of various vehicle categories according to their behavior during an interaction. Furthermore, ordinal logistic regression was used to develop a model for evaluating the most significant objective indicators relevant to people’s perceptions of danger. The findings indicated that the most crucial data for determining the severity of a traffic event is found in its earliest conditions, which are defined as the beginning of an evasive action. Moreover, factors affecting both closeness and collision consequences are significant and should be included in severity metrics.

1. Introduction

According to the global status report on road safety [1], 1.35 million road accidents occur globally in a year, of which developing countries account for around 90% of all casualties. Pedestrians, cyclists and motorcyclists constitute 54% of all road accident-related deaths worldwide, not only resulting in personal losses, but also national economic losses. Furthermore, due to rapid urbanization and the growing motorization rate, the rate of crashes has increased exceptionally, with an average of 1230 accidents and 414 deaths every day, and nearly 51 accidents and 17 deaths every hour [2]. This renders road safety a very crucial issue, especially in developing countries like India. One of the critical reasons for this is the diverse traffic conditions in India, with high-speed vehicles of differing characteristics sharing the same road space, creating a heterogeneous traffic condition, which makes road safety analysis complex. Moreover, intersections are particularly dangerous because of risky driving maneuvers, such as sudden shifts in vehicle speed, unforeseen lane changes and lane indiscipline [3].

For the safety analysis of intersections, traditional techniques have been used in India. However, one of the most substantial concerns with using the conventional techniques is their reliance on the occurrence of serious accidents before any hazardous site or situation can be identified and corrected [4]. Numerous studies have extensively discussed the drawbacks of relying solely on conventional traffic accident data [5,6,7].Therefore, surrogate safety measures have been suggested as a viable alternative to traditional accident data to address these issues. These measures are explanatory measures that can be easily recorded or gathered that relate to road networks and vehicle behavior. They are independent of direct crash data and have grown in importance in recent studies on traffic safety [8]. The main goal of these measures is to estimate the predicted frequency of crashes and injuries by evaluating non-crash incidents and to obtain a deeper understanding of the numerous causes and mechanisms that contribute to accident occurrence [9]. The key benefit of using surrogate safety measures is that they occur more often than crashes and have a proactive approach to analyzing traffic conflict, with a smaller observation period and better statistical results. The primary assumption underlying the entire surrogate safety measures theory is that traffic incidents can be classified into stages according to their severity level. Historically, traffic safety severity has been commonly presented as ‘proximity to an accident’. The adoption of the Vision Zero paradigm in traffic safety ((aims to eliminate all fatalities and serious injuries in traffic [10] marks a change from an overall focus on accident prevention to a more targeted approach that focuses specifically on the subset of accidents resulting in serious injuries and causalities. To align with this emerging perspective, the concept of severity for traffic occurrences should be updated and defined as “proximity to a serious injury”, instead of “proximity to an accident” [11]. However, in this definition, it is unclear how severity can be assessed using objective and accessible indicators, which is a requirement for surrogate measures to be helpful rather than merely a theoretical idea [6]. While there is empirical evidence suggesting the credibility and accuracy of how human observers perceive dangers in traffic situations (which is explained in detail in the following section), it is critical to recognize that using human observers as a measuring tool includes several drawbacks. When processing large amounts of traffic data, using humans can be costly and often unfeasible. On the other hand, as automated data collecting tools are becoming increasingly common in the analysis of surrogate safety, it is necessary to represent the theoretical severity using a combination of objective metrics and the indicators derived from the data that these tools generate. Therefore, the main hypothesis of this research is to conduct a comprehensive exploration into how human assessments of traffic situation severity can be translated into objective safety indicators under heterogenous traffic conditions. This involves creating a decision-making system that assesses the severity of two traffic situations and determining which of the objective indicators most closely aligns with the human decision when faced with the same choice.

In order to conduct this study, videographic data were collected during daytime hours, under normal weather conditions in the summer season at six uncontrolled intersections situated at Tier II cities of India. These conditions provided drivers with unobstructed visibility and a realistic portrayal of road safety in optimal circumstances. As visibility is one of the crucial factors in road safety [12] and it encompasses various aspects that can significantly impact driving conditions—especially at night times where drivers need to mitigate visibility-related risks [13]—it is crucial for drivers to adjust their behavior and use the appropriate precautions, depending on the specific conditions [14]. This may include reducing speed, using headlights or fog lights and maintaining and being vigilant of potential hazards. Therefore, as the data collection in this study was conducted under very specific weather and environmental conditions, the results will only be applicable if the specific conditions are maintained.

This paper is organized as follows: The following section presents the literature review relevant to surrogate safety measures and human perception of safety and shows the need for this study. The third and fourth sections present the data collection and data extraction-indicator estimation processes. The fifth and sixth sections discuss the analysis of road user behavior and the relationship between the human perception of safety and objective measures using ordinal logistic regression. Lastly, the concluding section summarizes the paper and provides conclusions regarding the study, including the limitations and areas for future research.

2. Literature Review

Over the past few years, road safety monitoring has evolved, and a more proactive approach has been adopted. Earlier road safety analysis was conducted using the police crash data report, but there are well-known issues with these kinds of reports. Being a reactive process, it has significant drawbacks like underreported cases, a lack of behavior analysis and is very time-consuming [15,16]. Therefore, surrogate safety measures have been introduced, and a traffic conflict technique has been developed. In the traffic conflict technique, in a scenario where two or more commuters are approaching one another in time and space, a collision will eventually occur if their movements do not change, referred to as a conflict [17]. Traffic conflict measures are typically used to identify when a traffic event transitions from a typical interaction to a conflict and, ultimately, to a collision [3]. Most (more than 50%) crashes occur at urban intersections due to dangerous driver actions and movements [4]. One of the reasons can be drivers from different directions occupying a single space at a junction, which reduces network capacity, delays drivers and poses a safety concern [7].

The definition of surrogate measures includes not only parameters like Post Encroachment Time (PET), Time to Collision (TTC) or TTC-Integrated, but also traffic characteristics such as traffic volume, delay and speed [6]. By incorporating these additional factors, the definition of surrogate measures becomes more comprehensive and inclusive and considers anything that could potentially lead to conflict on the road as a surrogate measure. The most often used safety indicators, such as Time-to-Collision [18] and Post-Encroachment Time [19], and their modifications only evaluate one aspect of safety [20], i.e., proximity between two road users who may collide. This measurement only accounts for one part of the possible accident severity. The other aspect of safety, the potential repercussions of a hypothetical conflict, has been considered only by a few researchers. The Swedish traffic conflict technique is one of the few techniques that considers both the TTC at the moment where the road user detects the risk and takes evasive action and the speed of the road user at that instant to evaluate the severity of a traffic event [21,22]. A higher speed with a low TTC value is believed to raise the severity of the potential repercussions, exacerbating the danger. In contrast, the Dutch objective conflict technique for operation and research (DOCTOR) uses a subjective score representing the likelihood of injuries in a collision [23,24]. The score is determined by objective criteria such as the road user and maneuver type, controlled or uncontrolled situation and specific attributes like the presence of evasive action. Other indicators, like Delta-V and combined risk indices, have also been proposed; however, their application is constrained as they rely on specified assumptions and are only valid in certain circumstances. Svensson [17], in a validation study of the Swedish traffic conflict technique, included a subjective measure of conflict danger. The conflicts chosen based on the danger rating showed the strongest association with accidents reported by the police. Human perception of danger is a comprehensive process that is essential for survival and decision-making to lessen the possible harm; it may inspire people to take preventative measures, stay away from dangerous circumstances or participate in protective behaviors. It is crucial to understand how people perceive danger in disciplines like risk assessment or traffic safety engineering.

One of the important questions is whether depending on human observers’ perception of danger in a traffic event is an appropriate way to determine ground truth or if it is biased. However, some empirical evidence suggests that human judgments are reliable and valid for detecting severity in traffic events. During the 1980s, which was a significant period for the advancement of traffic conflict techniques based on human observation, multiple studies were carried out to evaluate the reliability of observers. The findings showed that with the right initial training, there is good agreement between observers in terms of identifying traffic conflict [22,25]. Numerous calibration studies, comprising up to ten distinct traffic conflict techniques (TCT), have also confirmed a high level of agreement between observers regarding the severity-based rating of identified conflicts based on their risk level [24,26]. In conclusion, it seems humans have an innate ability to assess the level of danger in a traffic situation, particularly when it is based on an actual observation rather than a hypothetical scenario. Furthermore, this technique could be the most effective means of gauging the theoretical notion of “severity” as ratings derived from human judgments cannot contradict common sense [11].

Nonetheless, human observers have certain limitations and can be used to a certain extent as a measuring tool. Using human resources to analyze large amounts of traffic data can be expensive and sometimes impractical for analyzing extensive traffic data. Also, more recently, many researchers have used automated traffic data collection and extraction tools [15,20,27] and trajectory-based data for surrogate safety analysis [28,29,30,31,32,33]. Using micro-level behavioral data, Laureshyn et al. [30] proposed a conceptual framework to assess traffic safety using trajectory data. Continuous profiles were calculated for a detailed understanding of the interactive process, and the continuous trajectory profiles of indicators (TTC & GT) of individual interaction of pedestrians with vehicles were studied [32,33,34]. Considering that, it is important to establish the theoretical severity through the indicators available in the data generated by these tools.

This study aims to first conduct a detailed analysis of road user behavior traits in various vehicle–vehicle interactions, and then to thoroughly analyze how human assessments of the severity of traffic situations can be expressed using objective safety indicators. To achieve this, an ordinal logistic regression technique was used that compares the severity rating given by observers and investigates which objective indicators most closely align with human decision-making for the same selection.

3. Data Collection

A total of six uncontrolled intersections in two Indian cities (Nagpur, Visakhapatnam) were studied; namely: Nandanvan square, Coffee house square, Bhim square, Ambedkar square, M.V.P. Colony square and Kailash Nagar square. The video cameras were mounted at an elevated position with a clear and suitable view.

To analyze the traffic data, this study considered paired interactions involving two vehicles, and vehicle tracking was conducted by extracting the data, frame by frame, from the recorded videos. The videos were recorded at a frame rate of 30 fps, and the length and width of a reference grid from the study area were collected for calibration.

Table 1. Details of study sites.

Name of Site and Location ID	Image	City	Traffic Volume (Vehicles in Two Hour)
Nandanvan Square		Nagpur	5358
Coffee House Square		Nagpur	4567
Bhim Square		Nagpur	6129
Ambedkar Square		Nagpur	4782
MVP Square		Visakhapatnam	4843
Kailash Nagar Square		Visakhapatnam	5631

provides a summary of the observed intersections.

The following criteria were used to select the study sites:

(a)

Uncontrolled four arm intersection;

(b)

No horizontal curvature or vertical gradient;

(c)

Substantial volume of crossing vehicle traffic from all directions at the intersection;

(d)

Presence of an elevated point to obtain a clear view of the intersection and approaching arms for videographic data;

(e)

No obstructions or electric wires in the vicinity of the intersection that could hinder the trajectory extraction process following data collection.

After collecting the data, a frame-by-frame extraction technique was used to extract the data, with a focus on identifying vehicle–vehicle interactions. The trajectories of the vehicles involved in these interactions were extracted using a semi-automated tool (Kinovea 8.27). Figure 1 provides an overview of the study methodology.

The methodology used to assess the correlation between the surrogate safety indicators and human judgment of severity drew inspiration from a recent publication [11]. The objective of using this methodology was not to replicate the results of the prior study, but rather to ascertain whether applying a similar strategy—but using a different logistic model, involving three categorical variables—would result in different results under heterogenous traffic conditions.

4. Data Extraction and Indicator Estimation

To assess the overall behavior of the road users in our study, a comprehensive trajectory profile of the vehicles was required. After reviewing the literature, Kinovea (semi-automated tool) was found to be the most suitable tool for accurately tracking vehicles [33,35,36,37]. One of the key advantages of using Kinovea is that it is an open-source and free tool with a user-friendly interface. Thus, Kinovea 8.27 was used in our study to extract the linear kinematic characteristics—such as the trajectories, speed and distance—from the video data of all the intersections. Table 2 summarizes the various indicators that were derived from these trajectories, along with their brief description.

Several safety measures that can accurately calculate the safety of a traffic event have been proposed in earlier studies. For example, time to collision (TTC) and post encroachment time (PET) are some common safety measures [20]. These measures can be used to anticipate possible crashes and near misses, providing important information about the safety of traffic situations. Many of these measures can be derived from the trajectories of road users and a few other characteristics, like the weight and dimension of a vehicle [30].

Only those indicators that can be derived from the trajectories of vehicles were used in this study. Some clarification regarding the choice of indicators is presented in this section. Although TTC is the most commonly used surrogate safety indicator, its applicability is somewhat constrained; it requires the presence of a collision course to calculate its value and cannot be calculated for many of the less severe scenarios, which is a drawback. Given that, in this study, we are interested in situations spanning the complete severity continuum, $T_2$ (time remaining for the latest road user to arrive at the potential conflict area) was chosen over TTC as it is a more adaptable measure [20,30]. TTC counts the time before a potential collision, whereas $T_2$ measures the time needed for the latest road user to reach the conflict area. When a crash is about to happen, $T_2$ gives the same advantages as TTC, but also supplies helpful information when there is no chance of a collision. As a result, this study used $T_2$ rather than TTC as a reliable safety indicator. The other measure used in this study is distance. The main benefit of using distance as a measure is the simplicity of its calculation.

There is an advantage to using straightforward universal measurements in comparison to complex ones that may be subject to misinterpretation [38]. This study focused on two forms of distances: the shortest straight-line distance between the road users’ closest points and the distance along their predicted paths to the point of conflict (see Figure 2).

The other surrogate measure is PET, which is defined as a time interval between the first road user’s departure and the second road user’s arrival at the point of conflict [19], whereas gap time is used to check the temporal closeness of the vehicles [39].

The deceleration-based measures and speed were also estimated for the vehicles involved in the interaction to illustrate the possible consequences if the crash occurs.

Table 2. Objective Indicators.

Indicator	Definition
Evasive action (EA)	Evasive action is a categorical variable (If EA is present = 1, if not EA = 0) that indicates whether any of the road users have taken any evasive action or not.
Time until collision (T2)	The amount of time remaining until the latest road user reaches the potential collision point [30]. When on a collision course, this is equal to the TTC.
Shortest distance (D1)	Euclidean distance (Shortest distance).
Sum of distance (D2)	The sum of distance travelled by the road users to reach the potential conflict area.
Post Encroachment time (PET)	The time interval between the first road user’s departure from the potential conflict area (who arrived there first) and the entry of the second road user [19].
Deceleration rate (DR)	Deceleration rate of the road user. In cases of acceleration or no deceleration, DR is taken to be zero [40].
Speed (V)	Speed of the vehicles involved in an interaction.
Gap Time (GT)	The time interval between the second vehicle arriving in the potential conflict area after the first vehicle leaving the conflict zone when both proceed at the same speed and trajectory [39].

Table 2. Objective Indicators.

Indicator	Definition
Evasive action (EA)	Evasive action is a categorical variable (If EA is present = 1, if not EA = 0) that indicates whether any of the road users have taken any evasive action or not.
Time until collision (T2)	The amount of time remaining until the latest road user reaches the potential collision point [30]. When on a collision course, this is equal to the TTC.
Shortest distance (D1)	Euclidean distance (Shortest distance).
Sum of distance (D2)	The sum of distance travelled by the road users to reach the potential conflict area.
Post Encroachment time (PET)	The time interval between the first road user’s departure from the potential conflict area (who arrived there first) and the entry of the second road user [19].
Deceleration rate (DR)	Deceleration rate of the road user. In cases of acceleration or no deceleration, DR is taken to be zero [40].
Speed (V)	Speed of the vehicles involved in an interaction.
Gap Time (GT)	The time interval between the second vehicle arriving in the potential conflict area after the first vehicle leaving the conflict zone when both proceed at the same speed and trajectory [39].

5. Behavioral Analysis

This section presents a detailed analysis of various vehicle categories’ behavior involved in an interaction. The trajectories of the vehicles were extracted from the video data collected at multiple study locations, and various indicators were estimated using these trajectories. Three indicators—namely, $\left({\mathrm{T}}_2\right)$ time until collision, gap time (GT) and speed (V)—were used to evaluate the behavior of the road users during an interaction, and the remaining indicators were used in establishing the relationship with human perception of danger. An example of an interaction between two aggressive two-wheelers is presented to provide a better understanding.

Example

This segment shows an example of a behavioral pattern where none of the vehicles took any evasive action. The speed, time until collision ${\mathrm{T}}_2$ and GT profiles of both vehicles were estimated using extracted trajectories. Figure 3, given below, depicts the interaction trend between two two-wheelers at a right angle, along with the profiles of the indicators in Figure 4.

The following interaction occurred between two two-wheelers (labelled in a green and yellow box) and is individually determined as a risky case. The entire interaction phase was initiated from the point ${\mathrm{P}}_1$ when the vehicle ${\mathrm{V}}_1$ (green box) observed the approaching vehicle ${\mathrm{V}}_2$ (yellow box); at point ${\mathrm{P}}_2$, the second vehicle ${\mathrm{V}}_2$ shows up in the range of assessment. Meanwhile, the vehicles managed to maintain a high speed.

The ${\mathrm{T}}_2$ reduced until it attained the minimum value at ${\mathrm{P}}_3$ as both the vehicles approached the possible conflict point. The GT, which permits a whole vehicle to cross through the possible conflict point, also decreased after a 0.5 s lag and attained its lowest value between ${\mathrm{P}}_3$ and ${\mathrm{P}}_4$. ${\mathrm{V}}_1$ crossed the possible conflict point just before the second vehicle reached ${\mathrm{P}}_4$, indicating interaction completion, whereas at ${\mathrm{P}}_5$, both the vehicles crossed the conflict point.

In the research sites, various categories of vehicles were observed, such as two-wheelers, cars, auto rickshaws, buses, light motor vehicles, e-rickshaws, etc. Among the total traffic observed at all sites, the major vehicle categories were two-wheelers, cars and auto rickshaws, comprising approximately 95 percent of the total traffic. Hence, only these categories were used to conduct the subsequent detailed analysis in order to obtain unbiased results.

Figure 5, below, shows sample graphs of pair wise vehicle–vehicle interactions, plotted to analyze the pattern and to determine if there is any notable difference in the indicators’ profile with the changing vehicle categories. Road user behavior was classified into two categories according to the indicators’ profile shape and the presence of evasive action. The details of both categories are as follows:

(1)

Non-Aggressive interaction: When one or both vehicles take any evasive action, it can be categorized into receptive road user behavior (non-aggressive behavior). Upon analyzing the ${\mathrm{T}}_2$ and GT profiles in Figure 5a, it is apparent that the vehicle interaction with various other vehicle categories generates a similar profile shape. The minimum values for both ${\mathrm{T}}_2$ and GT occur towards the middle or end of the interactive process.

The GT value starts to drop as two vehicles get closer to a potential conflict point until it hits its lowest value, which is close to zero, signalling that the two are most likely to arrive at the conflict point simultaneously. However, because of evasive action taken by the road user, the gap time started to increase again. The lowest value of GT can therefore be described as a risky point.

In Figure 5a, when the speed profiles of different interactions were analyzed, it was observed that the speed profiles decreased over time. And, once it reached the minimum value, it started to increase again, indicating that one or both road users had taken significant measures to avoid a potential collision.

Therefore, this behavior can be classified as a non-aggressive interaction as it involves an evasive action.

(2)

Aggressive interaction: In this type of interaction, it was observed that despite having low values for ${\mathrm{T}}_2$ and GT, neither of the road users took any evasive action. As can be seen in the speed graphs in Figure 5b, the speed profiles are nearly horizontal with respect to time.

As the vehicles approach the potential conflict point, the distance between them starts to decrease until one of the vehicles crosses the conflict point. Therefore, the riskiest point occurs near the end of the interaction. Hence, this behavior can be classified as an aggressive interaction that involved no evasive action, despite having a risk of collision. Also, when observing the trends of different vehicles, the ${\mathrm{T}}_2$ and GT profiles are different.

Distinguishing road user behavior visually based on speed profiles is a challenging task. Hence, the behavior can be identified based on the time when either ${\mathrm{T}}_2^{\mathrm{m}\mathrm{i}\mathrm{n}}$ or ${\mathrm{G}\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ occurred. In non-aggressive behavior, it is noticeable that ${\mathrm{T}}_2^{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\mathrm{G}\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ occurred simultaneously (either at the end or middle of the process) for all vehicle categories. However, this was not the case for aggressive behavior. In this behavior, a clear differentiation can be perceived in the occurrence of ${\mathrm{T}}_2^{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\mathrm{G}\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$. This disparity in the occurrence time of ${\mathrm{T}}_2^{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\mathrm{G}\mathrm{T}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ was attempted to be illustrated mathematically, as shown in equation below:

$${\mathrm{g}}_{\mathrm{m}}={\mathrm{t}}_{\mathrm{m}}\pm \mathsf{\delta }\mathrm{t},{\mathrm{t}}_{\mathrm{m}},{\mathrm{g}}_{\mathrm{m}}\in ({\mathrm{P}}_1,{\mathrm{P}}_2)$$

(1)

It was assumed that, if the interaction starts at time ${\mathrm{P}}_1$, then the two vehicles will each arrive at the potential conflict zone at time ${\mathrm{P}}_2$ and ${\mathrm{P}}_3$, respectively. As a result, ${\mathrm{P}}_2$ represents the moment when the first road user reaches the conflict zone, and ${\mathrm{P}}_3$ represents the moment when the second road user reaches the conflict zone.

If Equation (1) is fulfilled, it can be inferred that an interaction belongs to the first type of road user behavior; otherwise, it belongs to the second type (aggressive) of road user behavior. Additionally, ${\mathrm{t}}_{\mathrm{m}}$ and ${\mathrm{g}}_{\mathrm{m}}$ represent the minimum ${\mathrm{T}}_2$ and GT values, respectively, and δt represents the interval between these values.

As indicated in

Table 3. Observed vehicle–vehicle interactions instances at multiple study locations.

Vehicle Involved	Non-Aggressive Road User Behavior	Aggressive Road User Behavior
Two-wheeler–Two-wheeler	324	156
Two-wheeler–car	465	54
Two-wheeler–Auto	116	26
Total	905	236

, 1141 interactions were divided into two types of road user behaviors using Equation (1). It can be observed from Table 3 that the vehicles most frequently involved in non-aggressive road user behavior are two-wheelers and cars; the bigger size and width of these vehicles, which can psychologically induce vehicles to take evasive action, is one of the important causes of this. On the other hand, in aggressive road user behavior, the most common vehicle interaction type is two-wheeler–two-wheeler, which shows that two-wheelers comprise the most risk-taking road users.

6. Human Perception of Severity and Objective Measures

Further analysis was conducted to develop a relationship between the observer ratings and the objective measures. The detailed study was conducted on all 1141 interactions, and the following behaviors were observed in their trajectories:

(a)

The First vehicle accelerates and/or alters trajectory to cross a conflict point before the second vehicle arrives;

(b)

The Second vehicle slows down, stops or changes trajectory to avoid a collision;

(c)

Both vehicles take evasive action, and one of the vehicles takes the lead and crosses a possible conflict zone before the second vehicle;

(d)

None of the vehicles take any evasive action.

A trained observer technique was then used to rate the severity of the interactions using the above behavior patterns. Five trained observers, all from different cities of India, were first informed of the purpose of the study, along with the fact that the likelihood of being involved in a collision depends on both how close the incident is to becoming a crash and what steps the involved vehicle or vehicles take to avoid a collision before they arrive at a potential conflict point. The observers were asked to categorize each interaction into three risk categories: low (0), medium (1) and high (2).

After the completion of the risk level ratings, Cronbach’s Alpha method was used to evaluate the consistency between all of the observers. This method is a simpler way to determine how consistent the responses are by providing a coefficient (α) of consistency [41]. The range of the Cronbach’s Alpha coefficient (α) is between 0 and 1, where a higher number denotes a higher level of consistency between observers.

The (α) value in the current study was determined to be 0.82, indicating an acceptable level of consistency [42,43].

The entire interaction is divided into three phases in this study; namely, the preliminary phase, peak phase and end phase. The indicators were organized based on a particular phase within the situation development process to which the indicators were most related (refer to Figure 6 and

Table 4. Moments for calculating objective measures.

Phase	Definition	Time Instance Notation	Indicators	Included in the Model
Preliminary Stage	The moment when first evasive action was taken.	EA	EA, $T_2$, $D_R$, V	D
Peak Stage	The point in time when T2 reaches its lowest value in the event.	$T_2^{min}$	$T_2$, $D_R$, V, $D_1$, $D_2$	A, B, C, D
	When the travel-to-collision-point distance of each road user reaches its minimum value during the interaction.	$D_2^{min}$	$T_2$, $D_R$, V, $D_1$, $D_2$	A, B, C, D
End stage	The point in time when the first road user arrives at the potential conflict zone.	$T_1$	$T_2$, $D_R$, V, $D_1$, $D_2$	A, B, C, D
	The point in time when the second road user reaches the potential collision zone.	$T_2$	PET	A, B, C, D

). It should be noted that some indicators are continuous, meaning that they generate values at many points in time and may, therefore, be present at several stages.

The preliminary phase refers to the start of the interaction, which can be understood in several different ways, such as when road users become visible in a camera view or when they begin interacting without any barriers. However, in the context of surrogate safety, the beginning of a conflict is frequently identified as the moment when a road user initiates evasive action, signifying a change from being uninformed of risk to taking measures to prevent it [20]. Therefore, in this study, the term “preliminary phase” refers to the moment when either of the road users took the first evasive action.

The term “peak phase” refers to the time when the relevant measure reaches its maximum or minimum value in an interaction. As different indicators may reach their maximum or minimum values at different time intervals, multiple values of the peak phase are provided in this study, as can be seen in Table 4. Lastly, the “end phase” of the interaction refers to the final stage, which is typically the last moment when a collision could still occur, even if theoretically. In this study, this stage refers to the moment when the first road user reaches the potential conflict point.

Model development: A model focused on human perception was created to assess the relationship between the human judgement of severity and surrogate measures. Five trained observers were asked to rank the perceived danger levels of interactions, classifying them as either safe, mild or severe. These ratings were collected using a Likert scale, which is an ordinal scale, meaning that the response variable had more than two categories and these categories had a predefined order. Therefore, an ordinal logistic regression model was used to develop this model.

Equation (2) of ordinal logistic regression can be expressed as below [44]:

$$\mathrm{logit}\left[P(y\le j)\right]=\log [\frac{P(y\le j)}{1-P(\mathrm{y}>\mathrm{j})}]={\alpha }_j+{{\beta }_{1}X}_1+{{\beta }_{2}X}_2+\dots \dots +{{\beta }_{k}X}_k,\mathrm{j}=1,2,3\dots ,\mathrm{c}-1$$

(2)

where:

• y = response variable;
• $X_1$, $X_2$,… $X_k$ = explanatory variables;
• c = number of categories for response variable;
• $P(y\le j)=$ cumulative probabilities for $jth$ category.
• P (y > j) = probability that y is greater than j;
• ${\alpha }_j$ = intercepts parameter;
• $\beta$ = parameters related to explanatory variable.

This study used the maximum likelihood approach to fit all of the logistic regression models. This test uses a chi-square distribution with n-k-1 degrees of freedom, where n represents the sample size and k represents the number of explanatory variables. The ordinal logistic regression technique was used to develop the above models. The regression coefficients were tested for significance at a level of 95%, which means that any variable with a p-value of less than 0.05 is considered to be statistically significant. Below,

Table 5. MODEL A.

Parameter		B	Std. Error	Hypothesis Test			Elasticity (Individual Percentage Contribution)
				Wald Chi-Square	df	Sig.
Threshold	[Severity = 2.00]	−10.200	1.0010	103.833	1	0.000
	[Severity = 1.00]	−0.294	0.9813	0.090	1	0.764
$T_2$ ($T_2^{min}$)		−0.570	0.1037	30.256	1	0.000	−0.205
$D_2$ ($D_2^{min}$)		−0.473	0.1184	15.953	1	0.000	−0.1822
$D_1$ ($D_2^{min}$)		−2.888	0.4982	33.602	1	0.000	−0.3514
$D_1$ ($T_1$)		−0.408	0.0932	19.186	1	0.000	−0.1982
V ($T_2^{min}$)		0.334	0.0890	14.090	1	0.000	0.213
$D_R$ ($T_2^{min}$)		−0.333	0.0946	12.391	1	0.000	−0.111
PET ($T_2$)		−0.877	0.3843	5.212	1	0.002	−0.197
EA		1.143	0.2880	15.747	1	0.000	0.2429
AIC = 624      BIC = 792

,

Table 6. MODEL B.

Parameter		B	Std. Error	Hypothesis Test			Elasticity (Individual Percentage Contribution)
				Wald Chi-Square	df	Sig.
Threshold	[Severity = 2.00]	−22.792	0.8587	704.498	1	0.000
	[Severity = 1.00]	−9.885	0.4568	468.193	1	0.000
$T_2$ ($T_2^{min}$)		−0.789	0.1154	46.717	1	0.000	−0.169
$D_R$ ($D_2^{min}$)		−0.263	0.0981	7.215	1	0.004	−0.098
$D_1$ ($T_1$)		−8.486	0.7121	141.991	1	0.000	−0.328
PET ($T_2$)		−1.591	0.2867	30.785	1	0.000	−0.182
AIC = 396            BIC = 512

,

Table 7. MODEL C.

Parameter		B	Std. Error	Hypothesis Test			Elasticity
				Wald Chi-Square	df	Sig.
Threshold	[Severity = 2.00]	−23.233	3.7402	38.585	1	0.000
	[Severity = 1.00]	−13.391	2.7741	23.300	1	0.000
$T_2$ ($T_2^{min}$)		−1.394	0.3234	18.569	1	0.000	−0.149
$D_1$ ($T_1$)		−8.183	1.6187	25.555	1	0.000	−0.374
$D_R$ ($D_2^{min}$)		−2.949	0.5994	24.214	1	0.000	−0.114
PET ($T_2$)		−4.059	1.4477	7.860	1	0.000	−0.208
AIC = 116      BIC = 160

and

Table 8. MODEL D.

Parameter		B	Std. Error	Hypothesis Test			Elasticity
				Wald Chi-Square	df	Sig.
Threshold	[Severity = 2.00]	−93.998	5.7783	264.627	1	0.000
	[Severity = 1.00]	−48.870	3.1290	243.936	1	0.000
$D_1$ ($T_1$)		−2.129	0.2511	71.917	1	0.000	−0.138
PET ($T_2$)		−0.410	0.0508	65.161	1	0.000	−0.210
$T_2$ (EA)		−15.616	1.6684	87.601	1	0.000	−0.397
$D_2$ (EA)		−2.071	0.2397	74.689	1	0.000	−0.134
$D_R$ (EA)		−2.171	0.3411	40.504	1	0.000	−0.037
AIC = 213      BIC = 356

show the regression co-efficient and goodness of fit test results for models A, B, C and D, which were developed using a forward selection method and only included statistically significant variables at 95% confidence level.

In the first model (Model A), a dataset including all 1141 interactions (with or without evasive action) was used as it was not feasible to estimate indicators for the moment of evasive action for the complete dataset.

Therefore, to determine a value for these indicators for every interaction, the present analysis was constructed with the following goals:

• At first, a logistic regression model (model A) was developed using the entire dataset (N = 1141), taking the human judgement of severity as a dependent variable and objective measures that could be estimated for every interaction in the dataset (excluding the indicators estimated at the moment of evasive action) as an independent variable. The aim was to determine if the presence of evasive actions held statistical significance in the model. The model can be represented as below:

MODEL A: Severity rating by human observers (Entire dataset = 1141)~Indicators from moments: ($T_2^{min}$), ($D_2^{min}$), ($T_1$), ($T_2$), class variable (EA).

The proxy indicator linked to evasive behavior, as demonstrated in Model A, was deemed significant and ranked second in significance, with the first being the distance. It appears that the pertinent information contained in the earliest conditions of a problem can be used to determine how serious it is.

2.

The dataset was then divided into two subgroups: the first subset is where evasive action was observed in one or both road users during an interaction, and the second subset is where no evasive action was observed by either of the road users. Using these subsets of data, two more models (models B and C) were then developed using the same set of explanatory variables. The aim was to examine whether the same indicators were statistically associated with the human judgement of severity in both subsets. The models can be represented as below:

MODEL B: Severity rating by human observers (With Evasive action, N = 905)~Indicators from moments: ($T_2^{min}$), ($D_2^{min}$), ($T_1$), ($T_2$).

MODEL C: Severity rating by human observers (With No Evasive action, N = 236)~Indicators from moments: ($T_2^{min}$), ($D_2^{min}$), ($T_1$), ($T_2$).

Models B and C were compared with the aim of determining whether the indicators associated with the evasive and non-evasive subsets were similar. The findings, presented in Table 6 and Table 7, revealed that $D_1$ ($T_1$) had the most considerable influence on both models, irrespective of the presence of other significant variables at different time intervals during the event, apart from ($T_1$).

Thus, it can be inferred that this group of variables could be employed for all events, irrespective of whether there was any evasive action taken or not.

Finally, the last model was developed using only those events where evasive action was observed, and all of the variables presented in Table 1 were considered. This model aimed to determine whether or not the indicators from the moment of evasive action were helpful in estimating the severity with respect to the human observer ratings. The model can be described as below:

MODEL D: Severity rating by human observers (With Evasive action, N = 905)~Indicators from moments: EA, ($T_2^{min}$), ($D_2^{min}$), ($T_1$), ($T_2$).

Models B and D have been compared to evaluate the impact of the variables estimated at the moment of the first evasive action.

Table 6 and Table 8 reveal that the significant variable sets for both models varied in terms of their emphasis on different stages of the event.

The highest contribution of variables in Model B are the moment of $D_1,$ ($T_1$) and PET ($T_2$), whereas, in Model D, the variables associated with the moment of evasive action (EA) have the greatest importance.

Akaike information criteria and Bayesian information criteria are used in this study to compare the models as the smaller the values, the better the model [45].

The AIC and BIC scores are defined as below:

     BIC = K × ln (N) − 2 × ln(l);
AIC = 2 × K − 2 × ln(l).

where:

• K = number of parameters;
• N = number of observations;
• ln(l) = maximized value.

From the data in Table 3, it is evident that Model D is the preferred model when compared to Model B as it had lower AIC and BIC values. Lastly, to validate the models, confusion matrixes were made for all four of the developed models. As can be seen in Figure 7, given below, the accuracy of all the models was above (95%), with Model D being the highest (98.1%).

7. Discussion

This research aimed to firstly analyze the different road user behavior and secondly to find out the objective measures that play a significant role in describing and reflecting human personal understanding of danger in a traffic event under heterogeneous traffic conditions.

Firstly, after analyzing the road user behavior at multiple intersections, it can be recommended that more attention should be given to educating drivers on road safety, as just focusing on infrastructure will not be sufficient. In education, they can be told about stopping, yielding at intersections and being more observant of traffic and pedestrians coming from different arms. This will aid in reducing the number of critical interactions.

One of the important findings of this study is that the existence of evasive action plays a critical role in determining the degree of perceived danger. As seen in Model A, the proxy indicator associated with evasive action was deemed significant and ranked second in significance. It appears that the severity of a situation can be concluded by the relevant information already present in its initial conditions. Secondly, no individual indicator could adequately explain the perceived level of risk in an interaction. The results presented in Table 5, Table 6, Table 7 and Table 8 above indicate that the variables related to the proximity (time, distance) and severity of the consequences (speed, deceleration rate) have the highest contribution for all the models.

Model D incorporates a traffic situation from all three phases (preliminary, peak and end), and it was observed that the most significant contributions were estimated in the preliminary phase, as seen in Figure 7. However, the peak phase made some notable contributions, while the end phase did not offer much important information. This observation is similar to the study conducted in 1991 and a recent study (2022), in which the author mentioned that the observers could judge the risk of a traffic conflict based on the first few seconds of its development [11,46].

8. Conclusions

By analyzing video-recorded traffic incidents under heterogenous traffic conditions involving right-angled interactions and by using an observer’s perception of the danger, the following are some of the main contributions of the study.

• The first contribution of this research is informing researchers about the importance of evasive action involved in an interaction. It has been established that interactions involving evasive action are always risky; therefore, these interactions should always be studied to calculate the road safety of an uncontrolled intersection.
• Through an examination of road user behavior at uncontrolled intersections involving different types of vehicles, the study revealed that two-wheeler users tend to exhibit a higher degree of risk-taking behavior. Consequently, when developing and designing road infrastructure, it is essential to pay special attention to this group. Furthermore, specific training programs should be implemented to make them aware of the risks associated with such aggressive behaviors.
• As, at present in India, it is still not clear which surrogate indicators should be used for particular conflict types and which phase of the interaction is the most important for analyzing road safety, this study will be considered as a step to guide researchers about the surrogate indicators that are significant and which phase is the most crucial while calculating safety at an uncontrolled intersection. This will save the time-consuming process of indicator selection, data extraction and the modelling process for the researchers working in this field.
• Also, this study suggests that no individual indicator could adequately explain the perceived level of risk in an interaction. The results presented in this research indicate that the variables related to both proximity (time, distance) and the severity of the consequences (speed, deceleration rate) should be used while calculating the risk associated with uncontrolled intersections.
• The model developed in this study can be applied to cities with similar socio-economic and demographic characteristics. However, for cities with distinct profiles, it is crucial to validate this model, as indicated in the limitations section.
• Researchers are not required to compute surrogate indicators for every phase (i.e., preliminary, peak and end phases). As the primary phase contains the most critical information about the impending interaction, calculating surrogate measures during the initial phase will yield accurate safety results.
• Moreover, it may be prudent, during the modeling process, to confine the scope of the surrogate analysis to events that clearly involve evasive actions, excluding interactions without such actions. This approach can significantly reduce the time-consuming data extraction and modeling efforts for researchers.