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category: literaturenote citekey: khandevelopmentroundaboutcrashspecific2025 title: Development of roundabout crash-specific safety performance functions in Kentucky using different techniques authors: "Khan, Tathagatha; Pathivada, Bharat Kumar; Banerjee, Arunabha; Haleem, Kirolos" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.jsr.2025.03.001 publication: Journal of Safety Research url: "https://doi.org/10.1016/j.jsr.2025.03.001" zotero_key: PI7FTB7G zotero_storage: WP8TXGP8 collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Khan, Tathagatha"

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Contents lists available at ScienceDirect

Journal of Safety Research

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

Development of roundabout crash-specific safety performance functions in Kentucky using different techniques

Tathagatha Khan , Bharat Kumar Pathivada , Arunabha Banerjee , Kirolos Haleem *

Center for Transportation Research (CTR), School of Engineering & Applied Sciences, Western Kentucky University, USA

ARTICLE INFO

Keywords: Roundabout Safety performance functions Conway-Maxwell-Poisson Negative binomial Unobserved heterogeneity Varying dispersion parameter Kentucky

ABSTRACT

Introduction: Roundabouts are one of the innovative intersection designs that can reduce the number of fatal and serious injury crashes compared to traditional intersections. Nevertheless, relatively limited studies are available that have developed roundabout crash-specific safety performance functions (SPFs) using different modeling techniques. This study develops roundabout crash-specific SPFs using crashes in the state of Kentucky over a four-year period (2019–2022). Method: Crash data exhibited over-dispersion; hence, negative binomial (NB) and heterogenous negative binomial (HTNB), as well as Conway-Maxwell-Poisson (CMP) modeling approaches with fixed and varying dispersion parameters (while accounting for unobserved heterogeneity) were investigated. The performance of the fitted models was evaluated using different goodness-of-fit (GOF) statistics, e.g., Akaike information criterion "AIC," Bayesian information criterion "BIC," and McFadden pseudo R2 . Results: The GOF measures showed that the heterogeneous CMP (or HTCMP) model was the best-fit model for developing roundabout SPFs. The results of the HTCMP model showed that annual average daily traffic (AADT) on major and minor approaches to the roundabout and inscribed circle diameter (ICD) were significantly associated with increased crash frequency at roundabouts. Conversely, single circulatory lanes, presence of two lanes along the major roundabout approach, and wider circulatory roadway width (greater than 16 feet) were significantly associated with reduced crashes at roundabouts. Practical Applications: Based on the study results, safety countermeasures were proposed to enhance safety at roundabouts. One example is ensuring roundabout circulatory roadway widths greater than 16 feet to provide adequate room for driving error rectification while navigating roundabouts.

1. Introduction and study objective

Intersections are one of the risky traffic facilities and present substantial safety concerns due to the presence of several conflicting points (Al-Omari et al. 2020; Khan & Mohapatra, 2021). According to the Federal Highway Administration (FHWA), around 2.5 million crashes occurred at intersections, consisting of 23% fatal crashes and 50% serious injury crashes (FHWA, 2022). In the state of Kentucky in 2022, more than 30% of traffic crashes occurred at intersections, consisting of ~ 18% fatal crashes (Kentucky Traffic Collision Facts, 2023). The reduction in crashes and their severities can be achieved through significant geometric design improvements at intersections, and one innovative improvement is the conversion to roundabouts.

Roundabouts are at-grade intersections having circular or elliptical

islands at the center, around which vehicular traffic moves in a single direction and traffic in the roundabout is given the right of way. Roundabouts are believed to be one of the safest intersection types, where drivers are required to reduce their speed, yield, and slowly merge with circulating traffic. Roundabouts have fewer conflicting points compared to traditional intersections. A typical two-way intersection has 32 vehicle-to-vehicle conflicts (16 crossing, 8 merging, and 8 diverging conflicts), whereas a single-lane roundabout has only eight conflicts (4 merging, 4 diverging, and no crossing conflicts).

Several researchers advocated the conversions of intersections into roundabouts based on their findings, due to significant reduction in traffic fatalities and injuries (Isebrands, 2009). Researchers also reported that the crash rates at roundabouts were comparatively less than other types of at-grade intersections (Daniels et al., 2011; Li et al., 2024).

* Corresponding author at: Center for Transportation Research (CTR), School of Engineering & Applied Sciences, Western Kentucky University, 1906 College Heights Blvd, EBS 2122, Bowling Green, KY 42101, USA.

E-mail addresses: tathagatha.khan@wku.edu (T. Khan), bharatkumar.pathivada@wku.edu (B.K. Pathivada), arunabha.banerjee@wku.edu (A. Banerjee), kirolos. haleem@wku.edu (K. Haleem).

Nevertheless, relatively few studies have developed roundabout crashspecific safety performance functions (SPFs) or crash prediction models at roundabouts. SPFs are developed using different statistical techniques by considering a hypothesis that the crash count data follows the NB distribution (Hauer et al., 2002). The Highway Safety Manual (HSM) considered the NB model primarily for SPF development. However, the NB model is restricted to over-dispersed count data and unable to handle small sample size (AASHTO, 2010; Lord & Mannering, 2010; Hosseinpour et al. 2022). The Conway-Maxwell-Poisson (CMP) model is a flexible approach which could appropriately accommodate both overdispersed and under-dispersed count data and low sample size (Geedipally & Lord, 2008; Lord & Park, 2008; Hosseinpour et al. 2022).

It should be noted that both NB and CMP models restrict the dispersion parameter to be fixed across sites, but the dispersion parameter could vary across the sites, in what so-called unobserved heterogeneity, where the influence of different independent variables on crash frequency may differ across different sites. Several researchers have reported that the dispersion parameters are often site-specific and vary from one site to another (Wang et al., 2020; Geedipally et al., 2009; Lord & Park, 2008). For this, this study applied two promising extensions of the NB and CMP models, the heterogeneous negative binomial (HTNB) and heterogeneous CMP (HTCMP) models (that exhibit varying dispersion parameter as a function of site-specific features), along with the random parameter negative binomial (RPNB) modeling approach. The RPNB is an extension of the NB model that has fixed dispersion parameter; however, accounts for unobserved heterogeneity. This study used roundabout-related crashes in the state of Kentucky over a fouryear period (2019–2022) and a comprehensive list of variables, as will be shown next.

2. Prior research

2.1. Roundabout-Related safety studies

Several researchers have evaluated the safety effectiveness of roundabouts across the globe (Persaud et al., 2001; Elvik, 2003; Daniels et al., 2010). In another study, Retting et al. (2001) reported that the conversion of intersections into roundabouts was safety-beneficial, where the overall crash severities and injury crashes were reduced by 38% and 76%, respectively. Isebrands and Hallmark (2012) investigated the safety effectiveness of roundabouts in rural areas with high-speed approaches by collecting data from 19 locations in the United States. They reported a reduction of 63% in total crashes and 88% in injury crashes, when intersections were converted to roundabouts.

The safety effectiveness of converting signalized intersections to roundabouts was carried out by Gross et al. (2013), while considering 28 sites in the United States and using the empirical Bayes (EB) method. The EB results suggested a roundabout safety benefit, with a reduction in both total and injury crashes. Elvik (2017) carried out a study in Europe and reported that the conversion of intersections to roundabouts reduced fatal crashes and injury crashes by 65% and 40%, respectively. Mamlouk and Souliman (2019) evaluated the safety effectiveness of single-lane and double-lane roundabouts on crash rates in Arizona. The authors reported that the roundabout conversion resulted in a reduction in crash severity. Furthermore, single-lane roundabouts reduced the crash rates, while double-lane roundabouts increased them.

2.2. Roundabout-Related crash frequency studies

Past studies have largely focused on investigating the safety effectiveness of roundabouts; however, relatively very few studies have developed roundabout crash-specific SPFs. For instance, Qin et al. (2011) evaluated the crash patterns at 41 roundabouts in Wisconsin and reported a reduction in crash severity. They developed nine models using the NB model by considering several variables such as annual average daily traffic (AADT), central island diameter, and number of

circulatory lanes. They reported AADT as the only significant variable in all nine models.

Kim and Choi (2012) explored crash data from 14 roundabouts to investigate the factors influencing roundabout crashes in South Korea. The authors developed models to associate the relationship between geometric design elements and occurrence of roundabout crashes. They reported that the NB model had a better ability to explain the occurrence of vehicle crashes at roundabouts compared to the Poisson model. Kamla et al. (2016) investigated the influence of geometric and traffic characteristics on the number of crashes at roundabouts by collecting data from 70 sites in the U.K. The authors developed two count data models (fixed parameter NB and RPNB) and reported RPNB to be the better crash prediction model for roundabouts. They also found that geometric features (e.g., entry width, inscribed circle diameter, number of lanes, and presence of traffic signals) and traffic characteristics (e.g., total approach traffic and truck percentage) significantly influenced the crash frequency at roundabouts.

Recently, Vinayaraj and Perumal (2023) employed the NB approach for developing SPFs and estimated the crash modification factors (CMFs) for roundabouts using historical crash data collected over five years (2015–2019) from 21 sites in India. The result showed that AADT, central island diameter, entry angle, posted speed limit, circulating roadway width, number of circulatory lanes, and central island height influenced the occurrence of crashes in the vicinity of roundabouts.

2.3. Safety-Related studies using NB-Extension and CMP-Extension models

The NB model has been extensively used for developing SPFs for different traffic facilities. However, the NB model is restricted to overdispersed count data only and is incapable of handling a small sample size (Lord & Mannering, 2010; Hosseinpour et al. 2022). On the other hand, the CMP model addresses the aforementioned issue; however, both NB and CMP models still restrict the dispersion parameter to be fixed across sites. Therefore, several extensions of NB and CMP model have been used in safety studies across the globe. For example, El-Basyouny and Sayed (2006) developed and compared NB and HTNB models using crash data for 392 arterial segments located in British Columbia, Canada between 1994 and 1996. The authors reported that the HTNB model outperformed the NB model. Anastasopoulos and Mannering (2009) carried out a study to investigate the use of random parameter count models as an alternative methodology for analyzing crash frequencies using five-year crash data (1995 to 1999). The authors reported that random parameter count models could provide a detailed understanding of the variables that influence the crash frequencies. They also highlighted that disregarding the possibility of random parameters could result in substantially different marginal effects and consequent interpretations relating to the magnitude of the effect of factors affecting crash frequencies.

Khattak et al. (2021) developed SPFs for crash severity for urban signalized and unsignalized intersections using six-year crash data, geometric design data, and traffic flow data by utilizing three different functional forms of NB models (i.e., NB- type 1, NB-type 2, NB-type P) and a generalized Poisson (GP) model. They compared all developed SPFs based on the goodness of fit and predictive performance measures. The authors reported that the NB-type P model outperformed the other models for signalized intersections and the GP model outperformed the other models for unsignalized intersections. Recently, Haleem and Hosseinpour (2023) developed SPFs for predicting commercial motor vehicle (CMV) crashes on interchange ramp segments using five-year (2015 to 2019) CMV-related crashes while employing four modeling approaches (NB, HTNB, CMP, and HTCMP). The study results indicated that the HTCMP model significantly outperformed the other three comparative models in terms of crash prediction accuracy and goodnessof-fit statistics. In another study, Haleem and Hosseinpour (2024) developed SPFs for CMVs at signalized and unsignalized intersections in

the state of Kentucky using five-year crash data (2015–2019) and employing different modeling approaches (NB, CMP, HTCMP, zeroinflated CMP "ZI-CMP," and ZI-HTCMP). The authors reported that the ZI-HTCMP model outperformed the other models for both unsignalized and signalized intersections.

2.4. Summary of literature review and study contribution

In summary, the majority of the research has been carried out to evaluate the safety effectiveness of roundabouts; however, relatively limited research has been carried out to develop roundabout crashspecific SPFs using different modeling approaches. Furthermore, most previous studies have applied the conventional NB model for developing roundabout specifics SPFs, which could restrict the dispersion parameter to be fixed across the sites and neglect unobserved heterogeneity. Therefore, this study aims to address these gaps by:

  • 1. Developing comprehensive roundabout crash-specific SPFs using multiple statistical approaches, including the NB and CMP models with fixed and varying dispersion parameters, along with a myriad list of variables, as shown in Section 4 "Data Collection and Extraction".
  • 2. Identifying the key operational and geometrical attributes influencing crashes at roundabouts.
  • 3. Recommending countermeasures to enhance safety at roundabouts.

3. Methodological approaches

3.1. NB, HTNB, and RPNB modeling approaches

The NB model has been extensively used for developing SPFs and for predicting the number of crashes (Mannering & Bhat, 2014; Vinayaraj & Perumal, 2023). The NB model accounts for over-dispersion data. The NB model incorporates an error term into Poisson means and allows the variance to differ from the mean. For example, let *λi*be the predicted number of crashes at roundabout i, then the NB model can be expressed as follows:

$$\lambda_i = \exp(\beta X_i + \varepsilon_i) \tag{1}$$

where: Xi is a vector of explanatory variables at roundabout i, β is a vector of estimable parameters, and exp (*ε*i) denotes the Gammadistributed error term with variance equal to α (i.e., the dispersion parameter) and mean equal to 1. The inclusion of εi permits the variance to differ from the mean. For more information about the NB model, readers are referred to Washington et al. (2003) and Anastasopoulos and Mannering (2009).

The NB model assumes the dispersion parameter (α) to be fixed across all observations, though this may not be true as the geometry of different facilities vary significantly from each other (Geedipally & Lord, 2008; Anastasopoulos & Mannering, 2009; Miranda-Moreno et al., 2011). Therefore, two prominent extensions of the NB model, namely the HTNB and RPNB models, were used in this study. The HTNB model is a flexible approach that addresses the issue of unobserved heterogeneity through allowing the dispersion parameters to vary across crash sites as a function of site-specific characteristics. The HTNB model uses the same probability density function as the NB model and the varying dispersion parameter is expressed as a function of site-specific attributes, as follows:

$$\alpha_i = \frac{1}{\theta_i} = \exp(\gamma Z_i) \tag{2}$$

where: *Z*i denotes the vector of site-specific variables and γ denotes the vector of regression coefficients corresponding to covariates *Z*i. If none of the variables are found significant in the dispersion parameter section, then the HTNB model is reduced to the traditional NB model.

The RPNB is an extension of the NB model, which accounts for the

unobserved heterogeneity issue. The estimable parameters in the count data model can be expressed as follows:

$$\beta_i = \beta + \varphi_i \tag{3}$$

where: *φ*i denotes the randomly distributed term (e.g., a normally distributed term with mean equals to zero and variance equals to σ2 ), which lets the effects of the parameter to vary across the observations. A parameter is considered random when the standard deviation is greater than zero or else it is considered as a fixed parameter. This suggests that if the parameter is considered as fixed, then *φ*i is zero.

3.2. CMP and HTCMP modeling approaches

The CMP distribution is a generalization of the Poisson distribution introduced by Conway and Maxwell (1962) to model queue and service rates. The CMP distribution is one of the most popular techniques used by researchers for modeling count data (Lord et al., 2008; Haleem & Hosseinpour, 2024). The statistical properties of the CMP distribution were further explained by Shmueli et al. (2005) and the conjugate distributions for the parameters of the CMP distribution were developed by Kadane et al. (2006). The probability mass function of the CMP distribution can be expressed as follows:

$$P(y) = \frac{1}{Z(\lambda, \nu)} \frac{\lambda^{y}}{(y!)^{\nu}} \tag{4}$$

$$Z(\lambda, \nu) = \sum_{n=0}^{\infty} \frac{\lambda^n}{(n!)^{\nu}}$$ (5)

where: y is a discrete count; λ is a centering parameter that is approximately the mean of the observations in many cases; and ν is defined as the shape parameter or dispersion parameter of the CMP distribution. The important attribute of the CMP distribution is that it can handle both under-dispersed (ν > 1) and over-dispersed (υ < 1) data. However, when (υ = 1), then the Poisson distribution is generated. Using an asymptotic approximation for Z (λ, υ), the approximation can be obtained as follows (Lord et al., 2008; Huang, 2017).

$$E[Y] \approx \lambda^{1/\nu} - \frac{\nu - 1}{2\nu} \tag{6}$$

The HTCMP is also a promising generalization of the standard CMP model that allows the dispersion parameter (ν) to vary across observations depending on site-specific characteristics (Geedipally & Lord, 2011). The (υ) of the HTCMP model can be expressed as follows:

$$\ln(v) = \gamma \psi_i \tag{7}$$

where: *ψi*denotes a vector of explanatory variables associated with υ and γ denotes a vector of regression coefficients corresponding to covariates ψi . If none of the variables are observed to be significant in the dispersion part, then the HTCMP model is reduced to the CMP model.

3.3. Goodness-of-Fit (GOF) statistics

3.3.1. Deviance (D)

The deviance statistic can be calculated as a Chi-square (x2 ) distribution as follows:

$$D = -2(LL0 - LL\beta) \cong \chi^2_{(df,=P)}$$ (8)

where: LLβ denotes the log-likelihood at convergence, LL0 denotes the log-likelihood of the null model (i.e., constant only model), and P denotes the number of predictors in the model.

3.3.2. McFadden pseudo R2

The McFadden pseudo *R*2 statistic is calculated as follows:

$$McFadden Pseudo R^2 = 1 - (LL_{\beta}/LL_0)$$ (9)

where: LLβ and LL0 denote the same as in Equation (8). Note that a higher value of McFadden pseudo R2 suggests a better fit model.

3.3.3. Akaike information criterion (AIC) and Bayesian information criterion (BIC)

The AIC and BIC statistics are calculated as follows:

$$AIC = -2*LL_{\beta} + 2*P \tag{10}$$

$$BIC = -2*LL_{\beta} + P*ln(n)$$ (11)

where: LLβ, LL0, and P denote the same as in Equation (8), and n denotes the number of site observations. Note that a lower value of AIC and BIC statistics signifies a better fit model.

3.3.4. Likelihood ratio test (LRT)

The likelihood ratio test (LRT) follows a Chi-square distribution with degrees of freedom equal to the difference in the number of estimated parameters between the two models (best-fit model and comparable model). The LRT statistic is calculated as follows:

$$LRT = 2*\left(LL{bestmodel} - LL{compared\ model}\right) \ \cong \ \chi^2{(df. = P{best\ model} - P_{compared\ model})} \eqno(12)$$

For more clarity, the adopted research methodology for this study is presented in Fig. 1. As shown in the figure, the flowchart displays the different techniques used in this study.

4. Data Collection and Extraction

Crash data from 33 roundabouts were collected over a four-year period (2019–2022) in the state of Kentucky. Initially, the locations of the roundabouts were identified from Kittelson & Associates (2023) and later confirmed from the Kentucky Transportation Cabinet (KYTC) database. Several geometrical and operational data were collected from all the roundabouts. For example, speed limits on major and minor roads were collected from Highway Information View and Extract Interface (HIVEi) KYTC-Query (2024). Area type and AADT were collected from the KYTC Interactive Statewide Traffic Counts Map 2024 as depicted in Fig. 2-a and 2-b.

It should be noted that AADT was collected at each roundabout during each of the four years (2019 through 2022), then the average AADT (for each of the major and minor approaches) was calculated and used to represent the specific major approach and minor approach

Fig. 1. Adopted Research Methodology.

Fig. 2. Sample Data Collected Manually at Roundabout Using Google Maps (2024) and KYTC Interactive Map 2024: (a) AADT, (b) Area Type, (c) Central Island Diameter (CID), and (d) Inscribed Circle Diameter (ICD).

AADTs. This ensures that the AADT represents an average daily traffic estimate before and during the COVID-19 pandemic. Regarding roundabouts with varying traffic volumes observed on different road directions around them, the average approach AADT in each of the four years (2019–2022) was calculated, then the overall average (for each of the major and minor approaches) was determined and used in the SPF development.

The geometric roundabout attributes, such as inscribed circle diameter (ICD), central island diameter (CID), number of lanes on major and minor approaches, entry width, number of circulatory lanes, circulatory width, and presence or crosswalk and yield markings, were collected manually using Google Maps (2024) (refer to Fig. 2-c and 2-d). Furthermore, a 250-foot radius from each roundabout's centroid was drawn using ArcGIS (2023) and all crashes within this buffer zone were considered as roundabout-related crashes (refer to Fig. 3). Note that this radius has been deemed sufficient for accurately capturing roundabout crashes (Hu & Cicchino, 2019).

The crash frequency at each roundabout was extracted from ArcGIS (2023) and further used as the dependent variable for developing the roundabout crash-specific SPFs. A total of 621 crashes occurred at 33 roundabouts in Kentucky. The composition of the roundabout crashes was as follows, 5.15% were either involved in suspected serious injuries (A), suspected minor injuries (B), or possible injury (C), whereas 94.85% were involved in property damage only (PDO) crashes. This illustrates that roundabouts have the potential to reduce the severity of crashes as advocated by several researchers across the globe (see for examples: Isebrands & Hallmark, 2012; Gross et al., 2013). Full descriptive statistics of the explored variables are presented in Table 1. Note that the mean and variance of roundabout crash data were found to be 18.81 and 1147.60, respectively, which signifies that the crash data were overdispersed. Furthermore, the crash distribution at the 33 roundabouts is depicted in Fig. 4.

5. Results and Discussion

5.1. Multicollinearity analysis

The two most used methods for determining data multicollinearity are the Pearson correlation matrix of predictor variables and the variance inflation factor (VIF) (Alin, 2010; Ali et al., 2021; Cheng et al., 2022; Pathivada et al., 2024). One major drawback of the Pearson correlation matrix is that it could potentially establish a correlation between only two independent variables at once. However, VIF is an effective methodology for determining multicollinearity, which overcomes the drawback of the Pearson correlation matrix. Note that higher VIF values indicate higher collinearity between the independent variables (Cheng et al., 2022). In this study, both multicollinearity detection techniques between the independent variables were used.

Fig. 3. Roundabout-Specific Crash Data Extraction Process: (a) Creating Buffer Zones (250 ft) around Roundabout Centroids and (b) Sample Crashes within a Buffer Zone.

The results of the Pearson correlation matrix of all the variables explored in the development of roundabout crash-specific SPF are shown in Fig. 5. It is suggested that any variable, having a correlation (≥ |0.7|) with other variables, should be removed before moving forward with model development. As shown in Fig. 5, no variables were found to have a correlation factor of 0.7 or greater. The VIF values of all the variables explored in the development of roundabout crash-specific SPFs are presented in Fig. 6. Cheng et al. (2022) reported that a VIF value of less than 10 indicates that there is no multicollinearity between the independent variables. As shown in Fig. 6, there existed no multicollinearity between the independent variables used for developing roundabout crash-specific SPFs in this study.

5.2. Roundabout-Specific SPF modeling results

The results of the five fitted SPF models (NB, HTNB, RPNB, CMP, and HTCMP) are presented in Table 2 with a 10% significance level threshold. The bottom portion of Table 2 represents the GOF measures for all five models. The deviance statistic for all the developed models was found to be statistically significant (P-value < 0.001), indicating rejection of the null hypothesis (i.e., the models had different prediction performances than their corresponding constant-only models).

The GOF measures presented in Table 2 indicated that the HTCMP model had the highest McFadden pseudo R2 (0.246) and lowest AIC (215.209) values compared to the other models. Overall, the HTCMP model outperformed the other comparative models for development of roundabout-specific SPFs in Kentucky. The difference in the degrees of freedom between (HTCMP vs. HTNB) was found to be zero; therefore, the LRT test was only conducted between (HTCMP vs. NB), (HTCMP vs. RPNB), and (HTCMP vs. CMP). As shown in Table 2, the HTCMP

Table 1 Descriptive Statistics of Explanatory Variables Used in Developing Roundabout Crash-Specific SPFs in Kentucky.

| Variable | Variable
Description | No. of Sites
Level
Level
1
0 | | Crash Frequency
Level 1 | Level 0 | | |--------------------------------------------------------|------------------------------------------------------------|------------------------------------------|--------|----------------------------|---------|--| | Indicator Dummy Variables | | | | | | | | Area type | If urban = 1, | 27 | 6 | 545 | 76 | | | Number of
circulatory | otherwise = 0
If single = 1,
otherwise = 0 | 25 | 8 | 195 | 426 | | | lanes "cln"
Circulatory road | If > 16 feet = 1, | 20 | 13 | 326 | 295 | | | width "crw"
Number of lanes
on major
approach | otherwise = 0
If two lanes = 1,
otherwise = 0 | 25 | 8 | 363 | 258 | | | Number of lanes
on minor
approach | If two lanes = 1,
otherwise = 0 | 27 | 6 | 416 | 205 | | | Crosswalk | If present = 1,
otherwise = 0 | 19 | 14 | 480 | 141 | | | Yield markings | If present = 1,
otherwise = 0 | 27 | 6 | 605 | 16 | | | Number of
approaches | If four = 1,
otherwise = 0 | 28 | 5 | '578 | 43 | | | Variable | Variable
Description | Min.* | Max.* | Mean | SD* | | | Continuous Variables | | | | | | | | Major approach
AADT | Major
roundabout
approach AADT | 496 | 19,181 | 6692.74 | 4530.73 | | | Minor approach
AADT | Minor
roundabout
approach AADT | 496 | 18,550 | 3896.87 | 3914.42 | | | Major approach
posted speed
limit
"majorpsl" | Speed limit on
major approach
(in miles/hour) | 25 | 55 | 36.36 | 10.10 | | | Minor approach
posted speed
limit
"minorpsl" | Speed limit on
minor approach
(in miles/hour) | 15 | 55 | 32.58 | 12.32 | | | Entry width
"ew" (ft) | Roundabout
entry width (in
feet) | 10.50 | 29.07 | 16.51 | 3.40 | | | Central island
diameter
"CID" (ft) | Diameter of
roundabout
central island (in
feet) | 31.18 | 181.46 | 107.79 | 32.18 | | | Inscribed circle
diameter
"ICD" (ft) | Diameter of
roundabout
inscribed circle
(in feet) | 71.10 | 237.88 | 147.48 | 39.34 | |

*Min. = minimum; Max. = maximum; and SD = standard deviation.

Fig. 4. Crash Distribution at Roundabouts in Kentucky (2019–2022).

Fig. 5. Pearson Correlation Matrix of Explored Variables.

Fig. 6. Variance Inflation Factor (VIF) Values of Explored Variables.

outperformed the NB, RPNB, and CMP models at the 90% confidence level (P-value ≤ 0.10).

The SPF model results in Table 2 indicated that higher AADT on major and minor roundabout approaches, larger central island diameter, and larger inscribed circle diameter were associated with increased crash frequency at roundabouts. On the other hand, single roundabout circulatory lanes, higher minor approach posted speed limit, circulatory roadway width (*>*16 feet), and two lanes on the major approach reduced the number of crashes at roundabouts.

For the HTNB model, the major and minor approaches' posted speed limits were found to be significantly associated with the dispersion parameter. Similarly, for the HTCMP model, presence of two lanes on minor roundabout approach road was found to be significantly associated with the dispersion parameter. This indicates that the HTCMP dispersion parameter significantly varied by the number of lanes on the minor roundabout approach.

The findings drawn from the best-fit model in Table 2, the HTCMP model, were intuitive. For example, AADT on major and minor roundabout approaches was significantly associated with increased crash frequency at roundabouts. This outcome is expected as AADT reflects the exposure and with higher exposure, the risk of crashes at roundabouts increases. This finding is consistent with previous studies (e.g., Kamla et al., 2016; Vinayaraj & Perumal, 2023). The ICD was observed to be associated with increased crash frequency at roundabouts. This could be since larger ICD provides a false sense of security for vehicles to increase their circulating speed, which in turn increases crash risk at roundabouts. This finding is consistent with prior studies by Rodegerdts et al. (2007) and Ferguson et al. (2018). The presence of single circulatory lanes was found to have a negative association with crash frequency. This implies that single-lane roundabouts tend to have lesser crash frequency compared to multi-lane roundabouts. This could be since multilane roundabouts are inherently more complex, with vehicles operating in multiple lanes simultaneously; hence, increasing the risk of collisions. Furthermore, this risk is further compounded by drivers' lack of awareness of multilane roundabout maneuvers. This finding is consistent with the study by Mamlouk and Souliman (2019).

Also, from the HTCMP model results, roundabouts with two lanes on the major approach were associated with lesser crash frequency. This is mainly since major roundabout approaches with two lanes are less prone to conflicting traffic movements compared to approaches with more

Table 2 Parameter Estimates for Roundabout Crash-Specific SPFs in Kentucky.

Variable NB HTNB RPNB CMP HTCMP
Coef. P-Value Coef. P-Value Coef. P-Value Coef. P-Value Coef. P-Value
Count part
Constant − 5.782 0.000 − 4.735 0.002 − 7.449 0.000 − 1.599 0.009 − 1.580 0.003
Natural logarithm of major approach AADT 0.714 0.000 0.905 0.000 0.475 0.002 0.160 0.026 0.164 0.017
Natural logarithm of minor approach AADT 0.345 0.023 N/S N/S 0.755 0.000 0.067 0.089 0.064 0.096
Single circulatory lanes − 0.958 0.000 − 1.282 0.000 N/S N/S − 0.205 0.018 − 0.186 0.026
Central island diameter (CID) (in 100 feet) N/S* N/S 1.283 0.009 N/S N/S 0.126 0.097 N/S N/S
Minor approach posted speed limit (mph) N/S N/S − 0.019 0.094 N/S N/S N/S N/S N/S N/S
Circulatory roadway width (>16 feet) N/S N/S − 0.742 0.026 N/S N/S − 1.997 0.000 − 0.214 0.019
Two lanes on major approach N/S N/S N/S N/S N/S N/S N/S N/S − 0.177 0.029
Inscribed circle diameter (ICD) (in 100 feet) N/S N/S N/S N/S N/S N/S N/S N/S 0.198 0.030
Random parameters
Two lanes on minor approach na** na na na − 0.549 0.077 na na na na
St. deviation of "Two lanes on minor approach" na na na na 0.421 0.012 na na na na
Dispersion part
Constant 1.044*** 0.001 − 3.444 0.037 2.866 0.013 − 1.997*** 0.000 − 1.710 0.000
Major approach posted speed limit (mph) na na 0.129 0.023 na na na na N/S N/S
Minor approach posted speed limit (mph) na na − 0.084 0.055 na na na na N/S N/S
Two lanes on minor approach na na N/S N/S na na na na − 0.298 0.017
Goodness-of-fit (GOF) statistics NB HTNB RPNB CMP HTCMP
Number of observations 33 33 33 33 33
Number of significant parameters 5 9 6 7 9
Log-likelihood at convergence (LLβ)
− 103.797		 − 100.944 − 107.010 − 101.35 − 98.604
Log-likelihood at zero (LL0) − 128.463 − 128.463 − 128.463 − 130.750 − 130.750
Deviance Chi-sq. statistic (2*(LLβ − LL0)) 49.33 55.04 42.906 58.80 64.29
(P-Value < 0.001)
(P-Value)		 (P-Value < 0.001) (P-Value < 0.001) (P-Value < 0.001) (P-Value < 0.001)
McFadden pseudo R2 0.192 0.214 0.167 0.225 0.246
Akaike Information Criterion (AIC)
217.594		 219.887 226.000 216.710 215.209
Bayesian Information Criterion (BIC)
225.077		 233.357 234.999 227.176 228.677
Likelihood Ratio Test (LRT): Chi-sq. (d.f., P-value) HTCMP vs. NB na HTCMP vs. CMP na
Chi-sq. = 10.386 HTCMP vs. RPNB
Chi-sq. = 16.812		 Chi-sq. = 5.492
(4, 0.034) (3, 0.000) (2, 0.064)

* N/S = not significant. ** na = not applicable.

than two lanes. The circulatory roadway (> 16 feet) was observed to have a significant negative association with crash frequency at roundabouts. This implies that roundabouts with circulatory roadways greater than 16 feet are safer than roundabouts with circulatory roadways lesser than 16 feet. This is mainly since wider circulatory roadway width provides adequate room for rectification of any errors committed by drivers while navigating roundabouts.

6. Conclusions and study recommendations

6.1. Main study Conclusions

Numerous studies have advocated the conversion of intersections into roundabouts due to their safety benefits. However, relatively limited research has been conducted to develop roundabout crashspecific SPFs (roundabout crash prediction models) using different modeling approaches. To fill this gap, this study investigated crash frequency at roundabouts in Kentucky and developed roundabout crashspecific SPFs using various geometrical and operational attributes of roundabouts. Crash data from 33 roundabouts over four years (2019–2022) in the state of Kentucky were retrieved from KYTC and used in the analysis. Furthermore, additional effort was made to manually collect the geometric attributes (e.g., CID and ICD) at each roundabout for developing the SPFs. The crash data exhibited overdispersion; therefore, the NB and CMP modeling approaches, with fixed and varying dispersion parameters, were applied in the study while accounting for unobserved heterogeneity across the roundabout locations.

Five modeling techniques (NB, HTNB, RPNB, CMP, and HTCMP) were employed for the development of roundabout crash-specific SPFs. The performance of all the models were evaluated using GOF measures, such as McFadden pseudo R2 , AIC, BIC, and LRT statistics. The results of the GOF measures indicated the HTCMP was the best-fit model for developing roundabout crash-specific SPFs in the state of Kentucky. Overall, the study findings reveal that it is imperative, when modeling roundabout crashes, to use a count data model that accounts for unobserved heterogeneity (i.e., a model with heterogeneous dispersion parameter, e.g., the HTCMP model) than using a model that merely accounts for random parameters (i.e., the RPNB model).

The results of the HTCMP model highlighted that AADT of both major and minor roundabout approaches and ICD had a significant association with increased crash frequency at roundabouts. Conversely, single circulatory roundabout lanes, presence of two lanes on major roundabout approach, and circulatory roadway width (> 16 feet) were significantly associated with reduced crash frequency at roundabouts.

6.2. Roundabout safety recommendations

The following recommendations are suggested based on the study findings to help improve roundabout safety:

  • 1. Consider adding single-lane roundabouts, wherever possible, in those areas where traffic is not generally high, as they are safer and less confusing than those multi-lane roundabouts.
  • 2. Provide roundabout circulatory roadway widths greater than 16 feet to provide adequate room for rectification of any errors committed by drivers who are navigating roundabouts.
  • 3. The study results could be amalgamated with driver assistance and vehicle-to-vehicle communication technology as part of Intelligent Transportation Systems (ITS) to help drivers navigate roundabouts safely and efficiently with a diminished risk of crashes.

*** Constant equivalent to "ln (dispersion parameter)" for NB and CMP models (i.e., models with fixed dispersion parameter).

6.3. Limitations and future scope

It should be noted that the findings and safety recommendations of this study are specific to roundabouts in Kentucky. However, the findings and safety recommendations can be transferable to other states in the United States or to other regions having similar roundabout configurations, roundabout crashes, and traffic characteristics as those in Kentucky. For future research, it is recommended to develop roundabout SPFs in other states/regions and compare the results to those SPFs developed in Kentucky. This will help compare the influence of the significant variables from the models and how they differ or concur.

CRediT authorship contribution statement

Tathagatha Khan: Writing – original draft, Software, Methodology, Investigation, Formal analysis. Bharat Kumar Pathivada: Writing – review & editing, Methodology, Formal analysis. Arunabha Banerjee: Writing – review & editing, Methodology. Kirolos Haleem: Writing – review & editing, Supervision, Conceptualization.

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.

Acknowledgment

The authors would like to acknowledge the Kentucky Transportation Cabinet (KYTC) for the grant provided to conduct this research and for providing the necessary crash and roadway data used in this research. The opinions, findings, and conclusions in this paper are those of the authors and not necessarily those of KYTC.

References

Tathagatha Khan, is a Postdoctoral Research Associate at the Center for Transportation Research (CTR) in the School of Engineering and Applied Sciences at Western Kentucky University. His main interests are traffic safety analysis, driver behavior, human factors, and traffic flow modeling. He also holds a Doctorate Degree in transportation engineering.

Bharat Pathivada, is a Post-Doctoral Research Associate at the Center for Transportation Research (CTR) in the School of Engineering and Applied Sciences at Western Kentucky University (WKU). He has over two years of research experience in the field of transportation engineering with a focus on traffic safety and human factors. His research interests include Traffic Safety Analysis, Crash Modeling, Road User Behavior, and Intelligent Transportation Systems (ITS). He has a Doctorate Degree in transportation engineering and has participated in accomplishing several externally funded projects.

Arunabha Banerjee, is a Postdoctoral Research Associate at the Center for Transportation Research (CTR) in the School of Engineering and Applied Sciences at Western Kentucky University. His main interests are traffic safety analysis, crash modeling, and pedestrian walking behavior modeling. He also holds a Doctorate Degree in transportation engineering.

Kirolos Haleem, is an associate professor of civil (transportation) engineering at Western Kentucky University (WKU). Dr. Haleem is the founder & director of the Center for Transportation Research (CTR) at WKU. Kirolos received his master's and Ph.D. degrees in civil (transportation) engineering from the University of Central Florida (UCF) in 2007 and 2009, respectively. He has more than 15-year experience in transportation engineering. His areas of expertise include highway traffic safety analysis, application of statistical models and data mining techniques in transportation data analysis, driving simulator studies, and intelligent transportation systems (ITS). Kirolos led and conducted numerous transportation research projects sponsored by the Kentucky Department of Transportation (Kentucky DOT), Alabama Department of Transportation (ALDOT), Florida DOT, and the U.S. DOT.