Development of New Performance Measures Based on Data Mining Weights for Hotspot Identification

Abstract

In this study, new performance measures are proposed for hotspot identification in urban intersections. These measures reflect severity factor weights, which are determined based on data mining. To estimate the severity factor weights of crashes at urban intersections, the study utilizes tree-based random forest (RF) and extreme gradient boosting (XGB) methods. The importance of variables in the severity classification model is standardized and utilized for calculating the score of each crash, which is aggregated into intersections. The aggregated score is used as a dependent variable for the safety performance functions (SPFs) in the network screening process. To illustrate the under-dispersed severity score aggregation data, SPFs that follow the COM-Poisson distribution as well as the negative binomial (NB) are developed. Independent variables in SPFs set up intersection geometry elements that can be collected from online GIS services. Four additional performance measures are proposed, each reflecting a severity weight. Data about a total of 42,513 intersection crashes from 2017 to 2018 in South Korea were collected for crash injury severity analysis. Hotspot identification was performed on 81 intersections, and three consistency tests were conducted to validate the four measures. Tests show that the RF-based weighted $N_{pred, RF}$ and $N_{EPDO, RF}$ have the best consistency. Since the severity factor weights of each crash are reflected, intersections vulnerable to dangerous crashes can be analyzed in more detail. Using this method, it is expected that effective safety improvement project plans can be established with the input of safety managers in the future.

Keywords

data and data science safety calibration crash analysis data mining network screening

The Highway Safety Manual (HSM) presents the network screening process used to identify sites that are expected to benefit most from implementing road safety improvement projects ( 1 ). Identified sites are commonly referred to as “hotspots” (or “black spots” or “high crash locations”). First, populations and sample groups for statistical analysis must be established to identify hotspots. Subsequently, collectable data are reviewed. Based on this review, analytical performance measures can be selected. Typical performance measures include average crash frequency and crash rate. In the HSM, measures using the empirical Bayes (EB) method, which is widely used for safety evaluations, are also detailed in the calculation procedure ( 1 ). The equivalent property damage only (EPDO) average crash frequency also reflects injury severity with weights based on crash cost. The EPDO measure can identify sites where there are a relatively large number of serious crashes.

According to the hotspot identification procedure, sites that are counted as having frequent crashes can be identified. However, human factors, environmental factors, and vehicle factors that might be fundamental to the occurrence of crashes are not considered in the hotspot identification process. Thus, in this study, various existing studies were considered to compensate for these shortcomings. First, studies using performance measures presented by the HSM and related to hotspot identification were reviewed. In addition, studies considering both crash severity factors and crash frequency for hotspot identification were reviewed. The latest research trends in traffic safety related to hotspot identification were analzyed considering predictive models and safety analysis studies using safety performance functions (SPFs). Finally, research related to validation of performance measures used for hotspot identification has been compiled.

First, studies related to hotspot identification were considered. Relevant studies on a variety of topics have been conducted in the past, and some studies have established performance measures that consider severity (2 –15). Wang et al. used and compared the crash frequency, EPDO, relative severity index, and excess predicted average crash frequency using the method of moments, a cross-sectional analysis, considering the situation in which traffic data were not collected ( 6 ). Gross et al. performed hotspot identification using four performance measures: crash frequency, network screening, expected crash frequency with EB, and excess expected crash frequency with EB ( 16 ). The performance measures of most hotspot identification studies, including the previous two, are based on the content of the HSM, and this study also considered the development of new measures based on the HSM ( 1 ). Because hotspot identification studies use crash-frequency-based methods, there is a limit to reflecting the severity of the crash. Despite these shortcomings, however, there have been attempts to incorporate the severity of crashes into frequency. Afghari et al. proposed a crash count and crash severity joint model for hotspot identification ( 14 ). Unobserved heterogeneity in the crash severity data is not explained, so the authors wanted to improve these shortcomings using a joint model. In a similar approach, Yasmin and Eluru used a joint model that combines crash severity in the development of crash count prediction models ( 15 ). Their analysis demonstrates that a model reflecting the severity in relation to statistical suitability is superior to existing crash count prediction models. These two studies show that it is difficult to prove statistical significance because severity data have an uncertainty distribution. Thus, in most studies, step-by-step joint modeling was performed for accurate modeling and to capture the uncertainty distribution of severity data ( 17 ). These studies performed additional severity analysis separately from frequency-based hotspot identification. In other words, it is not intuitive as a study that performed additional severity analysis rather than identifying hotspot as a severity indicator. Therefore, in this study, new performance measures were developed to integrate severity analysis into the hotspot identification procedure. In addition, a modeling procedure for developing measures was established in consideration of the uncertainty of the severity data based on the considered content.

Finally, related studies were considered for validation of consistency for new performance measures proposed in this study. Cheng and Washington proposed consistency assessment criteria for hotspot identification methods ( 5 ). The authors presented five tests to validate performance measures in Site, method units. They determined that EB-based methods are the best. Guo et al. also proposed generalized criteria for evaluating hotspot identification methods ( 18 ). Their evaluation method was designed by generalizing the target, such as by increasing the duration compared with the evaluation method proposed by Cheng and Washington. This study was designed to reflect the test methods used in the previous study so that the test can be performed to analyze consistency.

The purpose of this study is to: (1) propose performance measures that reflect factors affecting crash severity as weights, (2) derive major factors of intersection crashes in South Korea and identify hotspots, and (3) conduct consistency tests to determine if they are suitable for hotspot identification. The research framework is presented in Figure 1 to help describe the composition of the study.

Figure 1.

Research framework.

Methodology

Network Screening

Safety Performance Functions (SPFs)

SPFs can be used as a predictive model for estimating the number of crashes at a location. In the HSM, there are SPF-based performance measures that can be used for intersection network screening. In this study, an SPF-based performance measure suggested by the HSM was used to identify intersection hotspots.

Various studies have been conducted to develop SPFs at intersections (1, 19 –23). Crash data have an over-dispersion problem where the variance is greater than the average. Therefore, in most studies, a negative binomial (NB) regression model that can solve the problem of over-dispersion is used ( 1 ). However, with some data, low sample means result in under-dispersion during the data collection and modeling process. The NB model has limitations in modeling these under-dispersed data ( 24 ). The analysis area in this study consists of 81 intersections in South Korea, with relatively small samples. Additionally, over-dispersion parameters cannot be produced in the model because they are under-dispersed because of the application of severity weights. Therefore, SPFs that follow a Conway-Maxwell-Poisson (CMP or COM-Poisson) distribution that can account for under-dispersion were developed. The COM-Poisson distribution is a discrete probability distribution that can capture several variance types (21, 25 –27). Therefore, it can be used as an alternative in situations where the NB model cannot be applied because of under-dispersion ( 24 ). The probability density function of COM-Poisson can be defined as follows (Equations 1 and 2):

P (Y_{i} = y_{i}) = \frac{λ_{i}^{y_{i}}}{Z (λ_{i}, v) {(y_{i}!)}^{v}}, y = 0, 1, 2, \dots, n, λ > 0, v \geq 0,

(1)

Z (λ_{i}, v) = \sum_{k = 0}^{\infty} \frac{λ^{k}}{k!^{v}} .

(2)

where

$Y$ = random variable (discrete count),

$Z (λ_{i}, v) = \sum_{k = 0}^{\infty} \frac{λ^{k}}{k!^{v}}$ (a normalizing constant),

$v$ = dispersion parameter ( $v > 1$ is considered under-dispersed and $v < 1$ is over-dispersed), and

$λ$ = centering parameter.

The centering parameter $λ$ represents the approximate mean when v is close to 1. There is a big difference from the meaning of the small $v$ .

Guikema and Goffelt proposed a COM-Poisson distribution to replace $v$ with $μ = λ^{1 / v}$ to provide a centering parameter because $v$ is expected to be too small for over-dispersion ( 27 ). The COM-Poisson formula is as follows (Equations 3 and 4):

P (Y_{i} = y_{i}) = \frac{1}{S (μ_{i}, v)} {(\frac{μ_{i}^{y_{i}}}{(y_{i}!)})}^{v},

(3)

S (μ_{i}, v) = \sum_{k = 0}^{\infty} {\frac{μ^{k}}{k!}}^{v} .

(4)

The COM-Poisson model can model both over-dispersed and under-dispersed datasets ( 26 ). The link functions are as follows (Equations 5 and 6):

\ln (μ) = β_{0} + \sum_{i = 1}^{p} β_{i} x_{i},

(5)

\ln (v) = γ_{0} + \sum_{j = 1}^{q} γ_{i} z_{i} .

(6)

where

$β, γ$ = coefficients, and

$x_{i}, z_{i}$ = covariates.

It is assumed that there are p covariates used in the centering link function and q covariates used in the shape link function. This is similar to the varying dispersion parameters of the Poisson-gamma (NB) model (28, 29). Lord et al. modified the existing formula by removing Equation 6 and estimating a single shape parameter $v$ ( 30 ). The analysis in the current study follows the method proposed by Lord et al. ( 30 ). In the current work, the NB model and the COM-Poisson model were developed according to the variance of the dataset.

EPDO Weights by Crash Cost in South Korea

The EPDO method of calculating EPDO scores on a per-intersection basis is utilized. In this study, EPDO scores as a performance measure suggested in HSM’s network screening procedure is used (Equivalent Property Damage Only [EPDO] Average Crash Frequency using SPFs) ( 1 ). The weighting factors are calculated relative to property damage only (PDO) crashes. Additionally, the proportions of crashes are calculated from the reference population to calculate the EPDO measure. Weights corresponding to severity KA and BC (KABCO injury scale) can be obtained by multiplying the calculated proposition by the EPDO weighting factors. These equations are as follows (Equations 7 and 9):

f_{y (weight)} = \frac{Crash \cos t_{y}}{Crash \cos t_{C}}

(7)

w_{EPDO, KA} = P_{K} \times f_{K} + P_{A} \times f_{A},

(8)

w_{EPDO, BC} = P_{B} \times f_{B} + P_{C} \times f_{C} .

(9)

where

$f_{y (weight)}$ = EPDO weighting factor corresponding to crash injury severity $y$ ,

$Crash \cos t_{y}$ = crash cost corresponding to crash injury severity $y$ ,

$Crash \cos t_{C}$ = crash cost corresponding to non-incapacitating crash (C), and

$f_{K, A, B, C}$ = EPDO injury (K, A, B, C) weighting factor.

In this study, $Crash \cos t_{C}$ is the reference value for calculating $f_{(weight)}$ because PDO crashes are not aggregated. Crash costs shared by Korea Transportation Institute were used, as shown in Table 1 ( 31 ).

Table 1.

Equivalent Property Damage Only (EPDO) Weights by Crash Cost Standards of South Korea

Severity	Conversion	Cost (KRW)	Weight
Fatal injury (K)	K	₩720,582,000	53.5
Incapacitating injury (A)	A	₩141,729,000	10.5
Non-incapacitating injury (B)	B	₩18,264,000	1.4
Possible injury (C)	C	₩13,476,000	1.0

In this study, the following six performance measures were proposed, including measures reflecting the importance of severity factors based on RF and XGB: excess predicted average crash frequency using SPFs: $N_{pred}$ , $N_{pred, RF}$ , $N_{pred, XGB}$ , and EPDO-predicted average crash frequency using SPFs: $N_{EPDO}$ , $N_{EPDO, RF}$ , $N_{EPDO, XGB}$ . The evaluation methods were performed to validate the proposed measures, and specific methods and validation results are presented in the next section.

Injury Severity Analysis Based on Data Mining Techniques

Previous research tried to reflect severity indicators in the hotspot identification process in various ways (14, 15, 17, 32). In this study, severity classification models based on the data mining method were developed. The importance of variables derived from the model were translated into weights through standardization and defined as new performance measures. The tree-based model, random forest (RF), and extreme gradient boosting (XGB) methods were used to derive severity factor weights (33 –35). The models perform well by efficiently constructing trees to operate in parallel and can be used to solve classification and regression problems (36, 37).

Random Forest (RF)

The RF method proposed by Breiman is one of the high-performance machine learning methods ( 33 ). Each tree that makes up an RF is created based on randomly selected samples and tree characteristics. Finally, the optimal model is determined by the voting method in the tree. It is known to effectively overcome local optimization and overfitting problems of single classifier decision trees. The RF method extends the tree classifier collection using bootstrap sampling. The results of the tree can then be used to evaluate the importance of the variables used in tree modeling. With bootstrap sampling, RFs are also measured to have fewer Gini impurities in their child nodes than in their parent nodes by applying the Gini impurity criterion. The Gini reduction for each individual variable is aggregated for all trees in the forest and used to produce variable importance measurements. Indicators of the importance of variables in RF’s classification model, derived through these procedures, are mean decrease accuracy (MDA) and mean decrease Gini (MDG). According to existing research, RF is widely used in traffic safety, especially in the classification of accident severity and in solving prediction problems (37 –41). In this study, the values were standardized and weighted to use the importance of the variables. Subsequently, the intersection SPFs were developed by aggregating weighted reflection scores.

Extreme Gradient Boosting (XGB)

XGB is an improved algorithm based on gradient boosting (34, 35). It performs well by efficiently constructing trees to operate in parallel, and is used to solve classification and regression problems (36, 37). In XGB, there are three variable importance indicators: gain, cover, and frequency. First, gain is an indicator that defines the relative contribution of the model, which is calculated by considering the extent to which each variable contributes to the random tree. The higher the value, the more important it can be compared with the values of other variables. Cover is the number of observations in the tree and node where the variable is associated with the model construction. Because all variables are calculated, they are expressed as percentages and presented as relative values. Finally, frequency is the ratio that a particular variable represents by weighting the relative time of the segmentation induced in the tree. This value is also translated as a percentage of weights for all weights, so the sum of the frequency values for all variables is one. While all three variables have a significant effect on the determination of importance, gain is known as the most important indicator of interpretation of relative importance. Therefore, in this study, only gain was used to determine the intersection characteristic analysis indicators in the XGB model.

Calculation of Crash Severity Weights for Each Crash Score

Standardization procedures are designed for giving weights of variable importance, as derived from the injury severity model. Gain, which represents the relative importance in XGB, does not require a separate standardization procedure because the sum of the total variable values is 1. However, the gain of RF is calculated because the sum of the total values exceeds 1. The standardized variable importance values are weighted and applied to individual crashes. The applied values are defined as $Scor e_{w, n},$ and the formula for the aggregated values per intersection is shown in Equations 10 and 11:

Scor e_{w, n} = \sum_{i = 1}^{k} (x_{i} \times γ_{i}),

(10)

N_{obs, (method)} = \sum_{n = 1}^{m} (Scor e_{w, n}) .

(11)

where

$Scor e_{w, n}$ = severity-weighted score of an individual crash,

$n$ = crash number at each intersection,

$x_{i}$ = value of variables,

$γ_{i}$ = importance of variables,

$i$ = number of variables in each crash data, and

$N_{obs, (method)}$ = observed total severity score by the tree-based method (RF, XGB).

Data Collection and Preparation

In this study, the analysis was conducted with crash data from 2017 to 2018 at urban intersections in Seoul and Busan in South Korea. Injury severity analysis was performed for a total of 42,513 crashes, of which hotspot identification was performed using 1,990 crashes at 81 signal intersections.

The crash data were collected from KoROAD, which is the traffic crash analysis system in South Korea. The data include crash characteristics such as human factors, environmental factors, and vehicle factors, as well as variable definitions and detailed descriptions for injury severity analysis, as given in Table 2. The injury severity group, which is set as the dependent variable, is defined as K, A, B, or C, except for PDO crashes. In South Korea, crashes that are not reported to the police are not counted because the police aggregate crash data. Because of the characteristics of the insurance system in South Korea, even small crashes, such as PDO crashes, are accompanied by simple hospital care to claim insurance money. As a result, most crashes are recorded as at least a possible injury crash. Thus, fewer than 10 PDO crashes identified in this study were considered outliers and excluded. Finally, injury severity is classified into four categories: possible injury (severity C class), non-incapacitating injury (severity B class), incapacitating injury (severity A class), and fatal injury (severity K class).

Table 2.

Variable Definitions and Descriptions for Crash Injury Severity Analysis

Variable description	K		A		B		C		Total
Injury severity	324	0.76%	13,195	31.04%	25,991	61.14%	3,003	7.06%	42,513
Time
Dawn	60	1.48%	1,331	32.84%	2,430	59.96%	232	5.72%	4,053
Daytime	112	0.71%	4,774	30.41%	9,660	61.54%	1,152	7.34%	15,698
Evening	47	0.49%	2,927	30.35%	5,914	61.33%	755	7.83%	9,643
Morning	62	1.10%	1,864	33.00%	3,359	59.47%	363	6.43%	5,648
Night	43	0.58%	2,299	30.77%	4,628	61.95%	501	6.71%	7,471
Week
Weekday	244	0.78%	9,761	31.13%	19,135	61.03%	2,214	7.06%	31,354
Weekend	80	0.72%	3,434	30.77%	6,856	61.44%	789	7.07%	11,159
Season
Fall	95	0.86%	3,438	31.28%	6,719	61.14%	738	6.72%	10,990
Summer	66	0.62%	3,251	30.42%	6,554	61.33%	815	7.63%	10,686
Spring	78	0.73%	3,352	31.58%	6,448	60.76%	735	6.93%	10,613
Winter	85	0.83%	3,154	30.85%	6,270	61.33%	715	6.99%	10,224
Type of crash
Vehicle to vehicle	143	0.44%	8,644	26.68%	21,170	65.34%	2,442	7.54%	32,399
Vehicle to pedestrian	167	1.76%	4,372	45.99%	4,493	47.26%	474	4.99%	9,506
Single vehicle (no pedestrian)	14	2.30%	179	29.44%	328	53.95%	87	14.31%	608
Detailed type of crash
Rear-end crash	11	0.21%	1,052	20.28%	3,900	75.19%	224	4.32%	5,187
Side crash	72	0.43%	4,638	27.83%	10,656	63.93%	1,302	7.81%	16,668
Head-on crash	23	0.95%	898	36.97%	1,336	55.00%	172	7.08%	2,429
In a crossing	105	1.90%	2,744	49.53%	2,461	44.42%	230	4.15%	5,540
On the sidewalk	7	1.87%	168	44.80%	186	49.60%	14	3.73%	375
On the road	15	1.26%	499	41.97%	594	49.96%	81	6.81%	1,189
Driving in reverse	0	0.00%	30	11.54%	214	82.31%	16	6.15%	260
Overturn	4	4.82%	16	19.28%	39	46.99%	24	28.92%	83
Vehicle only	9	6.98%	47	36.43%	59	45.74%	14	10.85%	129
Unclassified	78	0.73%	3,103	29.13%	6,546	61.45%	926	8.69%	10,653
Type of violation
Unsafe driving	164	0.84%	5,487	28.25%	12,190	62.77%	1,579	8.13%	19,420
Signal violation	92	0.97%	3,760	39.71%	5,135	54.24%	481	5.08%	9,468
Violation of the obligation to maintain safe distance	2	0.07%	562	19.36%	2,176	74.96%	163	5.61%	2,903
Violation of driving method in intersection	4	0.11%	945	25.62%	2,463	66.77%	277	7.51%	3,689
Violation of road lane compliance obligations	1	0.16%	127	20.32%	456	72.96%	41	6.56%	625
Violation of pedestrian protection obligations	32	1.22%	1,208	46.12%	1,278	48.80%	101	3.86%	2,619
Violation over the center line	7	0.77%	332	36.36%	492	53.89%	82	8.98%	913
Illegal U-turn	3	1.07%	57	20.36%	167	59.64%	53	18.93%	280
Crash with a right-turn vehicle and a straight-line vehicle	1	0.06%	446	25.16%	1,173	66.16%	153	8.63%	1,773
Speeding	14	24.56%	33	57.89%	9	15.79%	1	1.75%	57
Unclassified	4	0.52%	238	31.07%	452	59.01%	72	9.40%	766
Surface condition
Dry	284	0.74%	11,919	31.09%	23,387	61.01%	2,743	7.16%	38,333
Wet/moisture	36	1.02%	1,090	30.84%	2,188	61.91%	220	6.23%	3,534
Frost/freezing	1	0.96%	26	25.00%	72	69.23%	5	4.81%	104
Snow	1	1.16%	23	26.74%	59	68.60%	3	3.49%	86
Unclassified	2	0.44%	137	30.04%	285	62.50%	32	7.02%	456
Weather
Sunny	275	0.73%	11,693	31.04%	22,997	61.05%	2,702	7.17%	37,667
Rainy	25	0.95%	832	31.50%	1,626	61.57%	158	5.98%	2,641
Cloudy	20	1.16%	540	31.38%	1,046	60.78%	115	6.68%	1,721
Snowy	3	1.68%	46	25.70%	124	69.27%	6	3.35%	179
Unclassified	1	0.33%	84	27.54%	198	64.92%	22	7.21%	305
Crash location
Inside	166	0.68%	7,729	31.80%	14,698	60.48%	1,709	7.03%	24,302
Near	92	0.63%	3,923	26.80%	9,567	65.35%	1,057	7.22%	14,639
Crosswalk	66	1.85%	1,543	43.20%	1,726	48.32%	237	6.63%	3,572
Vehicle type (offender)
Passenger car	148	0.52%	8,856	31.18%	18,339	64.57%	1,059	3.73%	28,402
Two-wheel	50	0.96%	1,502	28.81%	2,592	49.72%	1,069	20.51%	5,213
Freight car	47	1.30%	1,312	36.18%	2,149	59.27%	118	3.25%	3,626
Van	35	1.40%	922	36.78%	1,445	57.64%	105	4.19%	2,507
Special vehicles	22	5.29%	158	37.98%	223	53.61%	13	3.13%	416
Bicycle	22	1.54%	307	21.53%	672	47.12%	425	29.80%	1,426
Unclassified	0	0.00%	138	14.95%	571	61.86%	214	23.19%	923
Sex of offender
Male	291	0.85%	10,711	31.31%	20,810	60.82%	2,402	7.02%	34,214
Female	33	0.45%	2,341	31.84%	4,592	62.46%	386	5.25%	7,352
Unclassified	0	0.00%	143	15.10%	589	62.20%	215	22.70%	947
Age of offender
Youth (<17 years)	7	0.81%	213	24.68%	444	51.45%	199	23.06%	863
Younger (18–35 years)	48	0.51%	2,896	30.73%	5,641	59.86%	838	8.89%	9,423
Middle-aged (36–55 years)	124	0.79%	5,052	32.16%	9,640	61.37%	892	5.68%	15,708
Older (>56 years)	145	0.93%	4,891	31.42%	9,674	62.14%	858	5.51%	15,568
Unclassified	0	0.00%	143	15.04%	592	62.25%	216	22.71%	951
Vehicle type (victim)
Passenger car	44	0.22%	4,241	20.91%	14,417	71.08%	1,580	7.79%	20,282
Two-wheel	42	0.62%	2,822	41.96%	3,498	52.01%	363	5.40%	6,725
Freight car	13	0.76%	368	21.62%	1,106	64.98%	215	12.63%	1,702
Van	19	1.11%	496	28.99%	1,053	61.54%	143	8.36%	1,711
Special vehicles	6	4.11%	26	17.81%	103	70.55%	11	7.53%	146
Bicycle	18	1.03%	672	38.58%	942	54.08%	110	6.31%	1,742
Pedestrian	167	1.76%	4,372	45.99%	4,493	47.26%	474	4.99%	9,506
Unclassified	15	2.15%	198	28.33%	379	54.22%	107	15.31%	699
Sex of victim
Male	206	0.66%	9,114	29.39%	19,374	62.47%	2,321	7.48%	31,015
Female	104	0.96%	3,893	36.00%	6,246	57.75%	572	5.29%	10,815
Unclassified	3	2.34%	20	15.63%	68	53.13%	37	28.91%	128
Age of victim
Youth (<17 years)	6	0.40%	431	28.51%	917	60.65%	158	10.45%	1,512
Younger (18–35 years)	44	0.40%	2,932	26.79%	7,243	66.19%	724	6.62%	10,943
Middle-aged (36–55 years)	78	0.50%	4,404	28.16%	10,046	64.24%	1,111	7.10%	15,639
Older (>56 years)	182	1.33%	5,238	38.15%	7,411	53.98%	899	6.55%	13,730
Unclassified	14	2.03%	190	27.58%	374	54.28%	111	16.11%	689
Region
Seoul	232	0.71%	9,465	29.16%	20,372	62.77%	2,387	7.35%	32,456
Busan	92	0.91%	3,730	37.09%	5,619	55.87%	616	6.13%	10,057

Results of Injury Severity Analysis

In this study, injury severity analyses based on RF and XGB models were performed. The importance of the variables was converted into weights and applied to individual crashes, and the calculated individual crash severity scores are reflected in the performance measurement ( $N_{pred}$ , $N_{EPDO}$ ) through the hotspot identification process. Figure 2 shows graphs of the variable importance derived from RF and XGB performed for injury severity analysis. These results indicate the ranking of variables critical to classifying KA and BC crashes. The results of the RF model show significant variables in the following order: vehicle type (victim)—passenger car (0.0383), age of victim—older (>56 years) (0.0322), type of violation—signal violation (0.0263), age of offender—middle-aged (36–55 years) (0.0262), and age of offender—older (>56 years) (0.0260). The results of the XGB model show significant variables in the following order: vehicle type (victim)—passenger car (0.0683), age of victim—older (>56 years) (0.0435), region—Seoul (0.0391), week—weekday (0.0391), and type of violation—signal violation (0.0377). The importance of the variables applied to the content of each crash is relative. Therefore, if there are many crashes with significant factor characteristics at each intersection, this would result in higher weighted scores. Statistics summaries of the injury severity analysis results are presented in Table 3.

Table 3.

Statistics Summaries of Injury Severity Analysis Results

Severity score for each crash (n = 1,990)
Method	Mean	SD	Min.	Max.
RF	0.2963	0.0216	0.1787	0.3392
XGB	0.3366	0.0490	0.1249	0.4351
Aggregated severity score for each intersection in 2017 (n = 81)
Measure	Mean	SD	Min.	Max.
$N_{pred}$	0.0561	4.5179	−10.8836	12.9798
$N_{pred, RF}$	−0.3511	1.4904	−4.3325	4.4301
$N_{pred, XGB}$	−0.3436	1.7017	−4.8058	4.4606
$N_{EPDO}$	56.6439	30.5136	0	134.6728
$N_{EPDO, RF}$	16.6055	8.9370	0	37.9838
$N_{EPDO, XGB}$	18.4459	10.2203	0	45.5537
Aggregated severity score for each intersection in 2018 (n = 81)
Measure	Mean	SD	Min.	Max.
$N_{pred}$	−0.0422	4.6440	−7.0716	18.8931
$N_{pred, RF}$	−0.3714	1.5687	−2.9129	5.6343
$N_{pred, XGB}$	−0.3487	1.7230	−3.2445	6.7444
$N_{EPDO}$	48.0403	30.0659	4.0797	174.5774
$N_{EPDO, RF}$	14.1583	8.8479	1.2417	51.0280
$N_{EPDO, XGB}$	15.7322	9.6839	1.3171	52.5698

Note: EPDO = equivalent property damage only; Max. = maximum; Min. = minimum; pred = predicted; RF = Random Forest; SD = standard deviation; XGB = Extreme Gradient Boosting.

Figure 2.

Results of variable importance by random forest (RF) and extreme gradient boosting (XGB) (top 30 of 82 variables).

SPFs for Urban Intersections by Crash Severity Level

In this study, SPFs are developed to yield the predicted crash frequency of the performance measure presented by the HSM. With RF- and XGB-based severity-weighted applications, datasets representing under-dispersion are developed as COM-Poisson models. Basic datasets without severity weights are developed as models that follow an NB distribution. The development of SPFs used the COUNTREG (COM-Poisson) and GENMOD (NB) procedures in SAS 9.4. SPFs were developed only for urban signal intersections. Annual average daily traffic (AADT) in major roads and minor roads was collected from ViewT 3.0 (provided by the Korea Transportation Institute), and intersection geometric and operational data were collected from online GIS services, Kakao map, and Google maps. The collected geometric and operational data were used to develop the model by selecting variables that appeared to be significant in the analysis process. A total of 12 continuous variables was considered as inputs: AADT (major road), AADT (minor road), number of lanes (major road), number of lanes (minor road), number of left turn lanes (major road), number of right turn lanes (major road), number of channelization right turns (major road), number of medians (major road), number of left turn lanes (minor road), number of right turn lanes (minor road), number of channelization right turns (minor road), and number of medians (minor road). A total of 11 categorical variables was considered: presence of turn lane (major road), type of median in major road (island, closed, open), presence of parking (major road), speed limit (major road), presence of turn lane (minor road), type of median in minor road (island, closed, open), presence of parking (minor road), speed limit (minor road), skewed intersection, size of intersection, and region (Seoul or Busan).

Values of $scor e_{n}$ with severity weights per crash are aggregated into intersection units and defined as $N_{Obs, w (XGB), (total, KA, BC)}$ . SPFs were developed according to the aggregated observed crash frequency, and the predicted crash frequency was calculated according to the conditions of each intersection and the variable value of the crash determined by the model. A total of six SPFs was developed under the dependent variables, as follows: $N_{Obs, Total}$ , $N_{Obs, BC}$ , $N_{Obs, w (RF), Total}$ , $N_{Obs, w (RF), BC}$ , $N_{Obs, w (XGB), Total}$ , and $N_{Obs, w (XGB), BC}$ . The developed SPFs are presented in Table 4. For model fitting, variables were selected using the stepwise, forward, and backward methods. In this study, there was no problem with multicollinearity or significant variables at a 90% confidence level (P-value <0.1) in the final model.

Table 4.

Safety Performance Functions (SPFs) for Identifying Intersection Hotspots

Parameter	Crash severity level
	Total			B+C crashes
	Estimate	Standard error	P-value	Estimate	Standard error	P-value
(1) Negative binomial (NB) ( $N_{pred, Total}$ , $N_{pred, BC}$ )
Intercept	−3.2827	1.5777	0.0375	−7.7391	1.5718	<.0001
$\ln (AAD T_{maj})$	0.3793	0.1561	0.0151	0.6767	0.1569	<.0001
$\ln (AAD T_{\min})$	0.1880	0.1066	0.0778	0.3401	0.1223	0.0054
Number of lanes (major)	0.1319	0.0479	0.0059	NS	NS	NS
Number of left turn lanes (major)	0.0869	0.0330	0.0084	NS	NS	NS
Number of right turn lanes (major)	0.2032	0.1171	0.0829	NS	NS	NS
Number of channelization right turns (major)	−0.2031	0.050	<.0001	NS	NS	NS
Number of medians (major)	−0.3303	0.0987	0.0008	NS	NS	NS
Type of median (major) References: open	−0.4210	0.1742	0.0157	NS	NS	NS
Presence of parking (major)	0.3542	0.1249	0.0046	NS	NS	NS
Max. speed (major) Reference: 50 km/h	0.6882	0.2831	0.015	NS	NS	NS
Max. speed (major) Reference: 60 km/h	0.6218	0.2833	0.0282	NS	NS	NS
Presence of turn lane (minor)	−0.3813	0.1232	0.002	NS	NS	NS
Number of right turn lanes (minor)	−0.5464	0.1222	<.0001	−0.4371	0.1434	0.0023
Type of median (minor) Reference: island	0.2210	0.1068	0.0386	NS	NS	NS
Skewed intersection	0.4468	0.1439	0.0019	NS	NS	NS
Intersection type Reference: three-leg	−0.5658	0.1625	0.0005	−0.5674	0.2066	0.006
Dispersion	0.0117	0.0141	NA	0.0493	0.0250
Akaike information criterion (AIC)	468.7019	NA	NA	432.3065
(2) COM-Poisson ( $N_{pred, RF, Total}$ , $N_{pred, RF, BC}$ )
Intercept	−7.6953	1.3071	<.0001	−7.2741	1.3902	<.0001
$\ln (AAD T_{maj})$	0.6650	0.1285	<.0001	0.5500	0.1383	<.0001
$\ln (AAD T_{\min})$	0.2514	0.1009	0.0127	0.3034	0.1086	0.0052
Number of right turn lanes (minor)	−0.3060	0.1237	0.0133	−0.3430	0.1285	0.0076
Number of channelization right turns (minor)	−0.1085	0.0444	0.0145	NS	NS	NS
Skewed intersection	0.3012	0.1491	0.0433	NS	NS	NS
Intersection sizeReference: three-leg	−0.3680	0.1703	0.0307	−0.4826	0.1855	0.0093
$- \ln Nu$	−0.7986	0.1649	<.0001	−0.9444	0.1668	<.0001
AIC	286.9660			245.3792
(3) COM-Poisson, $N_{pred, XGB, Total}$ , $N_{pred, XGB, BC}$
Intercept	−6.4863	1.3314	<.0001	−9.1044	1.4929	<.0001
$\ln (AAD T_{maj})$	0.6173	0.1248	<.0001	0.6743	0.1459	<.0001
$\ln (AAD T_{\min})$	0.2407	0.0976	0.0137	0.3974	0.1138	0.0005
Number of left turn lanes (major)	0.0704	0.0324	0.0297	NS	NS	NS
Number of channelization right turns (major)	−0.1240	0.0443	0.0052	−0.1042	0.0500	0.0371
Presence of turn lane (minor)	−0.2378	0.1185	0.0448	NS	NS	NS
Number of right turn lanes (minor)	−0.5202	0.1238	<.0001	−0.4869	0.1359	0.0003
Skewed intersection	0.2822	0.1444	0.0506	NS	NS	NS
Intersection sizeReference: three-leg	−0.5084	0.1677	0.0024	−0.5049	0.1961	0.01
$- \ln Nu$	−0.7806	0.1643	<.0001	−0.7622	0.1692	<.0001
AIC	300.5892			270.4185

Note: AADT = annual average daily traffic; min = minimum; Max. = maximum; maj = major; NS = not significant; pred = predicted; RF = Random Forest; XGB = Extreme Gradient Boosting; NA = not available.

Results and Discussion

Results of Hotspot Identification

A total of six indicators, including the four previously proposed indicators, was used to identify intersection hotspots. The rank results were largely divided according to “excess predicted average crash frequency using SPFs” and “EPDO-predicted average crash frequency using SPFs.” The results are presented in Table 5.

Table 5.

Rank Results of Intersection Hotspot Identification

No. of sites	$N_{pred}$	Rank	$N_{pred, RF}$	Rank	$N_{pred, XGB}$	Rank
Excess predicted average crash frequency using safety performance functions (SPFs)
68	12.9798	1	2.9362	2	2.5300	5
35	10.8542	2	4.4301	1	4.4606	1
45	10.2044	3	2.8031	4	3.3280	3
76	9.4155	4	2.8529	3	3.9577	2
51	7.7884	5	1.4205	7	2.6319	4
53	6.9760	6	1.8981	6	2.1568	7
58	5.4506	7	0.7060	15	0.9962	14
54	5.4057	8	0.4505	24	0.7356	22
20	5.3067	9	0.8361	11	1.0500	13
44	5.2909	10	0.4734	23	1.7146	8
Equivalent property damage only (EPDO)-predicted average crash frequency using SPFs
68	134.6728	1	37.9838	1	43.8882	2
9	133.9220	2	37.8426	2	38.8787	4
80	121.0738	3	35.4789	4	40.7284	3
45	120.4646	4	37.5244	3	45.5537	1
21	115.6341	5	33.5695	5	33.2294	5
35	99.4570	6	29.7833	6	31.7763	9
13	96.7372	7	28.3200	7	28.3100	13
76	94.7682	8	27.9932	8	32.7555	7
40	89.9377	9	27.2335	9	32.5733	8
44	89.3286	10	27.0819	10	33.0845	6

Note: pred = predicted; RF = Random Forest; XGB = Extreme Gradient Boosting.

According to the results, hotspots not identified in the results of the base indicator ( $N_{pred})$ were newly identified in the results of the RF and XGB indicators ( $N_{pred, RF}$ , $N_{pred, XGB}$ ). This means that the newly identified hotspots in RF and XGB indicators require additional consideration and response in relation to safety improvements.

Validation of Consistency for New Performance Measures

Consistency tests were performed to verify that the proposed performance measures can play a significant role as hotspot identification measures by conducting similar evaluations “before” and “after.” Three consistency tests were constructed to validate the six performance measures: the site consistency test (SCT), the method consistency test (MCT), and the total rank difference test (TRDT) ( 5 ). The hotspot rank was derived according to measure. For the consistency test, the data were divided into a test set (before period, 2017) and a validation set (after period, 2018).

Site Consistency Test (SCT)

SCT is a test that compares the sum of the observed crash frequency during the after period of the hotspot intersection identified in the test set (before period). Comparisons are made between performance measures for the top 10% ( $α$ = 0.10) and 5% ( $α$ = 0.05) of the identified hotspots. The performance measure identifies hotspots in the before period. If the sum of the observed crash frequency during the after period is highest in the hotspot of the before period, the measure is the best in relation to consistency. The equation is as follows (Equation 12):

SCT = \sum_{i = n - n α}^{n} N_{obs, i, m (x), after} .

(12)

where

$n$ = total number of intersections ( $n$ = 81 urban intersections in this study),

$α$ = threshold of identified hotspot intersections ( $α$ = 0.05 with top 5% of $n$ intersections identified as hotspots),

$N_{obs, i}$ = observed crash frequency for ranked intersection $i$ ,

$m (x)$ = performance measure (m(1) = base measure, m(2) = RF measure, and

m(3) = XGB measure).

Method Consistency Test (MCT)

As with SCT, the number of hotspots corresponding to the top 10% and 5% are compared between “before” and “after” according to the performance measure. The results are presented as proportions, and the formula for this test is as follows (Equation 13):

MCT = \frac{{(k_{n - n α}, k_{n - n α + 1}, \dots, k_{n}}}_{before} \cap^{} {(k_{n - n α}, k_{n - n α + 1}, \dots, k_{n}}}_{after}}}{n - n α} \times 100 .

(13)

Total Rank Difference Test (TRDT)

The previously described MCT can verify consistency between “before” and “after” by identifying the top hotspots according to the top percentage. TRDT compares the sum of errors for hotspots in the top percentage group using the same concept as for MCT, comparing “before” and “after.” The formula for this test is as follows (Equation 14):

TRDT = \sum_{i = n - n α}^{n} (Rank (i_{m (x), before}) - Rank (i_{m (x), after})) .

(14)

where

$Rank$ = rank of the hotspot intersection for method $x$ .

Validation Results

SCT, MCT, and TRDT were performed to validate the performance measure. The rank was derived according to the performance measurement for 81 intersections in Seoul and Busan, South Korea, and the verification was based on the rank results and values. Validation results are presented in Table 6.

Table 6.

Results of the site consistency test (SCT), the method consistency test (MCT), and the total rank difference test (TRDT)

Performance measure	SCT		MCT		TRDT
	Top 10% ( $α$ = 0.10)	Top 5% ( $α$ = 0.05)	Top 10% ( $α$ = 0.10)	Top 5% ( $α$ = 0.05)	Top 10% ( $α$ = 0.10)	Top 5% ( $α$ = 0.05)
Excess predicted average crash frequency using safety performance functions (SPFs)
$N_{pred}$	136	85	0.25	0.25	159	27
$N_{pred, RF}$	170	85	0.5	0.25	77	25
$N_{pred, XGB}$	147	78	0.375	0.25	122	28
Equivalent property damage only (EPDO)-predicted average crash frequency using SPFs
$N_{EPDO}$	187	108	0.5	0.25	71	29
$N_{EPDO, RF}$	187	108	0.5	0.25	78	35
$N_{EPDO, XGB}$	164	108	0.375	0.25	178	34

Note: pred = predicted; RF = Random Forest; XGB = Extreme Gradient Boosting.

From the SCT results, in the top 10% ( $α$ = 0.10), groups identified as hotspots showed the highest number for the after period observed crash frequency (187 cases) for groups predicted by $N_{EPDO}$ , $N_{EPDO, RF}$ . Groups identified as hotspots in the top 5% ( $α$ = 0.05) showed the same observed crash frequency for groups predicted by $N_{EPDO}$ , $N_{EPDO, RF}$ , $N_{EPDO, RF}$ . The three performance measures showed the same 108 cases, all of which showed good consistency. In SCT, it was shown that the EPDO-predicted average crash frequency was excellent, regardless of $α$ .

From the MCT results, in the top 10% ( $α$ = 0.10), the highest MCT value of the group identified as hotspots was 0.5, with corresponding measures $N_{pred, RF}$ , $N_{EPDO}$ , $N_{EPDO, RF}$ . The total sample number is 81, meaning the sample size of the top 10% is eight: four of the eight intersections are duplicated as hotspots in the after period. In groups identified as hotspots in the top 5% ( $α$ = 0.05), that value was 0.25. Only one of the four samples was duplicated as a hotspot.

From the TRDT results, in groups identified as hotspots in the top 10% ( $α$ = 0.10), TRDT values for $N_{EPDO}$ , $N_{pred, RF}$ , $N_{EPDO, RF}$ were low in the order of 71, 77, and 78, respectively. In groups identified as hotspots in the top 5% ( $α$ = 0.05), TRDT values for $N_{pred, RF}$ , $N_{pred}$ , $N_{pred, XGB}$ were low in the order of 25, 27, and 28, respectively. $N_{pred, RF}$ showed the lowest sum of validation rank errors, indicating that it is a good performance measure.

In this study, the performance of six measures, including four based on proposed severity weights, was validated. Three hotspot identification validation methods were used for verification: SCT, MCT, and TRDT. The results of the validation method showed that EPDO measures were superior to excess predicted measures and EPDO measures. Comparing the six measures, $N_{EPDO}$ , $N_{EPDO, RF}$ , and $N_{pred, RF}$ were superior in consistency. However, the advantages of reflecting the severity weights of individual crashes are not reflected in consistency verification. Therefore, because $N_{EPDO, RF}$ , $N_{pred, RF}$ were identified as good measures means that measures with severity factor weights are unbiased and can serve as good performance measures. In other words, this can serve as a general crash-frequency-based hotspot identification measure, as well as a detailed form of analysis that reflects severity factors.

Conclusions and Recommendations

In the past, various hotspot identification methods and performance measures have been used in network screening to identify vulnerable intersections. A representative method used in intersection hotspot identification is the EB method, and commonly used performance measures include the crash frequency, crash rate, and so forth. (1, 5, 28). However, research using both crash frequency and severity factors of each crash in hotspot identification is lacking. Therefore, this study proposes new performance measures that reflect individual crash severity factor weights for more detailed hotspot identification. The excess predicted average crash frequency using SPFs and EPDO average crash frequency using SPFs, presented by the HSM, were set as default performance measures, and four new measures ( $N_{pred, RF}$ , $N_{pred, XGB}$ , $N_{EPDO, RF}$ , $N_{EPDO, XGB}$ ) were validated with severity factor weights applied to the default measures. SPFs were developed for each measure according to the procedure presented by the HSM. SPFs were developed as a model that follows the NB distribution or the COM-Poisson distribution according to the variance of the dependent variable. Using data from 2017 to 2018, RF and XGB models were developed using data from 42,513 crashes at intersections in Seoul and Busan, South Korea, resulting in variable-importance-based severity factor weights. Scores for each crash unit were calculated by applying weights, which were aggregated into intersection units.

As a result of identifying hotspots using the four proposed measures and two base measures, hotspots not identified with the basic indicators were partially identified in ranks reflecting severity weights. This means that the new hotspots were identified as a result of the severity weights, and these hotspots can be interpreted from a different perspective.

In addition, consistency testing (SCT, MCT, and TRDT) was performed to verify that the proposed measures could play a significant role as hotspot identification measures. According to the test results, compared with the base measures, none of the four proposed measures showed consistency problems when identifying hotspots. This means that not only can the proposed method provide performance measures based on the crash frequency, but it also applies a detailed analysis that reflects the characteristics of each crash occurring at intersections.

Research cases of other countries were reviewed for methodological verification of measure proposed in this study (6, 42, 43). However, few hotspot studies were conducted on intersections, and most of them were conducted on segments, and, as in this study, performance measures suggested by HSM were used. Among them, the measures using the EB method were found to have the best consistency. Consistency verification is used to evaluate whether it is appropriate to use the proposed indicators as a measure of hotspot identification. Therefore, since the consistency test result does not mean that the performance is excellent, it should only be referred to. Nevertheless, the EB method is known to have predictive performance and can reflect various elements of the section in the analysis, so it can be considered good enough. Unlike this study, it is difficult to directly compare existing studies because they did not target intersections, but EPDO and excess predicted crash frequency measures using SPFs proposed in this study can be expanded to the EB method if they solve future sample issues. In addition, since the consistency analysis results showed that there was no problem, it was judged that the possibility of utilization was sufficient. Finally, the biggest advantage of the proposed measures is that it reflects the severity analysis weight, so it is not reasonable to evaluate the proposed measures as a result of a simple consistency test. If this indicator is applied to overseas intersections in the future, it will be a good basis for verification.

In this study, new performance measures reflecting severity factor weights were proposed. However, there are several limitations to this study. More work is needed to increase the usability of these measures. First, a sufficient sample size is needed for validation. Data from a total of 42,513 incidents were learned for severity analysis. However, validation relied on data from 1,990 cases at 81 intersections. The analysis period was 2 years, which is insufficient compared with previous studies. Verification will be more reliable if the temporal and spatial ranges of data are expanded in the future. Second, on-site verification of the hotspot identification and crash analysis that occurred in the intersection are required. Hotspots identified by indicators reflecting severity weights can provide new insights for intersections, but it is impossible to judge whether the identification is right or wrong. Therefore, it is necessary to verify the analysis results through additional field analysis for some intersections. Finally, application of different variables in the intersection safety evaluation study is required. In this study, only data that can be collected from online GIS services were used as geometric variables because of the limited number of available variables. According to previous studies, variables such as signal sequence, number of conflicts, and walking traffic were also used (10, 22, 44 –47). These variables can be used as input variables of SPFs, which can then be used to calculate performance measures.

Using the new performance measures proposed in this study for hotspot identification, safety managers can track crash severity factors that were not identified with the original method. It is also expected to be possible to design a countermeasure suitable for each intersection based on the factors tracked in this study.

Footnotes

Author Contributions

The authors confirm contributions to the paper as follows: study conception and design: S. Son, J. Park, G. Lee, M. Abdel-Aty; data collection: S. Son; analysis and interpretation of results: S. Son, J. Park; draft manuscript preparation: S. Son, J. Park, G. Lee, M. Abdel-Aty. All authors 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) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT, and Future Planning (2019R1G1A1010209).

ORCID iDs

Seung-oh Son

Juneyoung Park

Gunwoo Lee

Mohamed Abdel-Aty

Data Accessibility Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author on reasonable request.

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