category: literaturenote citekey: wangmesolevelhotspotidentification2021 title: Meso-level hotspot identification for suburban arterials authors: "Wang, Xuesong; Pei, Yingying; Yang, Minming; Yuan, Jinghui" year: 2021 date: 2021-00-00 2021 doi: 10.1016/j.aap.2021.106148 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2021.106148" zotero_key: CD7TC4IB zotero_storage: F78CV93K collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Wang, Xuesong"

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Meso-level hotspot identification for suburban arterials

Xuesong Wang a,b, *, Yingying Pei a,b , Minming Yang a,b,d , Jinghui Yuan ^c

^a The Key Laboratory of Road and Traffic Engineering, Ministry of Education, China
^b School of Transportation Engineering, Tongji University, Shanghai, 201804, China
^c Department of Civil, Environmental, and Construction Engineering, University of Central Florida, FL, 32816, United States
^d China Academy of Urban Planning & Design, Shanghai Branch, Shanghai 200335, China

ARTICLE INFO

Keywords: Meso level Suburban arterials Hotspot identification Bayesian conditional autoregressive model Potential for safety improvement

ABSTRACT

Accurate identification of crash hotspots forms the foundation of roadway safety improvement. The Highway Safety Manual micro-level approach uses individual intersections and road segments as analysis units, and correspondingly identifies some isolated road entities as hotspots. However, because traffic police and administrative agencies routinely conduct safety improvement based on multiple continuous segments and intersections, the identification of hotspots at the micro-level is inefficient for field application. To better meet this need, this study proposes a new meso-level approach to identify hotspots, specifically on suburban arterials. Meso-level analysis units of three different configurations (201, 150, and 100 units) were obtained by combining a set number of intersections and their adjacent segments according to crash distribution and homogeneity. Their influence areas were determined according to the proportion of urbanized land in areas perpendicularly adjacent to the arterials. Three Bayesian Poisson-lognormal conditional autoregressive models (PLN-CAR) considering spatial correlations were developed for each unit configuration, using the full Bayesian (FB) method to ameliorate random fluctuation in crash counts. Potential for safety improvement (PSI) values were calculated based on the modeling results and were used to identify hotspots. Two measures, i.e., the concentrated degree of hotspots (CDH) and the hotspot identification accuracy (HIA), were proposed to make a quantitative and comparative evaluation. Results showed that 1) arterials with more parallel roads suffer lower crash risk, and 2) considering both the hotspot distribution and the identification accuracy, the 150 meso-level unit configuration was the best. The proposed meso-level hotspot identification method promises to be adaptive to safety improvement practices on suburban arterials.

1. Introduction

As suburban arterials are the main traffic corridors through cities' suburbs, their safety poses a public concern for many metropolitan areas. In Shanghai, suburban crashes account for over 70 % of the city's total crashes each year. The number of crashes has risen, likely in response to the burgeoning urbanization that has led to rapid change in land use development around arterials (Yuan and Wang, 2018). In addition, many road networks around arterials are improperly designed. For example, local roads often connect directly to the arterials without linking collector roads, producing connections that, by disturbing the arterials' lateral traffic flow, consistently threaten traffic safety. Roadway safety improvement depends on identifying crash hotspots so traffic police and administrative agencies can implement effective countermeasures on hazardous sites. Therefore, the accurate identification of hotspots as well as the relationship between crashes and the contributing factors is urgent.

Micro-level modeling methods, such as presented in the Highway Safety Manual (HSM; AASHTO (American Association of State Highway Transportation Officials), 2010), developed safety performance functions for roadway segments and intersections separately. Two limitations of this method point to the development of a new modeling strategy. First, the road network features surrounding the arterials play a critical role in the crash occurrence of adjacent intersections and segments. The entire impact of road network features on arterial safety may be misestimated by analyzing intersections and road segments separately. Second, for micro-level models, the isolated intersections and road segments were identified as hotspots, and they are usually scattered. However, the local transportation management agency preferred to conduct safety improvement actions based on multiple continuous

^* Corresponding author at: The Key Laboratory of Road and Traffic Engineering, Ministry of Education, China. E-mail address: wangxs@tongji.edu.cn (X. Wang).

intersections and road segments. The discrepancy between academic studies and field practices further highlights the need for a new modeling approach that treats combined intersections and segments as the analysis unit.

A promising type of analysis unit is at the meso level. The meso-level unit, which combines road segments and adjacent intersections, has occasionally been used (Fan et al., 2019; Li and Wang, 2017), but a systematic method for combining the segments and intersections has not yet been established. Moreover, no studies have used meso-level units to identify hotspots, and correspondingly, none have discussed the meso-level unit configuration suitable to hotspot identification in field application.

Therefore, the purpose of this study is to propose a meso-level unit configuration method, analyze the safety impact of road network features on suburban arterials, conduct hotspot identification, and identify the best meso-level unit configuration adaptive to field application.

This paper is organized as follows. The literature review discusses various analysis units and studies related to hotspot identification. The third section introduces the configuration of the meso-level units for the selected arterials and the methods for extraction of road features. The core sections of this paper develop three crash prediction models that consider the spatial correlations among the analysis units, and present quantitative and comparative analyses of hotspots identified by potential for safety improvement (PSI) method. The final section is devoted to the summary and discussion.

2. Literature review

2.1. Analysis units

Most of the existing traffic safety analyses have been conducted based on either micro- or macro-level analysis units (Wang et al., 2018b; Yang et al., 2020; Dong et al., 2016). Macro-level safety analysis focuses on zonal level influences, including socio-economic factors, traffic characteristics, road network, and land use features (Cai et al., 2019; Yang et al., 2020). The hot zones identified at the macro level are valuable for regional traffic enforcement, traffic safety education, and implementation of traffic policy (Lee et al., 2014a; Pei et al., 2021). However, because hot zones cover broad areas, routine traffic safety improvements are usually conducted on more limited hazardous road entities or hotspots.

Hotspots are typically identified at the micro level, in which roadways are separated into segment and intersection analysis units. The segment unit can be further subdivided into fixed-length segments (Miaou and Lum, 1993) or homogeneous segments based on, for example, median treatments or the number of lanes (Wang et al., 2014; Hauer et al., 2004). An intersection unit typically contains the area starting from the intersection's center to the stop bar, and includes the upstream safety influence area (Wang and Abdel-Aty, 2006; Wang et al., 2008). Use of these two micro-level units separately, however, neglects consideration of the interactions between intersections and their adjacent segments. Macro factors such as road network can affect these interactions, such as when the high access density caused by a lack of collector roads deteriorates traffic safety on both segments and intersections; analyzing segments and intersections separately may consequently underestimate the overall safety impact (Wang et al., 2014). Researchers have also found that incorporating other macro factors such as land use and area type into micro safety modeling can significantly improve the model's prediction accuracy (Quistberg et al., 2015; Lee et al., 2017; Cai et al., 2018), but macro-level factors have not yet been considered in existing micro-level safety studies of suburban arterials (Wang et al., 2014).

A few meso-level studies have been conducted. To explore both micro and macro-level safety influencing factors, Li and Wang (2017) combined intersections with adjacent segments of similar average speed into meso-level analysis units. Fan et al. (2019) combined each

intersection randomly with one of its adjacent segments and incorporated the units into one meso-level crash prediction framework. The results showed that the meso-level model was superior to the micro-model in prediction accuracy. However, as shown in the few available meso-level studies, the process of forming meso-level units is, as yet, relatively unestablished. A study by Ziakopoulos and Yannis (2020) may suggest a more intentional method. They proposed that the spatial correlations they found among analysis units were fundamentally related to the distribution of road safety indicators such as crash count. Meso-level analysis units allocated to consider the spatial distribution of crashes should therefore be expected to reduce the effect of spatial correlation and thus facilitate more accurate hotspot identification.

2.2. Hotspot identification methods

The main existing hotspot identification methods include crash frequency (CF), crash rate (CR), quality control (QC), equivalent property damage only (EPDO), empirical Bayes (EB), full Bayes (FB), and potential for safety improvement (PSI).

The CF method (Oppe, 1991) and the CR method (Lord and Park, 2008) are easy to implement, but CF tends to ignore the effect of traffic volume; thus, a segment with high volume tends to be associated with high crash frequency, and it will always be identified as a hotspot. CR, on the other hand, may misestimate the effect of the exposure variable. Neither method considers random fluctuation in crash count (Hauer, 1997).

Norden et al. (1956) proposed the QC method to identify hotspots. This method considers the discreteness of crash data and assumes that crashes follow the Poisson distribution. The probability of mistakenly identifying low traffic areas as safe is reduced by setting a comparison threshold. Tamburri and Smith (1970) proposed the EPDO method, which considers crash severity in identifying hotspots. However, this method tends to exaggerate the risk in a hotspot location where serious crashes occur but only occasionally. Neither of these methods considers the problem of regression to the mean (RTM) in crash count (Hauer, 1980), that is, incorrect identification results caused by random fluctuation in crash characteristics.

The EB method solves one of the problems with CF and CR by considering the random fluctuation in crash counts and has recently been in wide use (Hauer et al., 1988; Persaud et al., 1999; Sorensen and Elvik, 2007), including by the U.S. Highway Safety Manual (HSM). However, this method requires an abundance of samples to develop the safety analysis model, and the model forms cannot be too complex.

As an improvement of EB, Schluter et al. (1997) introduced the FB method into safety analysis by using it to estimate the posterior distribution of crashes and then taking the estimate as an index to identify hotspots. Miranda-Moreno and Fu (2007) compared FB with EB and found that when the number of samples was sufficient, the results produced by both methods were similar. However, when the sample size was small, the FB was superior to the EB. Huang et al. (2009) used a hierarchical model in a Bayesian framework considering spatial and temporal correlation. They demonstrated that FB can accommodate complex model forms and perform better in hotspot identification than EB.

Persaud et al. (1999) proposed the PSI method, which refers to the difference between the expected crash frequency at a certain location and the average predicted crash frequency for similar locations. Researchers have frequently used EB and PSI (Wang and Feng, 2019) or FB and PSI (Dong et al., 2016) together to handle the random fluctuation of crashes. PSI is defined as Eq. (1):

$$PSI = E[r|x] - E[r] \tag{1}$$

where PSI is the potential for safety improvement, E[r|x] is the EB or FB expected crash frequency, and E[r] is the crash frequency predicted by the crash prediction model.

3. Data preparation

3.1. Arterial selection and configuration of meso-level analysis units

In Shanghai, the Outer Ring Road circumscribes the city center. Outside the city center are Shanghai's suburbs, which are separated into inner and outer suburbs by the Suburb Ring. The arterial roadways located in both inner and outer suburbs are known as suburban arterials. This study selected nine suburban arterials in Shanghai, as shown in Fig. 1 and described in Table 1.

3.1.1. Configuration of meso-level units longitudinal to the arterials

Each meso-level analysis unit was configured to include an intersection and its adjacent segments. As the nine arterials were considered in their entirety, each segment adjacent to one intersection was also adjacent to the next intersection on a given arterial. Rather than allocating the segment to the adjacent intersections by simply splitting it at the midpoint, however, this study proposes spatial correlation as a new approach to meso-level allocation. Considering that the crash distribution on arterials might be an indicator of spatial correlation (Ziako poulos and Yannis, 2020), analysis units that take into account the

Table 1 Description of suburban arterials.

Arterial number in Fig. 1	Length (km)	Number of lanes	Number of intersections	Median treatments	Speed limit (km/h)
1	12.97	4	16	Undivided	40
2	9.98	4	14	Raised,	40
				undivided
3	10.77	4, 2	11	Raised	40
4	20.70	4, 2	21	Undivided	60
5	28.01	4, 6	33	Raised	40, 60
6	21.30	4	20	Raised	60
7	22.88	4	22	Raised	60
8	16.69	4, 6	32	Raised,	60
				undivided
9	20.87	6	32	Raised	80

spatial distribution of crashes are appropriate for modeling due to their potential strength in reducing the effect of the correlation.

In this study, intersection crashes, defined as crashes within an intersection's stop bars, accounted for 63 % of crashes, which was a significantly greater proportion than segment crashes at 37 %. To fully capture the spatial distribution of segment crashes, the Multiple Ring Buffer tool in ArcMap® was used to construct buffer belts at intervals of

Fig. 1. Location of the selected arterials in the Shanghai road network.

50 m from each intersection on all arterials. The crashes from all buffer belts were counted and then aggregated according to buffer distance. As shown in Fig. 2, segment crashes tended to aggregate to the intersections; that is, crash frequency on the portion of a segment nearest to an intersection was clearly higher than the portion far from the intersection.

As shown in Fig. 3, each road segment was subdivided into several 50-meter-long sub-segments and the crash frequency of each subsegment was counted. For the road segments with more crashes on both sides and fewer crashes in the middle, they were split at the location of the lowest crash count. For those road segments that do not conform to this characteristic, they were split at the midpoint. After each intersection was combined with its adjacent road segments, a total of 201 basic meso-level analysis units were obtained.

3.1.2. Influence area perpendicularly adjacent to the arterials

As mentioned, the land use types and road network patterns around an arterial inevitably affect the arterial's safety performance. To explore the specific safety impact of these variables, it is necessary to determine the arterial's influence area so that the variables can be extracted. In previous safety research on urban arterials, Li and Wang (2017) assumed the influence area to be approximately equal to the average signal spacing. However, as no research on suburban arterials has clearly confirmed this assumption, recent changes in the arterials' traffic efficiency and safety led to this study's use of a different influence area.

Shanghai's recent rapid urbanization has led to more urbanized land use around the arterials, and a consequent rise in the number of surrounding resident trips. As this increase in the number of trips appears to have affected traffic efficiency and safety (Wang et al., 2018a), this study elected to determine the influence area according to the proportion of urbanized land use in areas perpendicularly adjacent to the arterials.

The following steps were taken:

1) Extract the surrounding land use features for each arterial from Google Maps, and then use the ArcMap® Multiple Ring Buffer tool to develop 10 buffer belts for each arterial at intervals of 200 m.
2) Classify land use types as urbanized or non-urbanized to facilitate further quantitative analysis. Urbanized land use included residential, commercial, industrial, and science, culture, and public health; non-urbanized land use included agricultural, undeveloped, and green space, in accord with the Code for Classification of Urban Land Use and Planning Standards of Development Land (Housing and Urban-rural Development of the People's Republic of China, 2012).
3) Calculate the proportion of urbanized land perpendicularly adjacent to the suburban arterials.

As shown in Fig. 4, the proportion of urbanized land decreased with the increase in perpendicular distance from the arterials. The distance at which the proportion of urbanized land reached its minimum value was 1.6 km, so that distance was ultimately used as the suburban arterials' influence area. The subsequent rise evident at 2.0 km is due to the influence on land use of other surrounding arterials.

3.2. Independent and offset variables

3.2.1. Extraction of land use type

The land-use types in the influence areas of the meso-level units were extracted manually based on the Google Earth. In 3.1.2, land use was preliminarily classified as urban and non-urban for the purpose of determining the influence area. Now, in order to examine the relationship between land use and suburban arterial safety in more complexity, urbanized land use was aggregated into the four types noted above: residential, commercial, industrial, and science, culture, and public health. Non-urbanized land-use types included agricultural, undeveloped, and green space. The use type assigned to a unit was determined by the land use in the largest proportion. These three land-use types were not considered in the final analysis because of the relatively small areas of undeveloped, green space, and science, education, culture, and health land along the arterials.

3.2.2. Calculation of road network patterns

Road network patterns in the arterials' influence areas were extracted from Google Earth. In line with previous research, betweenness centrality was utilized to quantify the network patterns (Wang et al., 2018a; Li and Wang, 2017). Each route, or path, in the road network is abstracted as a set of nodes. The betweenness centrality of each node is determined by the frequency of its presence in the shortest routes in the road network. The betweenness centrality of node i is defined as (Freeman, 1978):

$$Ci^B = \frac{1}{(N-1)(N-2)} \times \sum{j \neq k \neq i} \frac{n{jk}(i)}{n{jk}}$$ (2)

where N is the total number of nodes, njk is the number of shortest paths between node j and k, and njk(i) is the number of shortest paths between j and k that contain node i.

UCINET® was used in this study to calculate the betweenness centrality of the road network patterns in each meso-level unit (Borgatti et al., 2002). The betweenness centrality value decreased with the increase of parallel roads around the arterials. The samples with values between 0 and 0.15 were regarded as grids, and samples with values between 0.15 and 0.35 were considered irregular grids (Li and Wang, 2017). The remaining samples were determined to be mixed, or tree-like based on the authors' visual observation and check of the road network around arterials (Wang et al., 2018a). As can be seen in Table 2, the irregular grid was the dominant pattern in over half the analysis units.

Fig. 2. Proportion of crashes at different buffer distances.

Fig. 3. Allocation process of basic meso-level analysis units.

3.2.3. Other variables

In addition to the macro-level factors of network pattern and land use, area type, the length of the meso-level units, access density, and traffic volume were included as variables. Area type, which included inner suburb and outer suburb (shown in Fig. 1), was selected due to area differences important to the safety performance of suburban arterials. The inner suburb road network, closest to the city center, is denser than that of the outer suburb network, and its urban construction is much older. The travel mode choices for residents also differ significantly: there are more bus and metro trips in the inner suburbs because of their more comprehensive public transport facilities.

The unit length was obtained from a GIS base map and was used as an offset variable. The unit length variable was transformed into a

logarithmic scale, and its coefficient was constrained to 1.0. After overlaying the access point layer and the unit layer, the number of access points within each unit was calculated in ArcMap®. The number of access points divided by the length of the corresponding unit defined the access density.

The annual average daily traffic (AADT) was obtained from the detection cameras installed along the arterials, and was processed in the form of passenger car units (pcu). Because each of the 201 meso-level traffic analysis units contained one intersection and portions of its two adjacent road segments, the traffic volume for each unit was calculated by averaging the AADT data of its two road segments. The volume data were logarithmically processed.

Fig. 4. Proportion of urbanized land by distance from the arterials.

Table 2 Summary of betweenness centrality in the four road network patterns in the 201 meso-level analysis units.

Road Network Patterns	Grid	Irregular Grid	Mixed	Tree-like
Betweenness centrality values (Li and Wang, 2017)	(0, 0.15)	[0.15, 0.35)	[0.35, 0.65]	[0.35, 0.65]
Roadway network figures
Description (Wang et al., 2018a)	Grid structure with continuous collector roads parallel to arterials	Grid structure with discontinuous collector roads parallel to arterials	Mixed structure with grid and tree-like patterns	Tree-like structure without continuous collector roads parallel to arterials
Sample Size	44 (21.89 %)	101 (50.25 %)	39 (19.40 %)	17 (8.46 %)

3.3. Crash data

The crash data were obtained from the Shanghai Road Traffic Crash Analysis and Warning System. In 2012, the system began to use ArcGIS® to geocode each crash, and the accuracy of crash location in the system's electronic database reached 98 %. This accuracy provided a reliable dataset for studying the spatial distribution of crashes. Total crashes in 2012 and 2013 on the nine selected suburban arterials were collected.

3.4. Combining of meso-level units

Each of the 201 meso-level traffic analysis units contained one intersection and its two neighboring segments on the arterial. A general modeling rule is that the independent variables within the same analysis unit should remain homogeneous, while the crashes and independent variables among different analysis units should be heterogeneous. Therefore, combining adjacent units that are homogeneous in crash frequency and other variables would make the model more reasonable. Additionally, the average 0.83-km length of the units may be too short for traffic police and administrative agencies to practically conduct safety improvement action.

This study, therefore, combined the 201 basic meso-level units to better fit the modeling rule and practical application. The homogeneity of the independent variables was determined for area type, land use, the road network pattern, traffic volume, and access density. Traffic volume and access density were divided into four levels based on quartile. The independent variables of adjacent units were regarded as homogeneous if 80 % of the five variables were the same.

To determine the homogeneity of crashes, the difference in crash frequency of adjacent units were calculated by the following equation (Lee et al., 2014b):

$$D{i,j} = \frac{|C{i,j-1} - C{i,j}| \bullet N}{\sum{j=1}^{N} C{i,j}} + \frac{|I{i,j-1} - I{i,j}| \bullet N}{\sum{j=1}^{N} I_{i,j}}$$ (3)

where *Di,j*is the relative crash level difference between unit j and unit j − 1 on arterial i, *Ci,j*is the crash rate of unit j on arterial i, *Ii,j*is the crash frequency of unit j on arterial i, and N is the number of basic analysis units on arterial i.

The mean value of *Di,j*was 1.57 in this study. For a given unit j on arterial i, if the *Di,j*value was less than 1.57, the crash frequency of unit j and unit j − 1 was considered homogeneous.

According to the homogeneity of independent variables (not considering crash homogeneity), about half of the 201 units were candidates for combining with adjacent units, or a combination ratio of 2:1. Approximately a quarter of the 201 units were homogenous in both independent variables and crash frequency, a combination ratio of 4:3. Therefore, using two combination ratios, 4:3 and 2:1, the 201 basic meso-level analysis units were combined into 150-unit samples and 100 unit samples. Table 3 itemizes by arterial the three different meso-level samples: 201-unit, 150-unit, and 100-unit. For example, Arterial 1 had 16 of the basic 201 units, 12 of the 150 combined units, and 8 of the 100 combined units.

Descriptive statistics of the independent variables for the basic and combined meso-level units are shown in Table 4. As can be seen, as the unit format decreases from 201 units to 150 and then 100, the unit length increases, as is desirable for practical safety improvement. At the same time, the minor changes in access density and traffic volume, as well as the stable percentages in the categorical variables, show that the units' homogeneity was relatively unaffected by the two combination ratios.

SPSS 22.0® was used to conduct collinearity diagnostics. Results showed that all variance inflation factors (VIF) were lower than 3,

Table 3 Description of the three meso-level unit samples for each suburban arterial.

| Arterial
number | | Number of analysis units on each
arterial | | | Number of analysis units on each
arterial that contain more than
one intersection | | | |--------------------|---------------|----------------------------------------------|------------------|---------------|-----------------------------------------------------------------------------------------|------------------|--| | (from
Fig. 1) | 201-
basic | 150-
combined | 100-
combined | 201-
basic | 150-
combined | 100-
combined | | | 1 | 16 | 12 | 8 | 0 | 3(2, 1, 0) | 4(2, 0, 2) | | | 2 | 14 | 11 | 6 | 0 | 3(1, 0, 0) | 4(1, 2, 1) | | | 3 | 11 | 10 | 5 | 0 | 1(1, 0, 0) | 4(3, 0, 1) | | | 4 | 21 | 15 | 10 | 0 | 4(2, 2, 0) | 7(4, 2, 1) | | | 5 | 33 | 22 | 17 | 0 | 8(5, 3, 0) | 11(7, 3,
1) | | | 6 | 20 | 18 | 14 | 0 | 2(2, 0, 0) | 6(6, 0, 0) | | | 7 | 22 | 19 | 14 | 0 | 3(3, 0, 0) | 5(3, 1, 1) | | | 8 | 32 | 24 | 15 | 0 | 5(2, 3, 0) | 8(2, 3, 3) | | | 9 | 32 | 19 | 11 | 0 | 8(3, 5, 0) | 11(3, 6,
2) | |

Note: Figures in parentheses denote the number of 2-intersection units followed by the number of 3- and then 4-intersection units. For example, 7(4, 2, 1) indicates that for Arterial 4, of the ten 100-combined units, 7 contain more than 1 intersection; and of these 7 units, 4 have 2 intersections, 2 have 3, and 1 has 4 intersections.

indicating there was no significant multi-collinearity among the variables.

4. Statistical modeling

201- basic

4.1. Bayesian Poisson-lognormal CAR model

The Poisson-lognormal model (PLN) and the negative binomial (NB) model have been widely used in safety modeling due to their strength in overcoming possible over-dispersion in crash data (Lord and Mannering, 2010). To determine the better model for this study, PLN and NB models were developed based on the three different meso-level analysis unit configurations, the 201-basic and the 150- and 100-combined. Results

showed that the PLN model outperformed the NB in prediction accuracy in all three formats, so the PLN was selected as the statistical modeling method. Since the units of a given arterial shared similar geometric and traffic characteristics, spatial correlations were evident. Conditional autoregressive (CAR) effects were used to account for the intra-arterial correlations (Oppe, 1991).

The PLN-CAR model in full Bayesian framework was adopted, as the full Bayesian (FB) method regards all parameters as random variables characterized by prior distributions. The posterior distributions were calculated after combining the prior distributions and the observed data. The theoretical framework for Bayesian inference is defined as Eq. (4):

$$\pi(\theta|y) = \frac{L(y|\theta)\pi(\theta)}{\int L(y|\theta)\pi(\theta)d\theta} \tag{4}$$

where y is the vector of the observed data, θ is the vector of parameters, ^L(y|θ) is the likelihood function, π(θ) is the prior distribution of θ, ^∫ L(y|θ)π(θ)dθ is the marginal distribution of observed data, and π(θ|y) is the posterior distribution of θ given y.

A random effect term θij was introduced to address overdispersion for unobserved or unmeasured heterogeneity. This model is defined as follows:

$$y{ij} \sim Poisson(\lambda{ij})$$ (5)

$$\ln(\lambda_{ij}) = \beta0 + \ln(Length{ij}) + X{ij}\beta + \theta{ij} + \varphi_{ij}$$ (6)

$$\theta{ij} \sim Normal(0, \sigma{\theta}^2)$$ (7)

where i is the consecutive number of an analysis unit on a given arterial starting from 1, j is the consecutive number per Fig. 1 of the arterial from 1 to 9, yij is the total crash frequency in a given unit, λij is the expectation of yij, Xij is the vector of explanatory variables of all units, β is the vector of regression coefficients, θij is the random effect term, and σ² *θ*is the variance of θij. A CAR prior is assigned to φij to account for the spatial correlations among the units. Crashes in units of the

Table 4 Descriptive statistics of independent and offset variables.

150- combined	Access density (1/km)	Number of accesses per km along arterial	10.59	0	26.42	6.38
	Ln_AADT (pcu/h)	Natural log of annual average daily traffic volume	7.34	6.44	8.05	0.24
	Length (km; offset)	Length of unit	1.67	0.25	7.57	1.22
100- combined	Access density (1/km)	Number of accesses per km along arterial	10.37	1.43	25.82	5.75
	Ln_AADT (pcu/h)	Natural log of annual average daily traffic volume	7.34	6.68	8.05	0.22
Categorical variables
		Number of observations (percentage)
Variable		201-basic	150-combined			100-combined
Area type
Inner suburb		131 (65.17 %)	99 (66.00 %)			69 (69.00 %)
Outer suburb		70 (34.83 %) 51 (34.00 %)				31 (31.00 %)
Land use type
Residential		54 (26.87 %)	43 (28.67 %)			29 (29.00 %)
Commercial		10 (4.98 %)	9 (6.00 %)			6 (6.00 %)
Industrial		113 (56.22 %)	81 (54.00 %)			52 (52.00 %)
Agricultural		24 (11.94 %)	17 (11.33 %)			13 (13.00 %)
Road network pattern
Grid		44 (21.89 %)	33 (22.00 %)			18 (18.00 %)
Irregular grid		101 (50.25 %)	70 (46.67 %)			44 (44.00 %)
Mixed		39 (19.40 %)	35 (23.33 %)			29 (29.00 %)
Tree-like		17 (8.46 %)	12 (8.00 %)			9 (9.00 %)

Sample Variable Description Mean Min Max SD

Length (km; offset) Length of unit 0.83 0.15 3.4 0.56 Access density (1/km) Number of accesses per km along arterial 10.25 0 33.78 6.62 Ln_AADT (pcu/h) Natural log of annual average daily traffic volume 7.35 6.44 8.05 0.24

Length (km; offset) Length of unit 1.12 0.15 4.08 0.83

Continuous variables

same arterial were confirmed by Moran's I to be positively spatially correlated.

The spatial correlations among the units can be shown by a proximity matrix W with entry wiji'^j ' representing the spatial relationship between unit ij and i'j . wiji'^j ' is defined as a function of the distance between units:

$$w{iji'j'} = \begin{bmatrix} \frac{1}{d{ij'j''}} & j = j' \ 0 & j \neq j' \end{bmatrix}$$ (8)

where dij,ⁱ ' is the distance between the midpoints of two units ij and i j . When the arterial index j ∕= j , wij,ⁱ ' = 0 indicates that the units located along different arterials are independent from each other.

However, units on the same arterial are spatially correlated, and the correlation of the units close to each other is expected to be greater than those far apart. As shown in Fig. 5, the spatial correlation between Unit pm and Unit qm was the inverse of the distance between the midpoints of two units, i.e., ¹ dpm,qm. The correlation between Unit pm and Unit kn was 0.

An intrinsic version of the CAR model proposed by Besag et al. (1991) was adopted. The parameter ρ was set as 1, and the conditional distribution of φij and φ⁻ ij followed a normal distribution with mean ∑ *i '*∕=i wi 'j,ij wj⁺ *φⁱ 'j*and variance ^σ² φ wj⁺ .

$$\varphi{ij} \left| \varphi{-ij} \sim N \left( \sum{j \neq i} \frac{w{ij,ij}}{w{j+}} \varphi{ij}, \frac{\sigma{\varphi}^2}{w{j+}} \right) \right. \tag{9}$$

4.2. Prior information

Reliable prior information is helpful for improving model fitting. According to previous research (Wang et al., 2018a), the maximum likelihood method is a promising way to formulate prior information. To obtain the maximum likelihood priors, SAS 9.3® was used to develop 15 negative binomial models for each of the 5 independent variables and 3 unit configurations. After estimating each parameter by the maximum likelihood method, the mean and variance of the estimates were then transformed into a normal distribution as the prior distribution. The maximum likelihood informative priors are summarized in Table 5.

4.3. Comparison of model prediction accuracy

The standardized absolute deviance (SAD) and mean standardized absolute deviance (MSAD) were used to compare the accuracy of the three models. SAD and MSAD are defined as follows (Bonissone et al., 2002):

$$SAD = \frac{|y_i^e - y_i^e|}{SD(y^e)} \tag{10}$$

Table 5 Maximum likelihood prior distributions for the three Bayesian models.

Independent Variables	Mean				Precision (1/variance)
Model	201	150	100	201	150	100
Access density	0.035	0.029	0.041	7181.8	4890.2	2183.6
Ln_AADT	1.244	0.987	1.984	23.982	11.413	7.597
Area type (Base: Inner suburb)
Outer suburb	0.381	0.450	0.593	42.607	31.526	17.565
Land use (Base: Agricultural)
Residential	1.148	1.206	1.574	17.146	11.163	9.078
Commercial	1.706	1.635	1.918	7.207	5.605	4.099
Industrial	0.259	1.403	1.719	20.475	12.548	10.950
Road network pattern (Base: Grid)
Irregular grid	0.115	0.386	0.669	31.245	21.714	13.647
Mixed	0.757	0.684	1.291	20.984	16.949	11.704
Tree-like	0.823	0.855	1.346	12.303	9.561	5.510

$$MSAD = \frac{1}{n} \sum_{i=1}^{n} SAD_i \tag{11}$$

where *y^o i*is the actual crash number of unit i, *ye ⁱ*is the predictive crash number of unit i, SD(yo) is the standard deviation of the actual crash number of all analysis units, and n is the number of units. Smaller SAD and MSAD values indicate higher prediction accuracy.

5. Modeling results

5.1. Parameter estimation results

Crashes were modeled as a function of land-use type, road network pattern, access density, traffic volume, and area type (inner or outer suburb). Results of the Pearson correlation coefficient, used to test for possible correlations between all explanatory variables, showed there were no significant correlations.

The three Bayesian PLN-CAR models, based on the basic and combined meso-level analysis units, were developed in WinBUGS®. To obtain the posterior distributions of parameters, the Gibbs sampling algorithm was adopted, and two chains were generated for each parameter. The first 10,000 iterations of each chain with numerical instability were excluded. After the two chains converged, another 40,000 iterations were set to estimate the posterior distribution of the parameters. The modeling results are summarized in Table 6.

It can be observed that the MSAD values of the three models varied significantly. As the 150-unit model had the lowest value, thereby outperforming the other two models. The 150-unit model was used to interpret variables in the next section.

Fig. 5. Meso-level units on one arterial and on two arterials.

Table 6 Bayesian PLN-CAR model comparison with parameter estimation results.

Independent variables	Model of 201 units Mean (95 % BCI)	Model of 150 units Mean (95 % BCI)	Model of 100 units Mean (95 % BCI)
Intercept	3.009	2.701	2.874
	(2.024, 3.796)	(1.822, 3.742)	(2.132, 3.597)
Access density	0.029	0.021	0.036*
	(0.007, 0.046)	(0.004, 0.042)	(-0.002, 0.062)
Ln_AADT	0.076*	0.096	0.059
	(-0.002, 0.189)	(0.005, 0.198)	(0.016, 0.179)

Land use type (Base: Agricultural)
Residential	1.078	1.096	1.159
	(0.669, 1.449)	(0.647, 1.524)	(1.045, 1.882)
Commercial	1.695	1.666	1.766
	(1.173, 2.283)	(1.060, 2.313)	(1.336, 2.256)
Industrial	1.202	1.403	1.423
	(0.867, 1.522)	(1.007, 1.858)	(1.013, 1.771)
Road network pattern (Base: Grid)
	0.121	0.373	0.458
Irregular grid	(0.013, 0.227)	(0.063, 0.683)	(0.124, 0.849)
	0.715	0.625	0.509
Mixed	(0.334, 1.100)	(0.318, 1.021)	(0.271, 0.967)
	0.730	0.668	0.554
Tree-like	(0.252, 1.177)	(0.168, 1.166)	(0.087, 1.045)
1	0.622	0.765	0.953
Random effect ( ) σ2	(0.197, 1.021)	(0.250, 1.367)	(0.374, 1.640)
θ	0.375	0.433	0.233
CAR effect (φij)	(0.258, 0.506)	(0.252, 0.696)	(0.126, 0.357)
MSAD	0.119	0.076	0.101

Note: Mean (95 % BCI) values marked in bold are significant at the 0.05 level; those noted by * are significant at the 0.1 level.

5.2. Analysis of results

The relationship between crashes and independent variables was investigated based on the 150-unit model. The significant variables included access density, traffic volume, land use type, and road network pattern.

5.2.1. Road network pattern

As can be seen in Table 6, all suburban arterial network patterns, in comparison with the base grid pattern, were significantly related to crash frequency. According to the estimated coefficients, arterials surrounded by an irregular grid tended to generate 45.2 % (e⁰.³⁷³ − 1) more crashes than those surrounded by the standard grid. Arterials surrounded by a mixed pattern were associated with 91.9 % (e⁰.⁶²⁵ − 1) more crashes than those with a grid. The tree-like pattern tended to bring a 95.0 % (e⁰.⁶⁶⁸ − 1) increase in crash frequency, making this pattern the most hazardous network structure among the four. The results of this study, including that the grid was the safest structure, are consistent with previous research by Wang et al. (2018a), who focused on the safety impact of network pattern on the macro level, and Li and Wang (2017), who drew similar conclusions when investigating the safety influencing factors on urban arterials. A likely explanation of the grid's safety is that in a standard grid pattern, several collector roads run parallel to the arterials; these collector roads may help to reduce the crash risk on arterials by distributing local traffic, thus reducing the number of vehicles accessing the arterials.

The collector road explanation appears consistent with the relative safety of the other network structures as well. The irregular grid pattern tends to increase crash risk less than the other two patterns, which can be attributed to its similarity to the standard grid. Both grid patterns have several collector roads parallel to the arterials, but the collector roads in the irregular structure are discontinuous, so they do not distribute local traffic as well. The collector roads in the mixed pattern are even more discontinuous than those in the irregular grid, and the

tree pattern has few collector roads of any kind. In networks with these structures, travel relies much more heavily on the suburban arterials, which must handle a greater mix of traffic, which, in turn, raises the potential for an increase in traffic conflicts.

5.2.2. Land use type

More crashes occurred on suburban arterials running through urbanized land (i.e., residential, commercial, industrial) than on agricultural land, which is similar to the results of previous research (Wang et al., 2014; Mane and Pulugurtha, 2018). The phenomenon can likely be explained by the density of public facilities and population on urbanized land. Areas with high public facility density and heavy population are more likely to generate and attract high trip numbers, which consequently increase the risk of crashes. This finding highlights the need to investigate the safety of suburban arterials because rapid urbanization is likely to increase the proportion of urbanized land along the arterials, and the rise of residential travel may adversely affect traffic efficiency and safety.

5.2.3. Other variables

The traffic volume (Ln_AADT) and access density were positively associated with crash frequency. It can be calculated that an increase of one access point per kilometer was associated with an increase in the crash frequency of 2.12 % (e⁰.⁰²¹ − 1). This finding is consistent with previous studies of suburban arterials on both the micro-level (Wang et al., 2014) and the macro-level (Wang et al., 2018a; Yuan and Wang, 2018). In all three studies, the authors concluded that higher access density tends to disturb the lateral traffic flow on arterials, which leads to more crash occurrences.

6. Hotspot identification at the meso level

6.1. Analysis method

6.1.1. Hotspot identification method

Potential for safety improvement (PSI) was selected as the performance measure to identify hotspots. PSI is the difference between the expected crash frequency at a certain location during a given time period, and the predicted crash frequency, that is, the predicted crash count for similar locations based on a crash prediction model. If the PSI value in a meso-level analysis unit was greater than zero, the unit was considered hazardous. Conversely, if the value was less than zero, the unit was regarded as safe.

In this study, three negative binomial (NB) models were developed as crash prediction models. The expected crash counts were estimated by three Bayesian PLN-CAR models (Table 6). PSI was calculated by the following equation:

$$PSI = N{expected} - N{predicted} = exp(\beta0 + X{ij}\beta) - exp(\beta0 + X{ij}\beta')$$ (12)

where i is the consecutive number of an analysis unit on a given arterial starting from 1, j is the consecutive number of the arterial from 1 to 9, Xij is the vector of explanatory variables of all units, β is the vector of regression coefficients of PLN-CAR model, β' is the vector of regression coefficients of NB model.

6.1.2. Comparison method of hotspot identification results

In field application, there are two main considerations in the evaluation of the hotspot identification results: one is the concentrated hotspot distribution, and the other is the high accuracy. To compare the identification results quantitatively, two measures were defined: the concentrated degree of hotspots (CDH) and the hotspot identification accuracy (HIA).

For a hotspot identification result, it can be considered as more concentrated if the average length was longer with less arterials involved. As for the accuracy, the hotspot identification result of the

201-unit model can be regarded as the most reliable among the three models because the PSI value of each basic unit was calculated separately. This study assumed that the HIA value of 201-unit model was 1. For the 150-combined-unit and 100 combined unit, the closer the HIA value was to 1, the more accurate the result was. Therefore, CDH and HIA were defined as follows:

$$CDH = \frac{\overline{L}}{N}$$ (13)

$$HIR = 1 - \frac{N_1}{N_2} \tag{14}$$

where L is the average length of hotspots, N is the number of arterials with hotspots, *N*1 is the number of hotspots in which the PSI values of some basic units are less than zero, *N*2 is the total number of hotspots, i. e., 15 in this study. A higher CDH value indicates higher concentrated hotspot distribution.

6.2. Hotspot identification results

The PSI values based on three different models (201, 150, and 100 unit model) were calculated and ranked. Table 7 shows the hotspot identification results for the top 15 rankings of the three models.

As shown in Table 7, there existed some differences in the hotspot identification results based on the three models. First, the average length and the spatial distribution of hotspots vary significantly. The hotspots identified by the 201-unit model were short and scattered across six arterials. In contrast, the hotspots identified by the 150-unit model were relatively long and mainly located on Arterials 4, 5, 6, and 9. A possible reason was that the 150-unit model combined the basic analysis units with homogeneous crash frequency and independent variables, such as unit 47 and unit 48, which makes the distribution of hotspots more concentrated.

Second, the 100-unit model seems to have an inadequacy in the rationality of the identification results. For example, in Table 7, units 193 and 194 were identified as hotspots by all three methods. However, in the 100-unit model, unit 195 was also identified as a hotspot. In both the 201-unit model and the 150-unit model, the PSI value of unit 195 was less than zero, indicating that unit 195 was not hazardous. The unreasonable result obtained by the 100-unit model may be due to the

Table 7 Top 15 hotspots for three models.

Hotspot Rank	201-basic units	150-combined units	100-combined units
	Arterial Number	Arterial Number	Arterial Number
	(Unit ID)	(Unit ID)	(Unit ID)
1	9 (193)	6 (106, 107)	6 (106, 107)
2	9 (194)	9 (193, 194)	4 (52)
3	9 (179)	9 (183, 184)	5 (63, 64)
4	4 (52)	9 (179)	8 (138)
5	9 (183)	4 (47, 48)	9 (193, 194, 195)
6	4 (47)	4 (52)	5 (71, 72, 73, 74)
7	8 (138)	5 (90, 91, 92)	8 (155)
8	4 (48)	5 (88)	3 (37, 38, 39, 40)
9	3 (41)	9 (187, 188, 189)	6 (96, 97)
10	2 (18)	9 (199, 200)	4 (47, 48)
11	8 (155)	5 (84, 85)	5 (84, 85)
12	9 (171)	5 (79, 80, 81)	6 (102, 103)
13	2 (23)	8 (138)	9 (187, 188, 189)
14	5 (81)	6 (102, 103)	5 (88)
15	5 (88)	9 (171)	9 (179)
Average Length (km)	0.91	1.79	2.21

Note: Figures in parentheses denote the unit ID from 1 to 201. For the 201-unit configuration, the unit IDs of adjacent basic analysis units are contiguous. For the 150-unit and 100 unit configuration, each combination analysis unit contains 1–4 basic analysis units.

combination of basic analysis units with heterogeneous crash frequency.

6.3. Comparison of hotspot identification results

To further compare the identification results quantitatively, the CDH and HIA values of the three models were calculated and summarized in Table 8.

As shown in Table 8, the CDH value of the 100-unit model was the highest, followed by the 150-unit model, and the 201-unit model was the lowest. This phenomenon indicated that the spatial distribution of the hotspots identified by the 100-unit model was the most concentrated, and the concentrated degree of hotspots identified by the 150 unit model was similar to the 100-unit model.

According to the HIA value, the accuracy of the identification result by the 150-unit model was the same as the 201-unit model. Both of them were significantly more accurate than the 100-unit model. This finding indicated that when combining the basic meso-level unit according to the homogeneity in both independent variables and crash frequency, the accuracy of hotspot identification result was relatively unaffected.

Though the CDH value of the 100-unit model was a little higher than that of the 150-unit model, considering both the spatial distribution of hotspots and the identification accuracy, the 150-unit meso-level modeling method was the best.

7. Discussion and conclusion

Traditional micro-level hotspot identification research focuses on specific hazardous intersections or road segments, often resulting in a scattered distribution of identified hotspots. Consequently, the local transportation management agency find it inconvenient to conduct field surveys and improvement actions. The consistency of the safety improvement countermeasures (e.g., number of lanes, speed limit, and signal control) for adjacent intersections and road segments cannot be guaranteed occasionally. On the other hand, the macro-level approach neglects the local and specific characteristics of the arterials, and maybe too geographically broad for practical application. Despite macro-level hot zones being conducive to the implementation of traffic regulations and the dissemination of traffic safety education, the larger size of the hot zones dilutes the effectiveness of countermeasures that must cover all road segments and intersections instead of making more targeted improvements to crash-prone spots.

This study begins from the assumption that, for implementation, the meso-level safety analysis models may be more readily interpreted and the meso-level hotspot identification results may be more practical. In Shanghai, traffic police usually improve crash-prone sites based on 1− 3 km of road. Meso-level analysis units, which are comprised of a limited number of multiple segments and intersections, incorporate both micro and macro influencing factors, and are in line with the need for road safety improvement. Therefore this study proposed and applied a mesolevel approach to identify hotspots on suburban arterials.

Considering that the spatial correlation among analysis units may be related to the crash distribution on an arterial, 201 basic meso-level analysis units were configured by combining each intersection and its adjacent segments according to the spatial distribution of crashes, an approach to the allocation that had the potential strength of reducing the spatial correlation effects among the analysis units. To better fit modeling rules and practical application, the 201 units were further aggregated into two test sets of 150 and 100 combined units according to the homogeneity of crash frequency and independent variables.

Table 8 The CDH and HIA values of three models.

	201 basic units	150 combined units	100 combined units
CDH	0.15	0.36	0.37
HIA	1	1	0.73

To account for the spatial correlation, three Bayesian PLN-CAR models were developed based on the 201 basic meso-level analysis units and the 150 and 100 combined units. According to MSAD values, the 150-unit model showed the greatest prediction accuracy. The low MSAD value of the 150-unit model may indicate that it is reasonable to develop a model based on units homogenous in both independent variables and crash frequency. The 150-unit model was therefore used for further analysis. Results showed that 1) the irregular grid, mixed and tree-like network patterns were associated with more crashes than the grid pattern; 2) arterials running through areas of urbanized land use were prone to more crashes than agricultural land; and 3) access density and traffic volume were positively associated with crash frequency. As these results were in line with previous safety research at both macro and micro levels (Mane and Pulugurtha, 2018; Wang et al., 2014), the consistency of modeling results verified our research.

The PSI method was used as a performance measure to identify hotspots. Based on the three different models, the PSI values were calculated and ranked. A comparative analysis among the top 15 hotspots was conducted for the three models. Results showed that the 150 unit meso-level hotspot identification result outperformed the other two in the spatial distribution of hotspots and the identification accuracy. These results further indicate the strength of meso-level units homogenous in both independent variables and crash frequency. Moreover, a look back at Table 1 reveals that the four arterials with the top 15 hotspots generally had higher speed limits (60/80 km/h) and a greater number of lanes (4/6) than the other arterials. These characteristics accord with observations commonly made by road traffic safety administrators: the arterials with high speed limits and multiple lanes usually carry substantial traffic and suffer from high crash risk.

Due to the meso-level hotspot identification method's strength in combining safety factors of both macro-level hot zones (in this study, land use types and road network patterns) and micro-level road entities (traffic volume and access density), the proposed method is expected to be useful in field application. Conclusions drawn from these meso-level models can be better incorporated into routine management. For example, traffic safety policymakers and police can more efficiently strengthen traffic control near urbanized areas, control or close excessive access, and construct parallel collector roads to diverge traffic flow.

There are a few possible extensions to this study. First, this approach is expected to be as useful in other countries and regions as it is in Shanghai, and it will be of interest to see if other data will verify the results of this study. Second, the models can be updated when new crash data and other independent variables are available in the future.

Declaration of Competing Interest

The authors report no declarations of interest.

Author statement

The authors confirm contribution to the paper as follows: study conception and design, data collection, analysis and interpretation of results, draft manuscript preparation: Wang X, Pei Y, Yang M, and Yuan J. All authors reviewed the results and approved the final version of the manuscript.

Acknowledgements

This study was sponsored by the International Science and Technology Cooperation Program of China (2017YFE0134500), and the Science and Technology Commission of Shanghai Municipality (18DZ1200200).

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