category: literaturenote citekey: manirulislamcomprehensiveanalysiseffectssignal2022 title: "A comprehensive analysis on the effects of signal strategies, intersection geometry, and traffic operation factors on right-turn crashes at signalised intersections: An application of hierarchical crash frequency model" authors: "Manirul Islam, Sheikh; Washington, Simon; Kim, Jiwon; Haque, Mazharul" year: 2022 date: 2022-00-00 2022 doi: 10.1016/j.aap.2022.106663 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2022.106663" zotero_key: TENUMTQ2 zotero_storage: XGQ27TB4 collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Manirul Islam, Sheikh"

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Accident Analysis and Prevention

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

Sheikh Manirul Islam a,* , Simon Washington ^b , Jiwon Kim ^a , Mazharul Haque ^c

^a School of Civil Engineering, Faculty of Engineering, Architecture, and Information Technology, The University of Queensland, St Lucia 4072, Australia
^b Advanced Mobility Analytics Pty Ltd., Australia
^c School of Civil Engineering and Built Environment, Faculty of Engineering, Queensland University of Technology, Brisbane 4001, Australia

ARTICLE INFO

Keywords: Crash frequency Signal strategies Multilevel Poisson Regression Model Random intercept models Right-turn crashes Signalised intersections

ABSTRACT

Right-turn movements (equivalent to left turn movements for countries that drive on the right) at intersections are among the most complex driving maneuvers and require a high level of attention for turning across (potentially) oncoming traffic by accepting a safe gap. Not surprisingly, right-turn-involved crashes are one of the most frequent collision types at intersections (e.g., 42% of all signalised intersection crashes in Queensland, Australia). Unfortunately, the causes and contributing factors to right-turn crashes are not well understood, particularly the effect of right-turn signal strategies on the crash risk. In the safety literature, signal strategies are coarsely considered in two generic categories-protected right-turns and permitted right-turns. In reality, rightturn signal strategies could be of various types (usually 5) based on the level of intersection complexity and potential traffic conflicts. The effects of these signal strategies, along with the geometric and traffic factors, have not been well studied. To fill this gap, this study investigates the effects of right-turn signal strategies, intersection geometry and traffic operations factors on right-turn crashes at signalised intersections. To achieve this aim, crash frequency models were estimated using crash data from 221 signalised intersections in Queensland from the years spanning 2012 to 2018. Hierarchical Poisson Regression Models (random intercept models) were employed to capture the hierarchical structure of influences on crashes, with upper-level capturing intersection characteristics and lower-level capturing approach characteristics. The hierarchical model structure, disaggregate exposure variables, and signal strategies examined in this study give rise to an entirely unique study in the literature.

1. Introduction

1.1. Background

Road traffic Accents are one of the leading causes of death across the world and cause substantial economic losses each year. About 1.24 million people die each year as a result of road traffic crashes (WHO, 2013). The annual economic cost of road crashes in Australia is estimated at \$30 billion (NRSPP, 2017). Road traffic crashes are, therefore, a major concern in contemporary societies. For improving traffic safety in the road Network, researchers are undertaking investigations on crashes along arterials and intersections. Of the two, intersections, as a connecting node of the roadway system, are considered the most

hazardous locations of the road network due to having a large number of vehicular conflict points. Actually, intersections constitute a small portion of the overall road network, but crashes happening at intersections represent about 40% of the total crashes (Wu et al., 2013; Kuciemba and Cirillo, 1992).

Vehicular movements at larger intersections with high traffic volume are usually separated by traffic control devices to minimise conflicts. Despite such efforts, vehicular conflicts still exist, resulting in crashes at intersections. Actually, signalised intersections are inherently high-risk spots for road users due to complicated interactions of various movements and higher traffic volume. In Queensland, signalised intersections accounted for about 34% of intersection crashes over the period 2010–2016.

E-mail addresses: sheikhmanirul.islam@uq.net.au (S. Manirul Islam), simon@amagroup.io (S. Washington), jiwon.kim@uq.edu.au (J. Kim), m1.haque@qut.edu. au (M. Haque).

^* Corresponding author.

Right-turn movements (equivalent to left turn movements for countries that drive on the right) are generally more critical of all movements at intersections due to turning movement and having more vehicular conflict points (vehicle paths and users are in conflicts). In addition, drivers have to accept a gap in the opposing traffic flow when right-turn movements are unprotected. Therefore, right-turn crashes are one of the most frequent collision types at intersections (Chen et al., 2015). Data showed that in Queensland, the average number of rightturn crashes per year over the period 2010–2016 is about 625, representing about 42% of total crashes at signalised intersections. Therefore, the number of right-turn crashes at signalised intersections is still significant. Hence, there is a scope for further improvement.

A number of signal strategies usually accommodate right-turn movements at signalised intersections (e.g., Permitted right-turn, leading right-turn, lagging right-turn, diamond overlap turn, and split approach). In the operation aspect, signal strategies are quite different from each other, and they have different levels of complexity and potential conflicts. Therefore, they offer different levels of safety effects at intersections. However, safety in a phasing sequence comes at the expense of operational efficiency. For instance, permitted right-turn, due to right-turn being unprotected, offers a higher opportunity to traffic conflicts resulting in a lower level of safety, whereas it provides the highest operational efficiency requiring no green time (Chen et al., 2015). In contrast, protected right-turn provides a higher level of safety, reducing traffic conflicts at the expense of operational efficiency by increasing cycle time or reducing the green time available for through movements. Another approach is to use the combination of protected and permitted options when full protection of right-turn causes a significant delay of through movements. Therefore, selecting an appropriate traffic control strategy for facilitating right-turn movements is important in balancing safety and operational efficiency at intersections. However, the selection of a signal strategy primarily depends on site conditions, including various geometric characteristics and traffic factors (Road Planning and Design Manual, 2002). Hence, there may be trade-offs between safety and efficiency and different factors (e.g., geometric and traffic factors) in selecting a signal strategy. To select an appropriate signal strategy, it is, therefore, needed to understand the impacts of signal strategies as well as different geometric and traffic factors on intersection safety.

2. Literature review

2.1. Factors to be considered

Numerous variables such as geometric characteristics (e.g., number of lanes, exclusive right-turn lane, type of intersections, horizontal curve, uphill/downhill grade), traffic factors (e.g., traffic volume, speed limit, queue) and signal control factors (e.g., signal strategy, green time, number of phases) have significant effects on crash occurrences at signalised intersections. In terms of geometric factors, the number of lanes was found to have positive effects on crash frequency (Poch and Mannering, 1996; Abdel-Aty and Wang, 2006; Guo et al., 2010; Dong et al., 2014), whereas exclusive right-turn lanes were found to be negatively correlated with crash occurrence (Abdel-Aty and Wang, 2006). Poch and Mannering (1996) also found that horizontal curve, as well as uphill or downhill grade of more than 5% on intersection approach, would increase the number of crashes at intersections. Moreover, 4-legged intersections were found to be associated with more crashes than 3-legged intersections (Abdel-Aty and Wang, 2006; Xie et al., 2013). In terms of traffic factors, traffic volume (e.g., total volume, right-turn volume, left turn volume, through volume) was found to be positively correlated with crash frequency (e.g., Poch and Mannering, 1996; Chin and Quddus, 2003; Abdel-Aty and Wang, 2006; Yuan and Abdel-Aty, 2018). In addition, speed limit (e.g., Xie et al., 2013; Dong et al., 2014; Yuan and Abdel-Aty, 2018) and longer queue length on through lane (Yuan and Abdel-Aty, 2018) were found to significantly increase the crash risk at signalised intersections.

Regarding signal control characteristics, the number of phases was found to be positively correlated with crash frequency at intersections (e.g., Wang et al., 2006; Abdel-Aty and Wang, 2006; Xie et al., 2013). Yuan and Abdel-Aty (2018) found that higher green time for the rightturn phase and through phase decrease crashes at intersections. In terms of signal strategies, the protected right-turn phase was found to be associated with fewer crashes than the permitted right-turn (e.g., Wang et al., 2006; Abdel-Aty and Wang, 2006; Chai and Wong, 2014). However, these studies evaluated the impact of signal strategies on crash occurrence only in two generic categories: protected right-turn and permitted right-turn, although right-turn movements at signalised intersections are operated by a number of distinct categories of signal strategy (a brief description of various signal control strategies for rightturn movements is given in the following section). In summary, the relationships between crash occurrence and different types of signal strategies remain relatively unexplored and unknown at signalised intersections. In determining the relationship between crash occurrence and signal strategies, the key consideration and one of the unique features of this study are linking crashes with signal strategies by analysing crash location, crash configuration or collision type, key vehicle approach direction to crash and signal phasing diagram, which has not received much attention in the literature.

Moreover, most studies estimated the simple effects of signal strategies on intersection crashes irrespective of their geometric and traffic conditions. There may have interactions between signal strategies and different geometric and traffic factors that may affect the crash occurrence at intersections. For instance, a simulation study by Chai and Wong (2014) showed that the permitted right-turn with a shared lane is able to reduce rear-end conflicts significantly. However, these interaction effects have not been well understood and reported in the previous studies. It is, therefore, needed to determine not only the simple effects of signal strategies but also the interaction effects between signal strategies and different geometric and traffic factors on intersection safety, which would enable signal designers and policymakers in selecting an appropriate phasing strategy for different site conditions as well as implementing potential safety measures at signalised intersections. Comprehensive studies focusing on the safety of right-turn traffic control strategies at signalised intersections are lacking, as previously articulated. To bridge this gap, this study investigated the relationships between crash occurrence and signal strategies, intersection geometry and traffic operation factors on right-turn crashes at signalised intersections, which provided unique contributions to the literature and fundamental understanding of right-turn involved crashes, characterised by signal strategies, intersection geometry and traffic operation factors.

2.1.1. Methodological issue

Crash occurrence, i.e., number of crashes over a time period, is a nonnegative integer value and rare event. Crash occurrences, as rare event count data, have been modelled with several modelling techniques, of which Poisson regression models as the most popular one have been commonly used to investigate the relationship between crash occurrence and intersection characteristics (Miaou and Lum, 1993; Kumara and Chin, 2005; Wong et al., 2007). However, the overdispersion of crash data fails to satisfy the Poisson distribution assumption that the mean and variance to be equal. Negative binomial models, with the ability to accommodate overdispersion in data by introducing an error term, have been used for crash prediction of overdispersed data instead of poison models (Poch and Mannering, 1996; Chin and Quddus, 2003; Wong et al., 2007). If crash data have excess zeros, a zero-inflated poison regression model or a zero-inflated negative binomial regression model is applied (e.g., Lee and Mannering, 2002; Lee et al., 2002; Shankar et al., 2003; Qin et al., 2004). However, Lord et al. (2005; 2007) questioned the validity of the basic zero-state assumption in these models. Conventional count data models such as Poisson Regression models and Negative Binomial models cannot capture correlation across

observations. To address this problem, random effects or random parameters models have been used (e.g., Chin and Quddus, 2003; El-Basyouny & Sayed, 2009; Guo et al., 2010; Dinu and Amirthalingam, 2011; Dong et al., 2014). Multivariate poison lognormal models (e.g., Ma et al., 2008; Wong et al., 2007) have also been used to address the potential correlation.

From the methodological point of view, an important approach is multilevel modelling when the data structure is hierarchical in which the lower-level observations are clustered with higher levels. In crash data of signalised intersections, the approaches are clustered within an intersection in which they are located, and this can be regarded as a twolevel hierarchy. It is reasonable that the characteristics of crashes occurring within the same intersection are similar because of similar characteristics. Therefore, it is likely that correlation exists among crashes within the same intersection as crashes may share unobserved/ unrecorded characteristics of intersections (Kim et al., 2007; Haghighi et al., 2018). For this correlated data structure, the limitation of traditional regression models (such as Poisson, Negative Binomial regression, etc.) is that they assume that residuals from the model are independent across observations (Jones and Jørgensen, 2003). Disregarding hierarchical structure with significant correlation within clusters may result in models with attenuation of effects (parameter estimates tend toward zero), biased estimates of parameters and standard errors (Bryk and Raudenbush,1992; Haghighi et al., 2018). Multilevel modelling techniques are used to overcome this problem.

In road safety, Abdel-Aty et al. (2011) and Haghighi et al. (2018) developed a multilevel ordered logit model to examine factors affecting crash severity/injury severity on highways considering crashes (lower level) being nested within road segments, and the results revealed that there is a significant correlation among crashes within the same road segment. In another study (Chen et al., 2016), a two-level hierarchical Bayesian logistic model was employed to explore the factors affecting truck driver injury severity on rural highways with cross-level interactions (interactions between vehicle level and crash level) where vehicle level is clustered within crashes. The results indicate that crosslevel interaction effects have an important role in predicting driver injury severities. In another study, Haque et al. (2010) applied different types of Bayesian hierarchical passion models to examine intersectionrelated factors on motorcycle crashes at 3-legged and 4-legged signalised intersections. Similarly, Kim et al. (2007) employed multilevel binomial logistic models with crashes being clustered with intersections. Xie et al. (2013) applied hierarchical negative binomial models in a Bayesian framework to identify crash risk factors of signalised intersections, assuming that intersection crashes (lower level) were correlated within the corridor (higher level). Like random parameter/ random effects models, a hierarchical model can accommodate the heterogeneity across groups. However, the advantage of a hierarchical model is that it allows adding variables at each level that influences the outcome on different levels (Gelman and Hill, 2007).

2.1.2. Summary of research gaps

Although several studies applied hierarchical models, a very limited number of studies applied hierarchical models for intersection crash modelling (Kim et al., 2007; Xie et al., 2013). In particular, no study has developed hierarchical models for right-turn crashes. Moreover, adding cross-level interaction in the model enables us to examine how the relationships between lower-level predictors and outcome variables change as a function of upper-level predictors, which have rarely been investigated in the intersection safety analysis. In this paper, a two-level hierarchical model with cross-level interactions has been proposed to quantify the effects of signal strategies, intersection geometry and traffic operation factors on right-turn crashes at signalised intersections.

2.2. Contributions of the current paper

The study provided some unique contributions to the theory as well as practice. The contributions to the theory are: i) Deeper and more fundamental insights into the signal strategy, intersection geometry and traffic operation factors that influence right-turn crashes at intersections. ii) Application of cross-level interactions for multilevel modelling of intersection crashes. Contributions to practice are enabling the selection of appropriate signal strategies for facilitating right-turn movements at intersections with minimal crash risk and identification of potential safety measures for right-turn crashes at signalised intersections.

2.3. Signal control mechanism for Right-turn movements

The operation of right-turn movements at signalised intersections is usually controlled by five types of signal strategies. They are 1) Through with permitted right-turn (also called Filtered only right-turn), 2) Leading right-turn, 3) Lagging right-turn, 4) Diamond overlap turn, and 5) Split approach. Signal strategies other than Through with permitted are called fully protected right-turn when no permitted right-turn is allowed along with them. However, except for the split approach, sometimes these protected right-turn signal strategies are operated with the combination of permitted right-turn for more efficient traffic flow in intersections. In combined options, the green time of right-turn movements is reduced with the addition of the permitted option, thus decreasing waiting time for opposite through movements as well as cycle time. Signal strategies with crash risk mechanisms are briefly stated in Table 1.

3. Data description

The data used for this research is limited to the intersections located in the state-controlled road network maintained by the Department of Transport and Main Roads (TMR) due to data availability and simplicity. TMR has a total of 425 metro signalised intersections. One of the key features of this study is linking right-turn crashes with signal strategies to evaluate the effects of right-turn signal strategies on safety. A crash during a right-turn signal phasing should involve at least one rightturning vehicle. To facilitate the linking process, TMR metro signalised intersections that have at least one right-turn crash over the period 2012–2018 are selected for the study. A total of 221 signalised intersections, including four-legged and three-legged intersections only, were selected for this study. The selected intersections are shown in the following figure.

The data set is constructed by the accumulation of three datasets, including i) crash data, ii) Intersection layout and phasing data, and iii) Traffic data.

3.1. Crash data

Crash data are collected from the TMR crash database. Crash data provide the following information: i) Number of crashes ii) Crash types by DCA (Definitions for Coding Accidents)* code, iii) Crash location (by latitude and longitude), iv) Key vehicle approach direction to the crash location, iv) Crash road horizontal and vertical alignment, v) Crash road vertical alignment, vi) Crash road speed limit, and vii) Crash time (Hour, Day of the week, Month and Year). This study has been articulated on right-turn crashes (i.e., crashes between right-turn vehicles and through

Table 1

A brief description of signal strategies with crash risk mechanism.

Through with permitted right-turn This signal phasing does not have

2. Leading right-turn

Signal strategies Crash risk mechanisms

any protected right-turn movement, and the right-turn movements are performed by selecting gaps in the opposing traffic flow (Signal Timing Manual-Second Edition, 2015). In a permissive right-turn phase, the right-turn vehicles generally conflict with vehicles in the opposing traffic. Permitted right-turn movements are performed during the circular green signal of through movements. Therefore, there is a concern that drivers turning right on a permitted green signal indication might mistakenly assume that the right turn has the right of way over opposing traffic (Srinivasan et al, 2018). To avoid such a situation, the flashing yellow arrow is used in some states (e.g., Nevada, North Carolina, Oklahoma, and Oregon) in the US to help drivers understand that the drivers are on the permissive rightturn, not on a protected right-turn. However, no intersections in Australia use the flashing yellow light signal in the permitted rightturn signal phasing. In this signal phasing, only one approach is protected in which opposite through movement (Phase-2) follows right-turn movement (Phase-1). Therefore, through movement is stopped when the leading right-turn phase starts. As a result, there is less opportunity to conflict between right-turn and through vehicles in phase transition period (inter-green period). It is noted that the opportunity to conflict between right-turn vehicles and other vehicles at signalised intersections is predominant in the transition period. Leading right-turn is, therefore, considered a safer operation. Leading right-turn is also used in combination with a permitted right-turn. In this case, permitted right-turn is allowed from either approach or both approaches in the following phase of protected right-turn along with through movements. Therefore, Leading right-turn can be subdivided into two types: Lead nonpermitted right-turn when no permitted right-turn is allowed [2(a)], and Lead permitted right-turn when permitted right-turn is allowed with Leading right-turn in Phase-2[2(b)]. approach is protected in Lagging

Lagging right-turn Like Leading right-turn, only one right-turn, but the main difference with Leading right-turn is that the right-turn movement (Phase-2) follows the opposite through movement (Phase-1). The through movement stops when the lagging right-turn phase starts. As a result, there is a higher chance of conflict between right-turn and through vehicles in the transition period. Like Leading right-turn, Lagging right-

Table 1 (continued )

Signal strategies Crash risk mechanisms

turn can be subdivided into two types: Lag nonpermitted right-turn when no permitted right-turn is allowed [3(a)], and Lag permitted right-turn when permitted right-turn is allowed with Lagging right-turn in Phase-1 [3(b)]. When Lagging rightturn is used with the permitted option, permitted movement from one approach only is allowed, as shown in the figure. Here, permitted right-turn from opposing the Lagging right-turn is usually banned because this permitted option can create a 'right-turn trap' situation, leading to crashes. This is because the filtering right-turn vehicles would face a yellow signal while the oncoming through traffic faces a green signal during the phase transition (from Phase 1 to Phase 2) (Austroads, 2016).

Diamond overlap turn It is the combination of diamond turn (right-turn movements from both approaches run simultaneously while the through movements are stopped) with alternative overlaps for one intersecting street, as shown in the figure. Here the through movement follows the right-turn movements. It is, therefore, the combination of a Diamond turn with a protected Leading right-turn. Being a Leading right-turn, it offers less opportunity to conflict during phase transition. It is more flexible and efficient than diamond turn phasing as it can cater for widely varying demands. Permitted right-turns are also allowed from either or both approaches. Thus Diamond overlap turn can be subdivided into two types: Diamond overlap nonpermitted turn when no permitted right-turn is allowed [4 (a)], and Diamond overlap permitted right-turn when permitted right-turn is allowed in the through phase [4 (b)].

phases to opposing traffic movements. The right-turn and associated through movements operate at the same time, whilst all opposing movements are stopped. So conflicts are eliminated here, and it is considered the safest approach. However, this type of phasing is very inefficient operation-wise and should only be used as a last resort ( Austroads, 2016).

Split Approach This phase allocates totally separate

*1, 2, 2a, 2b, 3 indicate the sequence of phasing.

vehicles, between right-turn vehicles and left-turn vehicles, and among right-turn vehicles) at signalised intersections. This gives a total of 804 right-turn crashes for 221 intersections over the period from 2012 to 2018.

3.2. Intersection layout and phasing data

Intersection phasing sequences (signal strategies) and geometric information in relation to right-turn crashes are extracted from the TMR intersection signal design plan (a typical signal design plan is shown in

Fig. 1. A typical Signal Design Plan.

Fig. 1). A signal design plan provides the following information: i) Signal strategy, ii) Number of right-turn lanes, iii) Number of conflicting lanes, iv) Right-turn lanes shared or not, v) Number of total phase, vi) Number of right-turn phase, vii) Number of right turn bay, and viii) Intersection type. Key consideration and one of the unique features of this study is linking crashes with signal strategies (i.e. it has considered crash time

signal strategy) to quantify the effect of each type of signal strategy, which has never been considered in a previous study. Linking crashes with signal strategy was done following the steps stated below.Fig. 2.

1. First, the location of a crash within an intersection was determined using latitude and longitude.
- 2. Then each crash associated with a right-turn movement is

Fig. 2. Selected Intersections.

identified using crash location, DCA crash type (DCA crash types are illustrated in Fig. 3), and key vehicle approach direction to crash location (all information taken from the TMR crash database).

Once a crash associated with a right-turn movement is identified, this right-turn movement corresponding signal strategy and geometric information are found in the signal design plan.

* DCA stands for Definitions for coding Accidents. Each crash is given a DCA code indicating the movements road users were making when the crash occurred. This code is created by the Australian Road Research Board.

A crash along with vehicle movements at intersections is presented in Fig. 4(a) to illustrate the linking process. Suppose C1 is the location of the crash, and the crash pattern is DCA 202 (conflicting between rightturn and the opposite through movement), and the direction of the key vehicle (right-turn vehicle) approaching the crash location is East. It is obvious from the figure that of four right-turn movements, the right-turn movement R1 is approaching East to C1 crash location (other right-turn movements approaching direction to crash location are not east) conflicting with opposite through movement T3. Here the crash-associated approach was the R1-T3 approach (consisting of R1 right-turn approach and T3 through approach). The crash associated right-turn movement is R1. Therefore, the crash was assigned to the R1 approach (In case of conflict between two right-turn vehicles, usually a rare crash, the crash was assigned to the approach of the key right-turn vehicle as defined in DCA codes). Now, R1 corresponding phasing sequence is found in the signal design plan. The corresponding signal sequence of R1 is presented in Fig. 4(b). It is associated with phase A, which is Leading right-turn. Thus, the Leading right-turn signal strategy is assigned to this crash. Geometric characteristics associated with R1 and T3 approaches were also assigned to this crash. In this way, intersection layout and phasing information for all selected right-turn crashes were incorporated into the crash database.

Fig. 3. DCA crash configuration (Australian Road Research Board).

Fig. 4a. Crash Movements for DCA 202 crash pattern.

3.3. Traffic data

Traffic data (Traffic volume and Occupancy) were extracted from the STREAM data stored in the server of The University of Queensland. Data streaming is a continuous flow of data generated from various sources. For example, in the STREAM platform, traffic data is being stored in the server every 3 s from the TMR intersections connected to the ITS system. The SQL language is used to extract traffic data from the STREAM channel. In previous studies, intersection crash analysis was conducted mostly based on highly aggregated traffic data (e.g., average annual daily traffic, AADT). However, these aggregated traffic data restrict the reliability of the findings simply because they don't reflect the actual scenario of traffic volume for the crash happening at intersections (Yuan, J. and Abdel-Aty, M., 2018). To capture the actual traffic condition of a crash hour, it is needed to identify the actual hour of a crash. TMR crash database discloses the year, month, day and time of a crash, but it does not disclose the actual date of a crash because of privacy concerns. As a result, it was not possible to identify the actual hour of a crash. To overcome this challenge, the average volume of the crash hour of all crash days in a month was used. For example, if a crash occurred on the 5th hour of Monday in January 2018, the average crash hour volume would be the average volume of the 5th hour of all Mondays in January 2018.

Fig. 4b. Signal sequence of the intersection presented in Fig. 4(a).

3.4. Variables

The dataset of this study was constructed with the accumulation of crash data, intersection layout and phasing data, and traffic data for 221 TMR intersections. The structure of the dataset is regarded as a two-level hierarchy, as depicted in Fig. 5, where N intersection approaches are clustered within J intersections. Therefore, level-1 variables are the approach level factors that can vary within the same intersection. For example, right-turn volume (level-1 variable) can vary on approaches within an intersection. Level-2 variables are the intersection level factors that don't vary within the same intersection. For example, the type of intersection (level-2 variable) is the same for all approaches within the same intersection. Descriptive statistics of the variables used in the study are provided in Table 2.

To analysis crash frequency, this study considered crash-based information of intersection approaches, e.g., crash associated with signal strategies, crash hour right-turn volume, crash hour conflicting volume, crash hour occupancy. Therefore, the intersection approaches were used as the unit of observation. Table 2 shows that the average number of crashes per approach is about 2 for the whole study period 7 years. As such, yearly crash counts may lead to excess zeros. To avoid excess zero issues, this study considered crash counts for the whole study period instead of a yearly crash as the unit of observation. Crash distribution by signal strategies on intersections as well as approaches is shown in Table 3, and it shows that Lag Permitted right-turns experienced the highest number of crashes per approach over the period (5.89 per approach), whereas Split approach right-turn had the lowest number of crashes per approach (1.53 per approach).

4. Model formation

Multilevel Poisson regression models were developed to quantify the effects of signal strategies as well as geometric and traffic factors on right-turn crashes at signalised intersections, where approaches were presumed as clustered within intersections.

4.1. Poisson Regression model

As explained earlier, crash-involved approaches were used as the unit of observation in this study. Therefore, the number of crashes per observation (per approach) over the period is greater than zero, i.e., Yi greater than 0. Poisson Regression Model truncated at zero is used for the count data where the value zero cannot occur. Hence, this study developed Zero-Truncated Poisson Regression Model. In a Zero-Truncated Poisson Regression Model, the probability of an approach i having Yi = K number of crashes over the specific period is given by:

$$Prob(Y_i = K | Y_i > 0) = \frac{\lambda_i^{Y_i} e^{-\lambda_i}}{Y_i! {1 - Prob(Y_i = 0)}} for Y_i = 1, 2, \dots ...$$

$$= \frac{\lambda_i^{Y_i} e^{-\lambda_i}}{Y_i! (1 - e^{-\lambda_i})} = \frac{\lambda_i^{Y_i}}{Y_i! (e^{\lambda_i} - 1)}$$

Where λi = E(Yi) = Expected number of crashes over the period in approach i.

Poisson Regression Models are estimated by specifying the Poisson parameter λi as a function of predictor variables. The most common relationship between predictor variables Xi and the Poisson parameter λⁱ is the log-linear model:

$$E(Y_i) = \lambda_i = e^{\beta_0 + \beta_1 X_i}$$ or this can be rewritten as $Log E(Y_i) = \beta_0 + \beta_1 X_i$ (1)

4.2. Multilevel Poisson Regression model

We have a hierarchical dataset with N approaches (level-1) nested within J intersections (level-2) as depicted in Fig. 4(b). Hence with the hierarchical data structure, equation (1) can be rewritten as a Level-1 multilevel model as follows:

Level-1 model:

$$LogE(Y{ij}) = \beta{0j} + \beta{1j}X{ij}$$ (2)

Here Yij is the number of crashes for approach i nested in intersection j, *β*0*j*is the intercept, *β*1*j*is the estimated coefficient for explanatory variable, Xij is the level-1(approach level) explanatory variable. The subscript j in the model indicates that both intercept (*β0^j*) and slope coefficient (*β1^j*) are allowed to vary across intersections (level-2).

In multilevel modelling, the β coefficients at level-1 are modelled as outcome variables at level-2. Level-2 models are formulated as follows: Level-2 Model:

Fig. 5. Hierarchical structure of data.

Table 2 Descriptive statistics of variables considered for modelling right-turn crashes.

Variable Name	Description		Statistics
Dependent variable: Number of Crash	Number of crashes per approach for the period 2012–2018	Sum 804	Mean 1.9052	Std. dev. 2.1797
Independent Variables:	Approach level (Level-1) variables Categorical variables (Yes ¼ 1, and No ¼		Percentage	Frequency
0):
Split Approach	If right-turn signal strategy is Split approach		30.81	130
Diamond overlap permitted	If right-turn signal strategy is Diamond overlap turn with		04.74	20
Diamond overlap nonpermitted	permitted If right-turn signal strategy is Diamond overlap turn without		15.40	65
Permitted only	permitted If right-turn signal strategy is Through with		13.51	57
Lag permitted	permitted If right-turn signal strategy is Lagging right-turn with		02.14	9
Lag	permitted If right-turn signal		13.27	56
nonpermitted	strategy is Lagging right-turn without permitted
Lead permitted	If right-turn signal strategy is Leading right-turn with permitted		04.98	21
Lead nonpermitted	If right-turn signal strategy is Leading right-turn without		15.17	64
Shared Right turn	permitted If the right-turn is shared with through movement		23.46	99
Right-turn bay	If the crash approach has a right-turn bay		61.14	258
Curve	If the horizontal alignment of crash approach is curve		16.35	69
Level	If the vertical alignment of crash approach is level		70.14	296
Grade	If the vertical alignment of crash approach is grade		16.59	70
Crest dip	If the vertical alignment of crash approach is crest or dip		13.27	56
Continuous variables:			Mean	Std. dev.
Number of conflicting lane	Number of lanes conflicting with right turn crash approach		1.8909	0.7079
Number of right turn lane	Number of right-turn lanes on right-turn crash approach		1.2749	0.4470
Traffic flow conflicting lane	Average traffic flow per conflicting lane in crash hour (veh)		194.43	156.15
Traffic flow right-turn lane	Average traffic flow per right-turn lane in crash hour (veh)		91.50	96.57
			21.78	19.94

Table 2 (continued )
Variable Name	Description	Statistics
Occupancy conflicting lane	Average occupancy* of vehicles on conflicting lanes in crash hour (%)
Occupancy right-turn lane	Average occupancy of vehicles on right-turn lanes in crash hour (%)	29.72	20.68
Length Right turn bay	Length of right-turn bay (m)	84.04	68.21
Speed limit	Speed limit of crash approach in km/h	63.39	6.54
	Intersection level (Level-2) variables
Categorical variable		Percentage	Frequency
4-legged intersection	Intersection Type: 1 = 4-legged intersection, 0 = 3-legged intersection	69.19	299
Continuous variables:		Mean	Std. dev.
Number of total phase	Number of total phases in a cycle	4.4502	1.6473
Number of right turn phase	Number of total right turn phase in a cycle	3.1303	1.6825
Vol major approach	Average Traffic Volume on Major approach in crash hour (veh)	1261.19	778.40
Vol minor approach	Average Traffic Volume on Minor approach in crash hour (veh)	340.73	334.93
Number of observations:	422

^*Occupancy is measured as the % of time vehicles occupied the lane (detector).

$$\boldsymbol{\beta}{0j} = \gamma{00} + \boldsymbol{\mu}_{0j} \tag{3}$$

where, var( *μ*0j = τ⁰⁰ *, μ0^j* ∼ (0, δu²

$$\boldsymbol{\beta}{1j} = \gamma{10} + \boldsymbol{\mu}_{1j} \tag{4}$$

Here for the intercept model, *γ*00 is the overall effect (fixed effects), and u0j (random effects) is the adjustment for each group's deviation from the overall effect. For the slope coefficient model, *γ*10 is the grand mean slope (fixed effects) and *μ1^j*(random effects) is the adjustment for the deviation of each group's slope from the grand mean slope across group.

Level-2 variables (intersection level variables) are added in equation (2) to get the direct effects of level-2 variables on crash frequency. In addition to direct effects, to get cross-level interaction effects (Interaction effects between approach level variables and intersection level variables), level-2 variables are also added in the slope coefficient equation. Therefore, adding level-2 variables, the equations (3) and (4) for random intercept and random slope models can be rewritten as follows:

Level-2 Model:

$$\boldsymbol{\beta}{0j} = \gamma{00} + \gamma_{01} \mathbf{Z}j + \boldsymbol{\mu}{0j} \tag{5}$$

$$\boldsymbol{\beta}{1j} = \gamma{10} + \gamma_{11} \mathbf{Z}j + \boldsymbol{\mu}{1j} \tag{6}$$

Zj is the intersection level explanatory variable.

The level-1 and level-2 models can be written as one combined model by substituting equations (5) and (6) into equation (2):

Combined Model:

$$LogE(Y{ij}) = \gamma{00} + \gamma_{01}Zj + \gamma{10}X{ij} + \gamma{11}X_{ij}Zj + \mu{1j}X{ij} + \mu{0j}$$ (7)

Here *γ*11 represents cross-level interaction coefficient.

However, the random slope makes the model highly complex,

Table 3 Crash distribution by signal strategies.

| Signal Strategy | Number of intersection | Number of approach | Number of crashes
% of total crashes | | No of crashes per approach | | | |------------------------------|------------------------|--------------------|-----------------------------------------|-------|----------------------------|--|--| | Diamond overlap permitted | 15 | 20 | 44 | 5.5% | 2.20 | | | | Diamond overlap nonpermitted | 43 | 65 | 108 | 13.4% | 1.66 | | | | Permitted only | 43 | 57 | 94 | 11.7% | 1.65 | | | | Lag permitted | 8 | 9 | 53 | 6.6% | 5.89 | | | | Lag nonpermitted | 40 | 56 | 118 | 14.7% | 2.11 | | | | Lead permitted | 19 | 21 | 39 | 4.9% | 1.86 | | | | Lead nonpermitted | 55 | 64 | 149 | 6.8% | 2.33 | | | | Split Approach | 94 | 130 | 199 | 24.8% | 1.53 | | |

resulting in intensive model computation (Snijders and Bosker, 2000). To avoid high complexity with retaining model reasonableness and accuracy, the random slope effect *μ*1*j*is excluded from the model. However, the cross-level interaction is retained in the model to examine the effects of level-2 variables over level-1 variables. Neglecting the random slope effect, the above model reduces to the following random intercept Poisson Regression model.

$$LogE(Y{ij}) = \gamma{00} + \gamma_{01}Zj + \gamma{10}X{ij} + \gamma{11}X_{ij}Zj + \mu{0j}$$ (8)

In this study, cross-level interactions are examined between signal strategies and intersection level variables only. In addition, same-level interactions between signal strategies and geometric and traffic factors at level-1 (approach level) are also included in the model. Based on the above model structure, a Multilevel Poisson Regression Model with

Table 4 Random effects Zero-Truncated Poisson Regression Model results.

| Variable | Coefficients | Std Error | z | Prob
z >Z* | 95% confidence interval | | | | |------------------------------------------------------------|--------------|-----------|--------|----------------|-------------------------|---|---------|--| | Null Model: | | | | | | | | | | Fixed effect: Intercept | − 0.253*** | 0.078 | − 3.24 | 0.001 | -0.406 | - | − 0.01 | | | Random effect: Intercept | 1.127*** | 0.057 | 19.95 | <0.001 | 1.016 | – | 1.238 | | | ICC (Intra-class correlation coefficient): 0.301 | | | | | | | | | | Log-likelihood function: − 583.998 | | | | | | | | | | Full model: | | | | | | | | | | Fixed effects | | | | | | | | | | Intercept | − 0.420*** | 0.106 | − 3.95 | <0.001 | -0.628 | – | -0.211 | | | Diamond overlap permitted | 1.023*** | 0.355 | 2.88 | 0.004 | 0.327 | – | 1.719 | | | Diamond overlap nonpermitted | 0.577** | 0.247 | 2.33 | 0.0197 | 0.092 | – | 1.061 | | | Permitted only | 1.297*** | 0.249 | 5.20 | <0.001 | 0.808 | – | 1.785 | | | Lag permitted | 1.810*** | 0.294 | 6.15 | <0.001 | 1.233 | – | 2.387 | | | Lag nonpermitted | 1.233*** | 0.212 | 5.83 | <0.001 | 0.818 | – | 1.647 | | | Lead permitted | 1.108*** | 0.317 | 3.49 | <0.001 | 0.486 | – | 1.730 | | | Lead nonpermitted | 0.969*** | 0.219 | 4.43 | <0.001 | 0.541 | – | 1.397 | | | Num right-turn lane | 0.334*** | 0.142 | 2.35 | 0.019 | 0.055 | – | 0.612 | | | Num conflicting lane | 0.300*** | 0.075 | 3.98 | <0.001 | 0.152 | – | 0.448 | | | Traffic flow right-turn lane | 0.003*** | 0.001 | 4.34 | <0.001 | 0.002 | – | 0.005 | | | Traffic flow conflicting lane | 0.001*** | 0.0004 | 3.07 | 0.002 | 0.001 | – | 0.002 | | | Occupancy conflicting lane | − 0.018*** | 0.004 | − 4.93 | <0.001 | -0.025 | – | -0.011 | | | Shared Right-turn | − 0.574*** | 0.211 | − 2.72 | 0.007 | -0.987 | – | 0.161 | | | 4-legged intersection | − 0.459*** | 0.146 | − 3.14 | 0.002 | -0.746 | – | -0.173 | | | Interaction effects | | | | | | | | | | Lag permitted*Traffic flow right-turn lane | 0.010*** | 0.002 | 5.56 | <0.001 | 0.007 | – | 0.014 | | | Diamond overlap nonpermitted* Traffic flow right-turn lane | − 0.003** | 0.002 | − 2.05 | 0.041 | -0.007 | – | -0.0001 | | | Diamond overlap permitted* Traffic flow conflicting lane | 0.008*** | 0.002 | 4.02 | <0.001 | 0.004 | – | 0.012 | | | Lag nonpermitted *Traffic flow conflicting lane | 0.004*** | 0.001 | 3.89 | <0.001 | 0.002 | | 0.006 | | | Lead nonpermitted * Curve | 1.290*** | 0.311 | 4.15 | <0.001 | 0.681 | – | 1.900 | | | Diamond overlap nonpermitted* Crest Dip | 1.326*** | 0.322 | 4.12 | <0.001 | 0.695 | – | 1.957 | | | Right-turn bay*Length right-turn bay | -0.003*** | 0.001 | − 2.85 | 0.004 | -0.006 | – | -0.001 | | | Cross-level interaction effects | | | | | | | | | | Lead nonpermitted*Num right-turn phase | -0.780*** | 0.141 | − 5.52 | <0.001 | − 1.057 | – | -0.5031 | | | Lead nonpermitted*4-legged intersection | 1.392*** | 0.321 | 4.34 | <0.001 | 0.763 | – | 2.021 | | | | | | | | | | | | | Random effect | | | | | | | | | | Intercept | 0.932*** | 0.063 | 14.71 | <0.001 | 0.807 | – | 1.056 | | | Log likelihood function: − 484.331 | | | | | | | | | | Restricted log likelihood: − 1269.117 | | | | | | | | | | Chi squared(dof = 23): 1569.571 | | | | | | | | | | Significance level: <0.001 | | | | | | | | | | McFadden Pseudo R-squared: 0.618 | | | | | | | | |

^{***, **, *} ==> Significance at 1%, 5%, 10% level.

The split approach is the reference case for signal strategies.

cross-level as well as same level interactions of variables is formulated as follows:

of model parameters when both the main effects and interaction terms are included in the subsequent analysis (Iversen, 1991; Wooldridge, 2004). Moreover, centring provides a potential advantage in terms of

$$LogE(Yij) = \gamma{00} + \sum{q=1}^{Q} \gamma{0q} Z{qj} + \sum{r=1}^{T} \gamma{r0} X{iij} + \sum{s=1}^{S} \sum{r=1}^{R} \gamma{sr} X{sij} X{rij} + \sum{s=1}^{S} \sum{q=1}^{Q} \gamma{sq} X{Sij} Z{qj} + u{0j}$$ (9)

Where Yij is the number of crashes in approach i over the period, E(Yij) is the expected number of crashes in approach i over the specific period, Q is the number of intersection level predictors, T is the number of approach level predictors, among which S is the number of signal strategies and R is the number of other predictors than signal strategies, γ⁰⁰ = the intercept, Zqj= a vector of intersection-level factors, Xtij = a vector of approach-level variables, Xsij = a vector of signal strategies, Xrij = a vector of approach-level variables other than signal strategies, *γ*0q= the regression coefficients for intersection-level variables andγ^t0= the regression coefficients for approach level variables, γsr and γsq are the regression coefficients associated with interactions of signal strategies with approach level variables and intersection level variables, respectively, *u0^j*is the group level random effect, where *μ0^j* ∼ (0, δu²).

4.3. Multilevel model adequacy

In multilevel modelling analysis, the proportion of variance within and between groups is required to examine model adequacy and analyse differences across groups (Park et al., 2017). The proportion of variance in the outcome between groups is examined by the intra-class correlation coefficient (ICC) (Kim et al., 2007; Kutner et al., 2004, Park et al., 2017). The ICC of a model is calculated from a fully unconditional multilevel model (a model without any predictor variables) and is defined as:

$$ICC = \frac{\sigma_u^2}{\sigma_u^2 + \sigma^2} \tag{10}$$

Where σ^u ²⁼ between-group variance (the variance of *μ*0j), σ2 ⁼ withingroup variance. ICC evaluates the portion of total variance explained by between-group variance with a range from 0 to 1. If ICC is sufficiently close to zero, then between-group variance is a small portion of the total variance, suggesting no significant variation in the subjects between groups, and the standard model is appropriate for the data. On the contrary, ICC sufficiently higher than zero indicates the significance of between-group variance in explaining total variance and demonstrates that a multilevel model is preferable (Huang et al., 2008; Kutner et al., 2004).

5. Results and discussion

At first, the null or fully unconditional model (a model without explanatory variables) was estimated (see Table 4 for model results). Then the adequacy of multilevel modelling was examined by determining the Intra-class Correlation Coefficient (ICC) using Eq (10). From the null model results, ICC is estimated at 0.3115, which is significantly higher than zero, indicating between-group variance is 31.15% of the total variance. Therefore, a significant correlation exists among crashes within the same intersection. This presence of within-intersection correlations justified the application of multilevel modelling on right-turn crash frequency analysis.

The next step is to estimate Random-Intercept Zero-Truncated Poisson Regression Model as described earlier. It is common practice to centre the variables to avoid collinearity problems in the standard errors interpretation of results (Finch et al., 2014). Variables used in the estimated model are grand-mean centred.

For this study, the main effects, interaction effects and cross-level interaction effects of signal strategy, intersection geometry and traffic operation factors were estimated. The final model reported in Table 4 excluded insignificant variables at a 5% significance level one by one. Results show that fourteen main effect variables, seven interaction effects and two cross-level interaction effects between signal strategies and geometric and traffic factors are significant. The log-likelihood ratio statistic comparing the fitted model and restricted model (the model with a constant term only) results in chi-squared (25) = 1570.09 (pvalue < 0.001), suggesting that the fitted model has sufficient explanatory power. In addition, McFadden's Pseudo R-squared statistic for the fitted model is 0.619.

5.1. Main effects

Model results show that a total of fourteen main effect variables are statistically significant. Of them, seven variables are associated with signal strategies. Out of the rest seven variables, four variables (number of right-turn lanes, number of conflicting lanes, traffic flow on the rightturn lane and traffic flow on the conflicting lane) have negative effects on safety, whereas three variables (occupancy on the conflicting lane, shared right-turn and 4-legged intersection) have positive effects on safety. For comparing the safety effects of signal strategies, partial effects of signal strategies are presented with bar diagrams in Fig. 6. The split approach (the safest one for right-turn movements) is used as the reference category, and therefore, the partial effects of signal strategies shown in the Fig. 6 indicate the increase in right-turn crashes relative to the split approach holding all other variables at their mean.

Results show that the Diamond overlap permitted signal strategy is associated with a 78% ((0.607–0.342)/0.342) higher number of rightturn crashes than the Diamond overlap nonpermitted signal strategy. Similarly, Lag permitted and Lead permitted signal strategies are associated with 47% and 14% higher crashes than Lag nonpermitted and Lead nonpermitted right-turn, respectively. So Lead permitted is a better option to be used with a less adverse effect on safety than other combined options (Diamond overlap permitted and Lag permitted). In summary, the right-turn crash is higher for right-turn signal strategies with permitted options than nonpermitted or protected options. During the permitted option, right-turn vehicles are required to accept gaps through the oncoming traffic, resulting in traffic conflicts and increased crash risk.

Among all the signal strategies with permitted options (shown in red), Lag permitted has the highest effect on right-turn crashes. Its partial effect of 1.073 indicates that the mean number of crashes in an intersection approach increases by 1.073 if the Split approach changes to the Lag permitted option. With regards to fully protected options (shown in green), the Lag nonpermitted signal strategy involves the highest number of crashes. In summary, the Lagging right-turns are associated with more crashes for both fully protected and protected with permitted options, and the Lag permitted right-turn is the highest-risk signal strategy. The Lagging right-turn has a relatively high potential for conflicts during the phase transition period (inter-green period). For

Fig. 6. Partial effects of Signal strategies.

a protected right-turn signal strategy, the opportunity to conflict between right-turn vehicles and other vehicles at signalised intersections is mainly in the transition period. In Lagging right-turn, right-turn movement follows the opposite through movement (see section 3). As a result, during phase transition, while the opposing vehicle is stopping, the right-turn vehicle starts. During this phase transition, when the opposing vehicle driver sees the yellow light at such a distance that it is not safe to pass through the intersection in the inter-green period, some drivers, due to their misjudging the distance or aggressiveness to avoid delay for next signal phase, drive through the intersections. As a result, when the through vehicle reaches the intersection, the right-turn vehicle also enters the intersection, getting the green light, which causes conflict between the two vehicles. Conversely, in the case of leading right-turn, the right-turn vehicle starts when the opposing through vehicle is

Fig. 7. Partial effects of Occupancy on conflicting lane.

Fig. 8. Expected number of crashes for conflicting traffic flow with occupancy.

already stopped in the previous phase. Thus, the Leading right-turn offers less opportunity to conflict. Therefore, the number of crashes is likely to be higher in lagging right-turn. Adding permitted options in the Lagging right-turn signal strategy will further increase collision risk by unprotecting the right-turn. Therefore, the probability of a crash happening is the highest in Lag permitted right-turn.

Among other significant factors, traffic flow on the right-turn lane (Coeff = 0.003, Z = 4.34, p-value < 0.001) and traffic flow on the conflicting lane (Coeff = 0.001, Z = 3.07, p-value = 0.002) are found to be positively associated with the crash occurrence. The results show that an increase of 100 vehicles per hour per right-turn lane would increase 34% (100*(e.00335-1)) of right-turn crashes, and similarly, it would

increase 13% (100*(e.0013-1)) per 100 vehicles for traffic flow on the conflicting lane. Higher traffic flows on the right-turn lane or conflicting lane increase the exposure to right-turn crash opportunities. With the increase of traffic flow on the right-turn lane, more right-turn vehicles are required to maneuver against conflicting traffic. Similarly, if the conflicting traffic flow increases, right-turn vehicles will be required to maneuver against higher conflicting traffic volume. This finding is consistent with previous studies (Poch and Mannering, 1996; Chin and Quddus, 2003; Abdel-Aty and Wang, 2006; Wang and Abdel-Aty, 2008). However, these studies considered highly aggregated traffic volume like AADT, whereas the current study considered traffic volumes during the hour of the crash.

Fig. 9. Interaction effects between signal strategies and traffic flow right-turn lane.

Although the probability of crash occurrence increases with the increase of traffic flow on the conflicting lane, the results suggest that the likelihood of right-turn crashes is negatively associated with the occupancy of conflicting lanes (Coeff = − 0.0179, Z = − 4.93, p-value=*<*0.001). Occupancy is the percentage of time vehicles at an intersection occupy the detector. A higher occupancy on the conflicting lane indicates a longer queue at intersections with interrupted traffic flow at intersections, thus promoting more through vehicles stopping at intersections. As a result, vehicles passing through the intersection without being stopped at intersections would decrease with the occupancy, thus allowing less opportunity to conflict between right-turn and through vehicles during phase transition due to interrupted through vehicles. The vehicles at signalised intersections with protected rightturn have the opportunity to conflict mainly during the phase transition period. The partial effects of occupancy on the conflicting lane are presented in Fig. 7. The figure shows that the reduction in mean-crash for per unit increase of occupancy decreases with the increase of occupancy, as it approaches a higher occupancy level, i.e., more interrupted traffic flow.

Figure 8 shows how the effects of conflicting traffic flow on rightturn crashes of an intersection approach vary with occupancy. It suggests that the expected number of crashes for the range of conflicting traffic flows is higher with lower occupancy. In addition, the lower occupancy curve is steeper than a higher occupancy curve (e.g., the 25% occupancy curve is steeper than the 50% occupancy curve), indicating that the crash increasing rate with respect to conflicting traffic flow is also higher with a lower occupancy of the conflict lane.

The likelihood of right-turn crashes increases by 40% (e.3335-1) with an additional right-turn lane. More right-turn lanes indicate more rightturn traffic for the maneuver against opposing traffic flow. Similarly, the number of conflicting lanes is positively correlated with right-turn crashes at intersections, with the corresponding likelihood of 35% (e.2998-1) more crashes for one lane increase of conflicting lane. A higher number of conflicting lanes require right-turn vehicles to cross a longer distance through the conflicting zone of an intersection and thus increase the crash risk.

The intersection approach with a shared right-turn approach is found to be associated with 44% (1-e-.5736) fewer right-turn crashes than an intersection approach with an exclusive right-turn lane. Shared rightturns are generally used in simple and small intersections, and thus the right-turn crash risk might be lower at those intersections.

Among intersection level variables, 4-legged intersections are found to be negatively associated with right-turn crashes (Coeff = -0.459, Z = -3.14, p-value = 0.002). Results suggest that 4-legged intersections experience 37% (1-e-.4594) fewer right-turn crashes than the 3-legged intersections. However, previous studies (e.g., Abdel-Aty and Wang, 2006, Xie et al., 2013) found that 4-legged intersections are associated with more crashes than 3-legged intersections. The effects of intersection configuration (4-legged and 3-legged intersections) on right-turn crashes need to be investigated further.

5.2. Interaction effects

This study examined the interactions between signal strategies and geometric and traffic factors, which provided new insights into how the effects of signal strategies on crashes change over a range of geometric and operation conditions. Right-turn crash risks in light of the identified interaction effects are discussed below.

5.2.1. Interactions: Signal strategies traffic flow right-turn lane*

To examine interaction effects between signal strategies and rightturn traffic flow, partial effects of signal strategies are plotted against right-turn traffic flow in Fig. 9. The partial effects shown in Fig. 9 indicate the change in right turn crashes at signal strategies due to an increase in right-turn traffic flow, holding all other variables at their mean. The plot illustrates that the number of crashes at Lag permitted and Diamond overlap nonpermitted change considerably with the increase in right-turn traffic flow indicating two significant interaction effects prevailing between signal strategies and right-turn traffic flow and these are between 1) Lag permitted (CLAF) and right-turn traffic flow (Coeff = 0.0101, Z = 5.56, p-value < 0.001), and 2) Diamond overlap nonpermitted (CDONF) and right-turn traffic flow (Coeff = -0.003, Z = -2.05, p-value = 0.041).

To analyse these two interaction effects on crash occurrence, they are plotted separately in Fig. 10 and Fig. 11 with confidence intervals.

Figure 10 shows the partial effects of Lag permitted (change in mean

Fig. 10. Interaction effects between Lag permitted and traffic flow right-turn lane.

Fig. 11. Interaction effects between Diamond overlap nonpermitted and traffic flow right-turn lane ccupanconflicting lane.

Fig. 12. Interaction: Lag permitted and Traffic flow right-turn lane for different conflicting traffic flow.

crashes) with respect to an increase in right-turn traffic flow. The plot illustrates that the number of crashes for Lag permitted right-turn is likely to increase with traffic flow right-turn lane. Lag permitted is the highest risk signal strategy due to having a high potential for collision between right-turn vehicles and through vehicles in the phase transition period. An increase in right-turn traffic flow also makes this collision risk higher, particularly with the permitted right-turn signal option.

Figure 11 suggests that the likelihood of crashes decreases with rightturn traffic flow for the Diamond overlap nonpermitted option. Diamond overlap turn is a complicated right-turn signal strategy, usually employed for large 4-legged intersections with high traffic volume both in right-turn and through lane. The number of right-turn phases and

cycle time are generally high for these intersections. As a result, through vehicles generally need to wait long for a green phase. This waiting time increases with the increase of right-turn traffic flow, making long queues at intersections. Hence, there would be fewer crashes because of the interrupted flow on the opposing lane. For a deeper insight into these interaction effects, they are also plotted for different values of conflicting traffic flow to examine how the interactions vary with conflicting traffic flow (Fig. 12 and Fig. 13).

Figure 12 indicates a further increase of crash likelihood in Lag permitted right-turn by conflicting traffic flow, which is rational as more traffic flow promotes a higher number of crashes. Interestingly, Fig. 13 illustrates that number of crashes increases with conflicting traffic flow

Fig. 13. Interaction: Diamond overlap nonpermitted and Traffic flow right-turn lane for different conflicting traffic flow.

Fig. 14. Interaction effects between signal strategies and traffic flow conflicting lane.

in Diamond overlap nonpermitted right-turn up to cut-off point of rightturn traffic flow (approximately at 270 v/h). After that cut-off point, the number of crashes is lower for a higher value of conflicting traffic flow because of queue developing at this point with higher conflicting traffic flow.

5.2.2. Interactions: Signal strategies traffic flow conflicting lane*

To examine interaction effects between signal strategies and traffic flow conflicting lanes, partial effects of signal strategies are plotted against conflicting traffic flow (Fig. 14). The plot illustrates that the number of crashes at Diamond overlap permitted and Lag nonpermitted increase considerably with the increase in conflicting traffic flow, indicating two significant interaction effects prevailing between signal strategies and conflicting traffic flow. These are between 1) Diamond overlap permitted (CDOF) and conflicting traffic flow (Coeff = 0.008, Z = 4.02, p-value < 0.001), and 2) Lag nonpermitted (CLANF) and conflicting traffic flow (Coeff = 0.004, Z = 3.89, p-value < 0.001).

The partial effects (changes in mean crashes) of Diamond overlap permitted and Lag nonpermitted are plotted against conflicting traffic flow including confidence interval in Fig. 15 and Fig. 16.

The figures show that number of crashes is likely to increase with conflicting traffic flow for both signal strategies with the rate of increase

Fig. 15. Interaction effects between Diamond overlap permitted and traffic flow conflicting lane.

Fig. 16. Interaction effect between Lag nonpermitted and Traffic flow conflicting lane.

being higher for Diamond overlap permitted right-turn because adding a permitted option in Diamond overlap turn increases the opportunity to conflict greatly. For a deeper insight into these interaction effects, they are also plotted for different values of right-turn traffic flow (Fig. 17 and Fig. 18).

Both figures show that probabilities of a crash happening due to interactions between the signal strategies and traffic flow on the conflicting lane are positively correlated with traffic flow right-turn lane.

5.2.3. Interaction: Lead nonpermitted curve alignment*

The partial effect of Lead nonpermitted is estimated at 0.45 when the horizontal alignment of the crash approach is straight, whereas it is 1.215 on curve alignment. Therefore, the crash frequency on Lead nonpermitted intersections is likely to be higher on curve alignment than straight alignment. Lead nonpermitted is a protected right-turn where right-turn movements are operated by green arrows and followed by opposite through movements in the following phase. However, despite being a protected right-turn, Lead nonpermitted right-turn also involves some crashes at the intersection. In particular, crashes may happen in a phase transition period due to errors in driving caused by unfavorable factors or conditions. Limiting visibility along the curve sections may increase the crash risk. This interaction effect provides useful information for signal designer in choosing signal strategies at curved intersections.

Fig. 17. Interaction: Diamond overlap permitted and traffic flow conflicting lane for different right-turn traffic flow.

Fig. 18. Interaction: Lag nonpermitted and traffic flow conflicting lane for different right-turn traffic flow.

5.2.4. Interaction: Diamond overlap nonpermitted crest dip alignment*

The partial effect of Diamond overlap nonpermitted is significantly higher on crest/dip alignment (partial effect = 1.0) than level/grade alignment (partial effect = 0.213). It indicates that the probability of crashes at Diamond overlap nonpermitted intersections is likely to be higher on crest or dip section than level or grade section. Diamond overlap nonpermitted right-turn is a complex protected right-turn used for 4-legged intersections with high traffic volume both in right-turn and through lane. As such, it is not surprising that the Diamond overlap nonpermitted right-turn phasings on the crest or dip section are associated with high crash risks. This finding provides useful information for a signal designer in choosing signal strategies at crest or Dip intersections.

5.2.5. Interaction: Right-turn bay length of right-turn bay* This interaction was included in the model to examine the effect of

length on right-turn bay (right-turn bay was coded as 1 = presence of a right-turn bay, 0 = otherwise). The partial effects of right-turn bay in relation to the length of bay is shown in Fig. 19.

The figure shows that the probability of right-turn crashes for intersections having a right-turn bay decrease with the increase of the length of the right-turn bay. It also suggests that the probability of crashes would remain almost the same for the length of the bay more than 300 m. The findings could be explained that a higher length of right-turn bay enables drivers easier and safer entrance to the right-turn bay by providing a longer length for lane change, and right-turn vehicles can safely wait there for a green light. Interestingly, a right-turn bay of more than 300 m is not found to provide any additional safety benefit. This finding would help designers in determining the optimum length of the right-turn bay in safety consideration.

Fig. 19. Interaction effects between right-turn bay and length of right-turn bay.

Fig. 20. Interaction effects between Lead nonpermitted and number of right-turn phase.

5.3. Cross-level interaction effects

This study examined the cross-level interaction effects between signal strategies and intersection level factors on right-turn crashes. The model identified two significant cross-level interactions, as reported in Table 5.

5.3.1. Interaction: Lead nonpermitted * number of right-turn phase The interaction effects between Lead nonpermitted and the number of right-turn phases are presented in Fig. 20.

The figure shows that crash risk at Lead nonpermitted intersections decreases with increasing the number of right-turn phases. Intersections

with a higher number of right-turn phases generally have a longer cycle time. Therefore, the phase transition of Lead nonpermitted right-turn would be less frequent with intersections having a higher number of right-turn phases, and subsequently, the opportunity to conflict between right-turn and through vehicles would be less compared to intersections having a lower number of right-turn phases.

5.3.1.1. Interaction: Lead nonpermitted * 4-legged intersection. The partial effects of Lead nonpermitted with respect to the 3-legged and 4 legged intersections are estimated at 0.005 and 0.719, respectively. It indicates that the crash risk of Lead nonpermitted right-turns is significantly higher at 4-Legged intersections than 3-Legged intersections. The key feature of Lead nonpermitted right-turn is that the right-turn phase precedes the phase in which the opposing through movements run. Hence, there is less chance of conflict during the phase transition period (when crashes usually happen) as the through movement is stopped when the right turn starts. As 4-legged intersections generally have a higher number of phase transitions than a 3-legged intersection, the crash risk of lead nonpermitted signal phasing is higher for 4-legged intersections. This finding would provide guidance for signal designers in selecting signal strategies with respect to intersection types.

6. Conclusions

This study developed unique, disaggregate safety models for a comprehensive understanding of the effects of signal strategies, intersection geometry and traffic operation factors on right-turn crashes at signalised intersections. The models provide unique contributions to the literature and contribute to a fundamental and deeper understanding of right-turn crashes. In addition to the main effects of signal strategy, geometric and traffic factors on right-turn crashes, interaction effects, as well as cross-level interaction effects between signal strategies and geometric and traffic factors on right-turn crashes, were estimated, leading to new insights into signal strategy effectiveness over a range of operational and geometric conditions. Key considerations and one of the unique features of this study was linking crashes with signal strategies that enabled quantifying the effect of each type of signal strategy on right-turn crashes, which has not been considered in previous studies to the authors' knowledge. Importantly, this study used average crash hour traffic volumes that reflect the actual exposure associated with the crash occurrence, thus increasing the reliability of the findings. In this research, crash frequency models were estimated using a data set constructed with an accumulation of 221 Queensland signalised intersections crash data from the years 2012–2018, intersection layout and phasing data, and traffic condition data. To address the hierarchical structure of crash data, Hierarchical Poisson Regression Models (using random intercepts to capture unobserved heterogeneity) were employed, capturing upper-level effects of intersection characteristics and lower-level effects of approach characteristics.

Multilevel model adequacy was assessed using intra-class correlation coefficient and supports that hierarchical structure in the crash data of Queensland signalised intersections, where crashes within the same intersections are correlated (between-group variance 36%). The presence of this spatial correlation within intersections justified the application of multilevel modelling techniques for analysing the effects of signal strategies, intersection geometry and traffic operation factors on right-turn involved crashes at signalised intersections. Examination of the random effects illustrates that there is a significant variation in the probabilities associated with right-turn crash occurrence across intersections (i.e., the random effect coefficient is significantly different from zero) that is unexplained by other factors.

One of the key findings is that fully protected right-turns are safer than protected with permitted options (combined options). Another important finding is that Lagging right-turns are associated with higher probabilities of crashes in both protected right-turn and protected with Permitted right-turn. Lagging permitted right-turns are the highest risk signal strategy with respect to right-turn crashes. Sometimes it may be possible to avoid Lagging right-turns by rearranging the phasing sequence.

Results show that several geometric and traffic factors (Traffic flow, right-turn lane, Traffic flow conflicting lane, curve alignment, crest or dip alignment, 4-legged intersections and number of right-turn phase) have significant interactions with specific signal strategies that influence right-turn crashes at signalised intersections. The major findings in relation to geometric and traffic factors are summarised below:

• Although traffic flow on conflicting lanes and right-turn lanes increases the probability of right-turn crash occurrence at signalised

intersections, occupancy on conflicting lanes is associated with a reduction of right-turn crashes.
The number of right-turn crashes at signalised intersections is likely to be less in 4-legged intersections than in 3-legged ones. However, the crash occurrence is likely to be higher at 4-legged intersections if the intersections operate with Lead nonpermitted right-turn.
The number of right-turn crashes at intersections is likely to decrease with the increase of the length of the right-turn bay. However, the probability of crashes remains relatively constant for the length of bays that are longer than 300 m, indicating the optimum length of a right-turn bay for safe operation is about 300 m.
Traffic flows on right-turn lanes and conflicting lanes increase the likelihood of right-turn crashes happening on Lag permitted, Lag nonpermitted and Diamond overlap permitted right-turns, whereas traffic flow right-turn lane decreases right-turn crash occurrence in Diamond overlap nonpermitted right-turn

It is expected that this research will enable signal designers and policymakers to select appropriate signal strategies for facilitating rightturn movements at intersections with minimal crash risk. The scope of this study is limited to signalised intersections in Queensland, Australia. Developing similar models with disaggregated level variables like this study for other jurisdictions will be helpful in developing more critical insights into right-turn crashes. Future research can extend the understanding of the effects of signal strategies on safety by incorporating other types of crashes (e.g., left-turn crashes). This study considered the spatial correlations among crashes within the same intersections. However, there might be potential spatial correlation (at intersection level) among crashes that occurred at intersections close to each other. A worthwhile research direction would be considering this intersection level spatial correlation in examining the effects of signal strategies on safety.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.