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category: literaturenote citekey: pathivadainvestigatingmotorcyclecrashespre2024 title: Investigating motorcycle crashes pre- and post-COVID-19 pandemic along Kentucky’s urban roadway segments authors: "Pathivada, Bharat Kumar; Banerjee, Arunabha; Haleem, Kirolos" year: 2024 date: 2024-00-00 2024 doi: 10.1016/j.jsr.2024.09.002 publication: Journal of Safety Research url: "https://doi.org/10.1016/j.jsr.2024.09.002" zotero_key: ES4ZCJ5T zotero_storage: MJBCGJAB collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Pathivada, Bharat Kumar"

status: converted

Contents lists available at ScienceDirect

Journal of Safety Research

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

Investigating motorcycle crashes pre- and post-COVID-19 pandemic along Kentucky's urban roadway segments

Bharat Kumar Pathivada , Arunabha Banerjee , Kirolos Haleem *

Center for Transportation Research (CTR), School of Engineering & Applied Sciences, Western Kentucky University, 1906 College Heights Blvd, EBS 2122, Bowling Green, KY 42101, United States

ARTICLE INFO

Keywords: Motorcycle Crashes COVID-19 Pandemic Urban Two-Lane Multilane Conway-Maxwell-Poisson Heterogeneous Conway-Maxwell-Poisson Empirical Bayes

ABSTRACT

Introduction: This study developed safety performance functions (SPFs) for motorcycle-related crashes along Kentucky's urban roadway segment facilities (separately along both two-lane undivided and multilane road segments) for each of the pre-COVID-19 pandemic (2015–2019) and post-pandemic (2020–2022) periods. A total of 2,963 motorcycle crashes over eight years (2015 through 2022) across 2,642 urban roadway segments and several road-specific features (e.g., shoulder width and annual average daily traffic "AADT") were used. Method: The Conway-Maxwell-Poisson (CMP) model and heterogeneous Conway-Maxwell-Poisson (HTCMP) model "that accounts for unobserved heterogeneity" were applied and compared. Results: For both urban two-lane undivided and multilane segment facilities, the HTCMP models outperformed their CMP counterparts pre- and postpandemic, based on various goodness-of-fit measures (e.g., Akaike information criterion "AIC" and pseudo R2 ) and prediction performance (e.g., mean absolute deviance "MAD" and mean square prediction error "MSPE"). From the fitted SPFs, higher AADT and presence of horizontal curve were significantly associated with increased motorcycle crash frequency, while the presence of roadside steel strong-post W-beam guardrail was significantly associated with reduced motorcycle crash frequency along all urban segments, both pre- and post-pandemic. Furthermore, posted speed limits (≥55 mph) were significantly associated with reduced motorcycle crashes along urban multilane segments, while collector and local road types were significantly associated with reduced motorcycle crashes along urban two-lane segments. Practical Applications: Countermeasures were then proposed to improve motorcyclists' safety along urban roadways (e.g., installing advance warning signs and/or chevrons along urban roadway segments with sharp horizontal curves).

1. Introduction

According to the National Highway Traffic Safety Administration (NHTSA), motorcyclists are overrepresented in traffic fatalities in the United States, with 3.5% of registered motorcycles contributing to 14% of all traffic fatalities and 17% of all motor-vehicle occupant fatalities (NHTSA, 2023a). Motorcyclists are highly susceptible to traffic casualties as they are vulnerable road users, primarily due to the inherent instability of motorcycles and the lack of in-vehicle protection for riders. For example, in the United States in 2021, the fatality rate for motorcyclists per 100 million vehicle miles traveled was 24 times and 40 times the occupant fatality rate of passenger cars and light trucks, respectively (NHTSA, 2023a). In Kentucky, less than 1% of registered motorcycles contributed to more than 7% of traffic fatalities (KTC, 2023). Furthermore, the emergence of the severe acute respiratory syndrome (SARS-

CoV-2), commonly referred to as the 2019 novel coronavirus (COVID-19), has led to drastic changes and disruptions in travel behavior and traffic safety. Several studies have highlighted reduced traffic flow while road fatalities and unsafe driving behaviors significantly increased during the pandemic (e.g., Chand et al., 2021; Yasin et al., 2021; Shaik & Ahmed, 2022).

A preliminary investigation of motorcycle crash density in Kentucky during pre- and post-pandemic periods revealed that motorcycle crashes were highly concentrated in urban areas (refer to Fig. 1a and b). Please note that the term "post-COVID-19" (or post-pandemic) in this study implies "during and post COVID-19." It is evident from Fig. 1 that, in both pre- and post-pandemic periods, motorcycle crashes were highly concentrated in urban metropolitan areas in Kentucky (e.g., Louisville, Lexington, and Covington). This is expected since urban areas have significant traffic exposure compared to rural areas. According to the

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

* Corresponding author.

Fig. 1. Motorcycle Crash Density in the State of Kentucky: (a) Pre-COVID-19 Pandemic (2015–2019) and (b) Post-COVID-19 Pandemic (2020–2022).

recent NHTSA report, motorcyclist fatalities in urban areas increased by 15% since 2020 (NHTSA, 2023b).

Despite motorcycle crashes accounting for a large percentage of traffic fatalities in the United States, studies that developed motorcyclespecific safety performance functions (SPFs) are relatively limited. Considering the relevance of motorcycle crashes and the impact of the pandemic, this study comprehensively investigates motorcycle crash frequency along urban roadway segment facilities in the state of Kentucky in each of the pre- and post-pandemic periods. The study objectives are three-fold: (i) develop motorcycle-specific SPFs along urban two-lane undivided and multilane road segments, separately for each of the pre-pandemic (2015–2019) and post-pandemic (2020–2022) periods; (ii) rank motorcycle-specific high-crash locations along each of the urban two-lane undivided and urban multilane segments using the Empirical Bayes (EB) method; and (iii) propose targeted safety countermeasures to enhance motorcyclists' safety along Kentucky's urban roadways. To comprehensively investigate motorcycle crashes while considering the effect of COVID-19, this study analyzes motorcycle crashes during the pre-COVID-19 pandemic (2015–2019) and post-COVID-19 pandemic (2020–2022) periods separately.

2. Literature review

2.1. Motorcycle-related safety studies

Scanning the safety literature, studies on motorcycle safety have mostly focused on analyzing crash injury severity. For example, Santos et al. (2023) investigated factors associated with motorcyclist injury severity while comparing several machine-learning algorithms. Tenyear crash records in Portugal between 2010 and 2019 were used. The results indicated that factors including alcohol consumption, road type, road condition, location, motorcycle age, and rider's gender were significantly associated with motorcyclist injury severity. Recently, Zubaidi et al. (2023) investigated factors contributing to motorcyclist crash injury severity using the random parameters logit model with heterogeneity in means and variance. A total of 10,067 motorcycle crashes in Florida involving senior motorcyclists (≥65 years old)

between 2012 and 2018 were used. The results showed that driver, temporal, spatial, roadway, and driver features were significantly associated with motorcyclist injury severity. Other motorcycle-related crash injury severity studies can be found in Cheng et al. (2017), Rezapour et al. (2021), and Islam (2021).

Within the safety literature, there are limited studies that have examined motorcycle crash frequencies in the United States. Harnen et al. (2006) employed a negative binomial (NB) model to investigate motorcycle crash frequency at urban intersections in Malaysia. Motorcycle crashes at 104 signalized and unsignalized intersections between 1997 and 2000 were used. The results showed that the number of vehicles entering the intersection, approach speed, lane width, number of lanes, control type, shoulder width, and land use type were significant in predicting motorcycle crash frequency. Haque et al. (2010) investigated motorcycle crash frequency at signalized intersections using Bayesian hierarchical models. A total of 2,348 motorcycle crashes at four-legged and T-signalized intersections in Singapore between 2003 and 2006 were used. The number of lanes, presence of wider medians, and uncontrolled left-turn lanes at major roads were significantly associated with increased motorcycle crashes at the four-legged intersections. On the other hand, the presence of exclusive right-turn lanes at both major and minor roads significantly increased motorcycle crashes at Tsignalized intersections in Singapore.

Manan et al. (2013) developed SPFs for fatal motorcycle crashes on Malaysian primary roads using the standard NB model. Fatal motorcycle crashes over 124 road sections between 2007 and 2009 were used. The results showed that motorcycle fatalities per kilometer were affected by the average daily number of motorcycles and number of access points per kilometer. Flask et al. (2014) investigated multivehicle-motorcycle crashes using the Bayesian negative binomial model. A total of 3,804 multivehicle motorcycle crashes on segments between 2006 and 2011 in Ohio were used. The findings showed that smaller lane and shoulder widths, increased horizontal degree of curvature, and vertical grade were significantly associated with crash frequency. Lyon et al. (2017) developed SPFs for motorcycle crashes while applying the standard NB model. A total of five-year motorcycle crash records from Florida, Pennsylvania, and Virginia were used. It was concluded that potential bias from missing motorcycle AADT was negligible and total AADT was adequate for developing motorcycle SPFs.

Recently, Ospina-Mateus et al. (2021) developed motorcycle SPF using the standard NB model. A total of 2,884 motorcycle crashes between 2016 and 2017 in Cartagena, Columbia were used. The results showed that the average volume of daily motorcyclists, commercial areas, number of access points per kilometer, and road type were significantly associated with motorcycle crash frequency.

2.2. Safety investigations along urban facilities

Sawalha and Sayed (2001) employed the NB model while estimating the safety performance of urban arterials in the Greater Vancouver Regional District, British Columbia, Canada using crash data on 58 arterials between 1994 and 1996. The results revealed that section length, traffic volume, intersection density, driveway density, pedestrian crosswalk density, number of traffic lanes, median type, and land use were significantly associated with crash frequency on urban arterials. Zhang et al. (2012) employed the generalized additive model to predict crash frequency on different urban roadway segments (urban freeway mainlines, freeway system interchange areas, urban arterials, and urban frontage roads). A total of 46,813 "KAB" crash records between 1996 and 2000 in Houston, Texas were used. The results showed a linear relationship between crash frequency and traffic flow for urban freeway mainlines, freeway system interchange areas, and arterial segments. However, at other urban facilities, a non-linear relationship existed.

Cunto et al. (2015) evaluated the applicability and transferability of the Highway Safety Manual (HSM) SPFs for urban intersections in Fortaleza, Brazil. A total of 89 urban four-legged signalized and 92 urban

unsignalized intersections were investigated. The results indicated that the baseline HSM SPFs can be cautiously applied to Brazilian roads. Alkaaf and Abdel-Aty (2015) developed local SPFs using an NB model for urban four-lane divided road segments with angle parking in Riyadh, Saudi Arabia. The results showed that fatal and injury crash frequency on Riyadh's urban four-lane divided road segments were best described as a function of AADT, segment length, speed limit, and driveway density.

Al-Omari et al. (2021) developed simple and full SPFs based on areatype classification in Florida between 2015 and 2019 while applying the standard NB model. The results showed that crash frequency was influenced by AADT, presence of signalized intersections, speed limit, and shoulder width. Recently, Alkaaf and Abdel-Aty (2022) investigated the transferability of SPFs for urban four-lane divided roadways in Muscat, using a total of 627 crashes during the 2010–2011 period. The study results indicated that HSM-calibrated SPFs provided the best fit for the crash data in the city of Muscat. Furthermore, crash frequency on urban four-lane divided roadways was best predicted as a function of AADT, segment length, and speed limit.

2.3. Study contribution to the motorcycle safety state-of-the-art

A comprehensive review of motorcycle safety studies revealed that, to the best of the authors' knowledge, limited studies have developed motorcycle crash-specific SPFs in the United States, especially along urban roadway segments and for each of the pre-pandemic and postpandemic periods separately. This study takes the initiative and develops motorcycle-specific SPFs along each of the urban two-lane undivided and urban multilane roadway segments in Kentucky. Furthermore, considering the significant impact of COVID-19 on traffic patterns, this study separately investigates motorcycle SPFs during the pre-pandemic (2015–2019) and post-pandemic (2020–2022). The study findings will aid in more effective countermeasure selection to enhance motorcyclist safety along urban roads, particularly post the COVID-19 pandemic.

3. Methodology

3.1. Conway-Maxwell-Poisson (CMP) model

Despite being widely used as an SPF tool, the NB model is limited to over-dispersed count data (i.e., when crash variance is greater than its mean). In this study, motorcycle crash variance was found to be less than its mean (i.e., under-dispersed data), so a more flexible Conway-Maxwell-Poisson (CMP) distribution was used as an SFP tool. The CMP (or COM-Poisson) distribution generalizes the well-known Poisson distribution and is suitable for fitting both over-dispersed and underdispersed count data (Shmueli et al., 2005). The probability function of a CMP distribution is given as follows (Shmueli et al., 2005; Sellers & Shmueli, 2010):

$$P(Y = y) = \frac{\lambda^{y}}{(y!)^{y}Z(\lambda, y)}, \ y = 0, 1, 2, \dots$$ (1)

$$Z(\lambda, \nu) = \sum_{n=0}^{\infty} \frac{\lambda^n}{(n!)^{\nu}}$$ (2)

where: Y is the discrete count, λ is a centering parameter that approximates the mean of the observations, Z(λ, v) is a normalizing constant, and v is the dispersion parameter, such that v > 1 represents under-dispersion and v < 1 represents over-dispersion. The CMP distribution does not have closed-form expressions for its moments in terms of the parameters λ and v. Using an asymptotic approximation for Z(λ, v), the expected value and variance can be approximated as follows (Sellers & Shmueli, 2010; Sellers et al., 2012):

$$E[Y] = \frac{\partial log Z(\lambda, \nu)}{\partial log \lambda} \approx \lambda^{1/\nu} - \frac{\nu - 1}{2\nu}$$ (3)

$$Var[Y] = \frac{\partial E[Y]}{\partial log\lambda} \approx \frac{1}{\nu} \lambda^{1/\nu}$$ (4)

3.2. Heterogeneous Conway-Maxwell-Poisson (HTCMP) model

An extension of the CMP model is the heterogeneous CMP (or HTCMP) model, which accounts for unobserved heterogeneity by allowing the dispersion parameter to vary as a function of site-specific features. The HTCMP uses the same probability density function as the CMP model, where the dispersion parameter is expressed as a function of site-specific attributes, as follows:

$$ln(v) = \gamma \psi_i \tag{5}$$

where: *ψi*is the vector of site-specific characteristics and γ is the vector of regression coefficients corresponding to ψi . Note that if none of the variables are statistically significant in the dispersion part, the HTCMP model reduces to the CMP model, where the dispersion parameter is fixed across the sites (or segments).

3.3. Model comparison and selection

For each of the CMP and HTCMP models, goodness-of-fit (GOF) measures, including deviance statistic (D), Akaike information criterion (AIC), Bayesian information criterion (BIC), and McFadden pseudo R2 were used to evaluate the overall fit and compare the fitted models. The GOF measures are calculated as follows:

$$D = 2*(LL0 - LL\beta) \tag{6}$$

$$AIC = -2*LL_{\beta} + 2*P \tag{7}$$

$$BIC = -2*LL_{\beta} + P*ln(n) \tag{8}$$

$$\textit{McFadden pseudo } R^2 = 1 - \left(\frac{LL_{\beta}}{LL_0}\right)$$

where: *LL*0 is log-likelihood of the null model (i.e., constant-only model), LLβ is log-likelihood at convergence, P is the number of model parameters, and n is the number of observations (or segments). Models with lower AIC and BIC values and higher pseudo R2 imply better-fit ones.

Furthermore, the likelihood ratio test (LRT) was also applied to evaluate the relative performance of the fitted models. The LRT is based on the differences in the log-likelihoods of the fitted models (LLβ1 ,LLβ2 ), which follows a chi-squared distribution with degrees of freedom equal to the difference between the number of estimated parameters in both models (k).

$$LRT = 2*(LL_{\beta2} - LL{\beta1}) \cong \chi^2{(df.=k)}$$ (10)

To evaluate the predictive performance of the fitted SPFs using the validation dataset, mean absolute deviance (MAD) and mean square prediction error (MSPE) were used. The model with lower MAD and MSPE values provides better prediction performance. These measures are calculated as follows:

$$MAD = \frac{\sum_{i=1}^{n} |\mu_i - y_i|}{n}$$ (11)

$$MSPE = \frac{\sum_{i=1}^{n} (\mu_i - y_i)^2}{n}$$ (12)

where: yi and *μi*are observed and predicted number of crashes at urban road segment i, respectively, and n is the number of sites (or segments) in the validation dataset.

3.4. Empirical Bayes (EB) method

The Empirical Bayes (EB) method, widely employed in safety studies to rank high-crash locations, was used to rank motorcycle-specific highcrash urban road segments. The expected number of crashes is calculated as the weighted average of the observed and predicted number of crashes estimated by the fitted SPF model. The EB estimate (NE) is calculated as follows:

$$EB = N_E = w^*N_P + (1 - w)^*N_O$$ (13)

$$w = \frac{1}{1 + \nu^* N_P} \tag{14}$$

where: NP is the precited number of crashes estimated by the fitted SPF, NO is the number of observed crashes, v is the dispersion parameter from the SPF model, and w is the weighting factor. It is important to note that for the HTCMP model, the weighting factor (w) will vary by segment i, as a function of varying dispersion parameters (vi).

High-crash segments were then ranked in descending order based on the excess expected crashes (EEC) (i.e., difference between the expected and predicted crashes at the sites), as follows:

$$EEC = N_E - N_P (15)$$

4. Data collection and processing

The used data were collected from two separate databases provided by the Kentucky Transportation Cabinet (KYTC). These include the crash database (consisting of eight-year "2015–2022" motorcycle-related crashes) and the roadway inventory database extracted from KYTC's Highway Information Extract View and Interface (HIEVi) (KYTC, 2023). These two databases were then merged based on the roadway ID and milepost of each crash. Since this study focuses on investigating motorcycle crashes along urban roadway segments, crashes on rural roadways and other facilities, such as intersections and ramps, were excluded from the analysis.

To investigate crash frequency along road segments, the road sections were divided into homogeneous segments based on the homogeneity of roadway geometric and traffic characteristics. In this regard, area type (rural or urban), roadway type (undivided or divided), number of traffic lanes, posted speed limit (PSL), and AADT were used to produce homogeneous segments. A homogeneous segment ended where at least one of these five features changed, and a new homogeneous segment subsequently started.

Fig. 2 illustrates imaginary homogeneous segments produced based on changes in roadway type, PSL, and AADT. For example, homogeneous segment 1 concluded where AADT and PSL changed from 1,500 to 1,200 and 55 mph to 35 mph, respectively, while other roadway features (i.e., urban area, undivided roadway, and four traffic lanes) remained unchanged. Similarly, homogeneous segment 2 ended where PSL and roadway type changed from 35 mph to 25 mph and undivided to divided, respectively, while the other roadway characteristics remained consistent. The segment length for each homogeneous segment was computed as the difference between each segment's beginning and ending milepost. It is important to note that any segments shorter than 0.1 miles were excluded to avoid the issue of low exposure (Hosseinpour et al., 2022).

As mentioned earlier, eight-year crash records were analyzed separately in two periods, i.e., pre-pandemic (2015–19) and post-pandemic (2020–2022), and the segmentation process was done separately for pre- and post-pandemic crash data. A total of 1,676 homogeneous segments were produced for the pre-pandemic period, with lengths varying from 0.101 to 4.65 miles and an average segment length of 0.79 miles. Of the 1,676 segments, 830 segments were urban two-lane undivided segments, and the remaining 846 segments were urban multilane ones. Similarly, a total of 966 homogeneous segments were produced for the post-pandemic period, with lengths varying from 0.1 to 4.65 miles and an average segment length of 0.80 miles. Of the 966 segments, 482 segments were urban two-lane undivided segments, and the remaining 484 segments were urban multilane ones. Note that approximately 20% of the total segments, i.e., 335 and 193 in the pre- and post-pandemic periods, respectively, were zero motorcycle-crash urban segments randomly collected across Kentucky to develop valid SPFs. Furthermore, for each roadway facility, homogeneous segments were randomly split into calibration (75%) and validation (25%) datasets, where the former was used to develop the motorcycle SPFs, and the latter was used to evaluate the prediction performance of the fitted SPFs.

In total, 2,963 motorcycle crashes along urban roadway segments were analyzed. Of these, 1,272 crashes (841 pre-pandemic and 431 postpandemic) occurred on two-lane roadways, while 1,691 crashes (1,167 pre-pandemic and 524 post-pandemic) occurred on multilane roadways. Overall, the annual average crash frequencies decreased post-pandemic

Fig. 2. Illustration Sketch Showing Homogeneous Urban Roadway Segments.

across both urban two-lane and urban multilane segments. This reduction was expected, mainly due to reduced traffic volumes during and post-pandemic, which aligns with findings from other studies (e.g., Islam et al., 2022; Shaik & Ahmed, 2022). Fig. 3 shows the histograms of motorcycle crash frequencies in the pre- and post-pandemic periods by the urban facility type (i.e., urban two-lane undivided and urban multilane roadway segments). As observed in Fig. 3a and b, both urban two-lane undivided and multilane segments had the highest representation of "one crash count" in each of the pre-pandemic and postpandemic periods. Thus, zero-inflated models were not the ideal modeling solution and were not used in the study. Table 1 shows descriptive statistics of the explanatory variables used in the SPF development.

5. SPF results along urban two-lane undivided roadway segments

5.1. Motorcycle SPFs' interpretations

Table 2 shows the results of CMP and HTCMP SPF models for motorcycle crashes along urban two-lane undivided roadway segments for each of the pre- and post-pandemic periods. All the fitted models had significant deviance statistics, rejecting the hypothesis that they performed similarly to their constant-only models. The LRTs comparing the fitted HTCMP versus CMP models for each of the pre- and postpandemic periods indicated that the HTCMP models outperformed their respective CMP models at the 0.1% level of significance (P-value < 0.001).

Overall, the GOF measures including Pseudo R2 and AIC suggested that HTCMP models provided better fit compared to their CMP counterparts. In addition, the HTCMP models had the lowest MAD and MSPE values based on the model validation performance, indicating better prediction capability. The superiority of the HTCMP models indicated that this model, with a varying dispersion parameter, could appropriately capture the under-dispersion in motorcycle crashes along urban two-lane undivided segments. For example, the HTCMP models for both pre- and post-pandemic periods showed significant roadway parameters (e.g., right shoulder width and presence of horizontal curve) in the dispersion part, which explained the under-dispersion.

From Table 2, the model results showed that motorcycle crashes (pre- and post-pandemic) along urban two-lane undivided road segments were significantly associated with AADT, road functional class (collector and local roads), presence of horizontal curve, and presence of roadside guardrail. Pre-pandemic, posted speed limit (15–35 mph) was found to be a significant factor and was associated with a reduced motorcycle crash frequency. However, post-pandemic, posted speed

Fig. 3. Motorcycle Crash Frequencies along: (a) Urban Two-Lane Undivided Roadway Segments and (b) Urban Multilane Roadway Segments.

Table 1 Descriptive Statistics of Explanatory Variables for Urban Segments Pre- and Post-Pandemic.

| Variable Description | | | Pre-Pandemic (2015–2019) | | | | | | | | Post-Pandemic (2020–2022) | | | | | | | |--------------------------------------------|--------------------------|-------|--------------------------|------|-----------------|------|-------|--------------------------|------|------|---------------------------|-----------------|------|-------|-------|-------|--| | | Urban Two-Lane Undivided | | | | Urban Multilane | | | Urban Two-Lane Undivided | | | | Urban Multilane | | | | | | | | Min. | Max. | Mean | SD | Min. | Max. | Mean | SD | Min. | Max. | Mean | SD | Min. | Max. | Mean | SD | | | Continuous variables (Calibration dataset) | | | | | | | | | | | | | | | | | | | Natural logarithm of AADT | 4.04 | 10.08 | 8.34 | 0.96 | 7.04 | 12 | 9.92 | 0.8 | 4.79 | 10.1 | 8.45 | 0.87 | 7.64 | 12.04 | 9.91 | 0.79 | | | Lane width (in feet) | 6 | 21 | 10.91 | 1.74 | 9 | 13 | 11.68 | 0.7 | 8 | 20 | 10.95 | 1.69 | 10 | 13 | 11.7 | 0.64 | | | Right shoulder width (in feet) | 0 | 12 | 2.99 | 2.64 | 0 | 16 | 5.63 | 4.4 | 0 | 11 | 2.86 | 2.62 | 0 | 13 | 5.3 | 4.34 | | | Number of lanes | 2 | 2 | 2 | 0 | 3 | 12 | 4.41 | 1.2 | 2 | 2 | 2 | 0 | 3 | 11 | 4.41 | 1.09 | | | Median width (in feet)* | na** | na | na | na | 0 | 99 | 16.71 | 21 | na | na | na | na | 0 | 99 | 15.48 | 18.34 | |

Variable Variable Description Pre-Pandemic (2015–2019) Post-Pandemic (2020–2022)
Urban Two-Lane
Undivided		 Urban Multilane Undivided Urban Two-Lane Urban Multilane
No. of
Sites		 No. of
Motorcycle
Crashes		 No. of
Sites		 No. of
Motorcycle
Crashes		 No. of
Sites		 No. of
Motorcycle
Crashes		 No.
of
Sites		 No. of
Motorcycle
Crashes
Calibration dataset Number of sites and
motorcycle crashes in the
calibration dataset		 622 628 634 876 361 319 363 383
Validation dataset Number of sites and
motorcycle crashes in the
validation dataset		 208 213 212 291 121 112 121 141
Indicator dummy variables (Calibration dataset)
Paved shoulder If true = 1, otherwise = 0 541 568 626 876 225 212 361 383
Horizontal curve If present = 1, otherwise =
0		 253 296 164 231 148 153 92 96
Vertical grade If present = 1, otherwise =
0		 205 206 233 331 179 167 138 153
Roadside guardrail
(steel strong-post
W-beam)		 If present = 1, otherwise =
0		 57 42 152 156 29 12 86 68

| Variable | Variable | | Pre-Pandemic (2015–2019) | | | Post-Pandemic (2020–2022) | | | | | | |--------------------------------------|-------------------------------|-----------------|------------------------------|-----------------|------------------------------|---------------------------|------------------------------|--------------------|------------------------------|--|--| | | Description | | Urban Two-Lane Undivided | Urban Multilane | | | Urban Two-Lane Undivided | | Urban Multilane | | | | | | No. of
Sites | No. of Motorcycle
Crashes | No. of
Sites | No. of Motorcycle
Crashes | No. of
Sites | No. of Motorcycle
Crashes | No.
of
Sites | No. of Motorcycle
Crashes | | | | Flat terrain type | If true = 1,
otherwise = 0 | 220 | 222 | 272 | 389 | 142 | 128 | 167 | 181 | | | | Road Functional Class: | | | | | | | | | | | | | Interstate/
principal
arterial | If true = 1,
otherwise = 0 | 20 | 31 | 377 | 619 | 8 | 6 | 194 | 239 | | | | Minor arterial | If true = 1,
otherwise = 0 | 227 | 268 | 215 | 277 | 156 | 158 | 147 | 135 | | | | Major collector | If true = 1,
otherwise = 0 | 269 | 260 | 36 | 30 | 148 | 116 | 20 | 9 | | | | Minor collector/
local | If true = 1,
otherwise = 0 | 106 | 69 | 6 | 0 | 49 | 39 | 2 | 0 | | | | Undivided* | If true = 1,
otherwise = 0 | na | na | 270 | 356 | na | na | 151 | 163 | | | | Posted Speed Limit: | | | | | | | | | | | | | ≤ 35 mph | If true = 1,
otherwise = 0 | 413 | 400 | 162 | 190 | 248 | 211 | 99 | 99 | | | | 40–50 mph | If true = 1,
otherwise = 0 | 111 | 125 | 248 | 377 | 72 | 71 | 151 | 153 | | | | ≥ 55 mph | If true = 1,
otherwise = 0 | 98 | 103 | 224 | 309 | 41 | 37 | 113 | 131 | | | | Type of Median Barriers:* | | | | | | | | | | | | | Cable barriers | If true = 1,
otherwise = 0 | na | na | 31 | 49 | na | na | 15 | 20 | | | | Concrete barriers | If true = 1,
otherwise = 0 | na | na | 63 | 109 | na | na | 39 | 53 | | | | Other barriers | If true = 1,
otherwise = 0 | na | na | 9 | 14 | na | na | 7 | 9 | | |

Note: Min. = minimum; Max. = maximum; SD=standard deviation; and AADT=annual average daily traffic.

Table 2 Results of CMP and HTCMP Models for Motorcycle Crash SPFs along Urban Two-Lane Undivided Road Segments.

| Variable | | Pre-Pandemic (2015–2019) | | | | | Post-Pandemic (2020–2022) | | | | | | | |------------------------------------|-----------|--------------------------|------------|-------------|---------------|------------|---------------------------|---------------|------------|-------------|---------------|------------|--| | | CMP Model | | | HTCMP Model | | | CMP Model | | | HTCMP Model | | | | | | Coef. | Std.
Error | P
Value | Coef. | Std.
Error | P
Value | Coef. | Std.
Error | P
Value | Coef. | Std.
Error | P
Value | | | Mean-Parameter Count Part | | | | | | | | | | | | | | | Constant | − 4.269 | 0.998 | < 0.001 | − 3.432 | 0.896 | < 0.001 | − 4.974 | 1.313 | < 0.001 | − 3.114 | 1.898 | 0.101 | | | Ln(AADT) | 0.567 | 0.112 | < 0.001 | 0.535 | 0.098 | < 0.001 | 0.713 | 0.153 | < 0.001 | 0.572 | 0.210 | 0.007 | | | Principal Arterial | 1.016 | 0.352 | 0.004 | N/S* | N/S | N/S | N/S | N/S | N/S | N/S | N/S | N/S | | | Major Collector | − 0.364 | 0.174 | 0.037 | − 0.368 | 0.177 | 0.037 | − 0.717 | 0.239 | 0.003 | − 1.736 | 0.400 | < 0.001 | | | Minor Collector/Local | − 0.900 | 0.274 | 0.001 | − 0.946 | 0.271 | < 0.001 | N/S | N/S | N/S | − 1.785 | 0.557 | 0.001 | | | Posted Speed Limit (15–35
mph) | N/S | N/S | N/S | − 0.532 | 0.254 | 0.036 | N/S | N/S | N/S | N/S | N/S | N/S | | | Presence of Horizontal Curve | 0.689 | 0.144 | < 0.001 | 0.719 | 0.146 | < 0.001 | 1.077 | 0.246 | < 0.001 | 1.600 | 0.351 | < 0.001 | | | Presence of Roadside
Guardrails | − 0.951 | 0.255 | < 0.001 | − 1.933 | 0.322 | < 0.001 | − 2.163 | 0.452 | < 0.001 | − 2.530 | 0.494 | < 0.001 | | | Dispersion Part | | | | | | | | | | | | | | | Constant | 1.463 | 0.050 | < 0.001 | 1.813 | 0.153 | < 0.001 | 1.801 | 0.065 | <0.001 | 1.695 | 0.120 | < 0.001 | | | Principal Arterial | na** | na | na | − 0.572 | 0.102 | < 0.001 | na | na | na | N/S | N/S | N/S | | | Major Collector | na | na | na | N/S | N/S | N/S | na | na | na | − 0.340 | 0.124 | 0.006 | | | Minor Collector/Local | na | na | na | N/S | N/S | N/S | na | na | na | − 0.633 | 0.187 | 0.001 | | | Posted Speed Limit (15–35
mph) | na | na | na | − 0.195 | 0.095 | 0.040 | na | na | na | 0.182 | 0.083 | 0.028 | | | Right Shoulder Width | na | na | na | 0.041 | 0.013 | 0.002 | na | na | na | N/S | N/S | N/S | | | Presence of Horizontal Curve | na | na | na | N/S | N/S | N/S | na | na | na | 0.270 | 0.112 | 0.016 | | | Presence of Paved Shoulder | na | na | na | − 0.244 | 0.123 | 0.047 | na | na | na | N/S | N/S | N/S | | | Presence of Roadside
Guardrails | na | na | na | − 0.863 | 0.206 | < 0.001 | na | na | na | 0.219 | 0.084 | 0.009 | | | Presence of Gradient | na | na | na | N/S | N/S | N/S | na | na | na | N/S | N/S | N/S | | | Fixed Disp. Parameter | 4.317 | 0.217 | < 0.001 | na | na | na | 6.057 | 0.396 | < 0.001 | na | na | na | |

Pre-Pandemic (2015–2019) Post-Pandemic (2020–2022)
CMP Model HTCMP Model CMP Model HTCMP Model
Goodness-of-Fit (GOF) Statistics
Number of observations 622 622 361 361
Number of parameters 8 13 6 12
Log-likelihood at convergence (LLβ) − 580.23 − 545.18 − 259.98 − 245.76
Log-likelihood at zero (LL0) − 657.40 − 657.40 − 302.86 − 302.86
Deviance (D) = (2*(LLβ − LL0)) 154.34 224.44 85.76 114.20
(df = 6, P-Value < 0.001) (df = 11, P-Value < 0.001) (df = 4, P-Value < 0.001) (df = 10, P-Value < 0.001)
LRT (HTCMP vs CMP) 70.10 28.44
(df = 5, P-Value < 0.001) (df = 6, P-Value < 0.001)
McFadden pseudo R2 0.117 0.171 0.142 0.189
AIC (Akaike Information Criterion) 1176.46 1116.36 531.95 515.52
BIC (Bayesian Information Criterion) 1211.93 1173.98 555.28 562.19
MAD (Mean Absolute Deviance) 0.508 0.504 0.372 0.363
MSPE (Mean Square Prediction Error) 0.497 0.481 0.315 0.288

* N/S=not statistically significant at 10% significance level.

limit (15–35 mph) was not found significant along urban two-lane road segments.

In the count part, higher AADT was associated with increased number of motorcycle crashes. This is expected since AADT reflects exposure and with higher exposure, motorcycle crash frequency increases. This finding is consistent with past studies (e.g., Haque et al., 2010; Manan et al., 2013; Ospina-Mateus et al., 2021). Road functional class (major collector and minor collector/local roads) was associated with reduced motorcycle crash frequency. This could be since these roads have frequent stops and intersections, which compel motorcyclists to reduce speeds and proceed with caution. The presence of horizontal curve was associated with increased motorcycle crash frequency. This is plausible due to the heightened risk of losing motorcycle control at sharp curves/bends; thereby, increasing motorcycle crashes. This finding is consistent with Flask et al. (2014). The presence of a roadside guardrail

was associated with reduced motorcycle crash frequency. This is likely since motorcyclists perceive guardrails as a potential hazard (Michie & Bronstad, 1994) and drive cautiously; thereby, reducing motorcycle crash frequency (Elvik, 1995; Ben-Bassat & Shinar, 2011).

Pre-pandemic, urban two-lane undivided road segments with posted speed limits of 15–35 mph were also associated with reduced motorcycle crash frequency. This could be attributed to lower motorcycle speeds, allowing more time to react to potential hazards and community awareness in urban areas. On the other hand, posted speed limits did not affect motorcycle crash frequency post-pandemic. This could be attributed to the reduced traffic volumes and increased vehicle speeds during and post-pandemic (Islam et al., 2022).

* only applicable to urban multilane segments.

** na = not applicable.

** na = not applicable.

5.2. Identification of motorcycle-specific high-crash urban two-lane roadway segments

The results of the HTCMP models pre- and post-pandemic were incorporated into the EB method to compute EECs and rank the highcrash urban two-lane undivided road segments in Kentucky. Table 3 shows characteristics of the top 10 motorcycle-specific high-crash urban two-lane undivided road segments in each of the pre- and post-pandemic periods.

From Table 3, pre-pandemic, the average AADT for the top 10 highcrash road segments listed was 10,076, which is greater than the overall average of all studied segments (AADTallsegments = 5,974). Similarly, postpandemic, the average AADT for listed road segments was 6,811, while the overall average of all studied segments (AADTallsegments = 6,183) was lower. Furthermore, an in-depth investigation of motorcycle crashes along these high-crash locations (HCLs) was performed to facilitate targeted safety countermeasures to enhance motorcyclists' safety along urban two-lane undivided road segments. Fig. 4 shows details of the most frequent crash characteristics within the top 10 high-crash urban two-lane undivided segments for both pre- and post-pandemic periods.

It can be seen from Fig. 4 that single-vehicle collisions were the most frequent manner of collision pre- and post-pandemic, but they have significantly increased post-pandemic. Furthermore, the review of police crash narratives revealed that "lost motorcycle control," "unable to stop in time," and "failed to yield" were the most frequent causes of crashes along these top 10 high-crash segments. Specifically, postpandemic, "lost control of motorcycle" was responsible for 50% of crashes at these sites (almost three times higher than pre-pandemic period), which substantiates that unsafe driver behavior, such as speeding, significantly increased post-pandemic. This is consistent with the study by Shaik and Ahmed (2022). Furthermore, it is evident from Fig. 4 that motorcyclists were the most frequent at-fault vehicle types and were responsible for 68% of motorcycle-related crashes (postpandemic) at the high-crash locations.

6. SPF results along urban multilane roadway segments

6.1. Motorcycle SPFs' interpretations

Similar to the SPFs fitted along urban two-lane undivided segments, CMP and HTCMP models were fitted along urban multilane segments for each of the pre- and post-pandemic periods. Table 4 shows the model results and GOF statistics of the fitted models for motorcycle SPFs along urban (fitted HTCMP versus CMP model indicated that the HTCMP models outperformed their respective CMP models at the 0.1% level of significance (P-value < 0.001). The HTCMP models had the highest Pseudo R2 and lowest AIC and BIC values; hence, indicating good model fit. Furthermore, from the model validation performance, the HTCMP models had the lowest MAD and MSPE values, indicating better

prediction capability. Once more, the superiority of the HTCMP models suggested that the varying dispersion parameter could appropriately capture the motorcycle crash data under-dispersion at urban multilane segments. For example, the HTCMP models for both pre- and postpandemic showed significant roadway parameters in the dispersion part (e.g., presence of roadside guardrail and presence of cable median barrier).

From Table 4, the model results showed that motorcycle crashes along urban multilane segments (pre- and post-pandemic) were significantly associated with AADT, right shoulder width, posted speed limit (≥55 mph), presence of horizontal curve, and presence of roadside guardrail. Pre-pandemic, the presence of concrete median barrier was also associated with reduced motorcycle crash frequency. However, post-pandemic, it did not affect motorcycle crash frequency.

In the count part of the HTCMP models, higher AADT was associated with increased motorcycle crash frequency. This is expected as the number of vehicles on the road segment increases, the exposure to motorcycle crashes also increases (Lu, et al., 2013). The posted speed limit (≥55 mph) was associated with a reduced frequency of motorcycle crashes along urban multilane road segments. This might be because road segments with higher posted speed limits generally have better geometric design features (e.g., sight distance and wider lanes), which could contribute to the reduced motorcycle crash frequency. Similar findings were reported by Hauer et al. (2004). To verify this finding, the average lane widths at urban multilane segments were contrasted by different posted speed limits, as shown in Fig. 5. From this figure, it is evident that segments with 55 mph or higher posted speed limits had wider lanes (i.e., better geometric design cross-section) compared to segments with lower posted speed limits.

Wider right shoulders were associated with increased motorcycle crash frequency along urban multilane segments. This is likely since wider shoulders might give drivers a false sense of security, encouraging some to treat them as an additional lane for overtaking slower vehicles; hence, increasing the frequency of crashes. This is consistent with the findings of Li et al. (2013). Also, to better investigate the impact of right shoulder widths on motorcycle crash frequency, Fig. 6 shows the plot of normalized motorcycle crash frequency (i.e., crash frequency per year) versus the right shoulder width (in feet). As seen from Fig. 6, motorcycle crashes significantly increase when the shoulder widths are less than 3 feet and 9 feet or greater.

The presence of horizontal curve was associated with increased motorcycle crash frequency at the urban multilane segments. As discussed previously, this is likely since the risk of losing motorcycle control at horizontal curves increases (Flask et al., 2014). The presence of a roadside guardrail was associated with reduced motorcycle crash frequency at urban multilane segments, possibly since motorcyclists drive cautiously nearby guardrails as they perceive these as potential hazard (Elvik, 1995; Ben-Bassat & Shinar, 2011).

During both pre- and post-pandemic, urban multilane segments with

Table 3 Top 10 High Motorcycle-Crash Urban Two-Lane Undivided Segments.

| | Pre-Pandemic (2015–2019) | | | | Post-Pandemic (2020–2022) | | | | | | | | |------|--------------------------|-------|-------|--------------|---------------------------|---------|----------|-------|---------------|--------------|--|--| | Rank | Nobs.* | Np* | EB* | EEC* (EB-Np) | Segment AADT | Nobs.** |
Np | EB | EEC** (EB-Np) | Segment AADT | | | | 1 | 10 | 2.730 | 8.975 | 6.245 | 15,403 | 4 | 1.587 | 3.804 | 2.217 | 5,077 | | | | 2 | 5 | 1.647 | 4.577 | 2.930 | 11,937 | 3 | 1.081 | 2.804 | 1.723 | 15,403 | | | | 3 | 5 | 1.770 | 4.696 | 2.925 | 5,221 | 3 | 1.007 | 2.660 | 1.653 | 5,331 | | | | 4 | 5 | 1.969 | 4.691 | 2.722 | 9,822 | 3 | 0.913 | 2.499 | 1.586 | 1,612 | | | | 5 | 4 | 1.445 | 3.741 | 2.296 | 13,013 | 3 | 1.331 | 2.834 | 1.503 | 12,370 | | | | 6 | 4 | 1.512 | 3.670 | 2.158 | 2,944 | 3 | 1.239 | 2.734 | 1.496 | 3,280 | | | | 7 | 4 | 1.085 | 3.148 | 2.063 | 15,403 | 3 | 1.309 | 2.779 | 1.470 | 2,532 | | | | 8 | 4 | 1.673 | 3.735 | 2.062 | 1,978 | 2 | 0.696 | 1.772 | 1.076 | 12,825 | | | | 9 | 4 | 1.825 | 3.594 | 1.769 | 9,104 | 2 | 0.465 | 1.515 | 1.049 | 5,188 | | | | 10 | 3 | 0.787 | 2.540 | 1.753 | 15,932 | 2 | 0.293 | 1.277 | 0.984 | 4,487 | | |

* Unit of "crashes in five years" (note: Nobs. = Observed crashes; Np = Predicted crashes). ** Unit of "crashes in three years" (note: Nobs. = Observed crashes; Np = Predicted crashes).

Fig. 4. Most Frequent Crash Characteristics within Top Ten Motorcycle-Specific High-Crash Urban Two-Lane Undivided Segments.

cable and concrete median barriers were significantly associated with reduced motorcycle crash frequency. This is likely since the presence of cable and concrete median barriers could lead to hazard strikes, prompting motorcyclists to drive cautiously; thereby, reducing the frequency of motorcycle crashes. This is in line with the findings of Donnell and Mason (2006) and Zou and Tarko (2016).

6.2. Identification of motorcycle-specific high-crash urban multilane roadway segments

Once more, the results of the HTCMP model for pre- and postpandemic were incorporated into the EB method to compute EECs along urban multilane segments in Kentucky. Table 5 shows characteristics of the top 10 urban multilane segments with a high number of motorcycle crashes ranked with respect to the EEC values in each of the pre- and post-pandemic periods.

Along the top 10 urban multilane segments, the average AADT prepandemic (AADTtop− ten = 31,415) and post-pandemic (AADTtop− ten = 44,289) were greater than the corresponding overall average across all studied roadway segments (AADTpre− pandemic,allsegments = 30,167, AADTpost− pandemic,allsegments = 29,242). Furthermore, an in-depth investigation of motorcycle crashes at these high-crash locations (HCLs) was performed to facilitate targeted safety countermeasures to enhance motorcyclists' safety along urban multilane segments. Fig. 7 shows details of the most frequent crash characteristics within the top 10 highcrash urban multilane segments for both pre- and post-pandemic periods.

It can be seen from Fig. 7 that single-vehicle, rear-end, and angle collisions collectively accounted for over 80% of motorcycle crashes in both pre- and post-pandemic periods, with increased rear-end and angle collisions post-pandemic. Regarding the at-fault vehicles, motorcyclists were responsible for 73% of crashes post-pandemic at the high-crash segments, an increase of around 28% compared to the pre-pandemic period. Furthermore, the review of the police crash narratives revealed that the increase in rear-end and angle collisions postpandemic correlates with the following motorcyclists' errors: "unable to stop in time," "improper lane change," and "lost motorcycle control" along the top 10 high-crash segments. These findings show that unsafe driver behaviors, such as speeding and aggressive driving, experienced a

significant increase during and post-pandemic. These findings highlight the need for advance assistance systems in motorcycles (e.g., lane change assistance, brake assistance systems) to account for motorcyclists' errors.

7. Proposed motorcycle safety countermeasures

Based on the results of best-fit models (i.e., the HTCMP models in Tables 2 and 4) for pre- and post-pandemic and crash-specific characteristics at high motorcycle-crash segments (in Figs. 4 and 5), several motorcycle safety countermeasures are proposed to improve motorcyclists' safety along urban segments in Kentucky, as follows:

Common countermeasures along urban two-lane and multilane roadway segments:

  • Installing advance warning signs and/or chevrons along sharp horizontal curves (based on the SPF model results).
  • Installing roadside guardrails (based on the SPF model results).
  • Promoting the adoption of latest safety technologies in motorcycles (e.g., lane change assist, collision warning, and brake assistance) to reduce motorcycle crashes related to driver error (e.g., inability to stop in time and improper lane changes) (based on in-depth investigation of HCLs).

Countermeasures specific to urban two-lane undivided segments:

• Installing edge line rumble strips to alert inattentive or speeding drivers drifting from their driving lane (since single-vehicle collisions were the most-frequent manner of collision from the in-depth investigation of HCLs).

Countermeasures specific to urban multilane segments:

• Providing right shoulders between 3 and 9 feet along urban multilane segments (since there is a significant increase in motorcycle crashes on road segments with right shoulder widths less than 3 ft and greater than 9 ft) (as previously highlighted in Fig. 6).

Table 4 Results of CMP and HTCMP Models for Motorcycle Crash SPFs along Urban Multilane Road Segments.

| Variable | | Pre-Pandemic (2015–2019) | | | | | | Post-Pandemic (2020–2022) | | | | | | |------------------------------------|-----------|--------------------------|------------|-------------|---------------|------------|-----------|---------------------------|------------|-------------|---------------|------------|--| | | CMP Model | | | HTCMP Model | | | CMP Model | | | HTCMP Model | | | | | | Coef. | Std.
Error | P
Value | Coef. | Std.
Error | P
Value | Coef. | Std.
Error | P
Value | Coef. | Std.
Error | P
Value | | | Mean-Parameter Count Part | | | | | | | | | | | | | | | Constant | − 8.275 | 1.024 | <0.001 | − 6.785 | 0.932 | <0.001 | − 9.722 | 1.424 | <0.001 | − 3.542 | 2.529 | 0.161 | | | Ln(AADT) | 0.843 | 0.108 | <0.001 | 0.689 | 0.096 | <0.001 | 1.115 | 0.151 | <0.001 | 0.441 | 0.264 | 0.095 | | | Interstate/Principal Arterial | 0.402 | 0.115 | 0.001 | N/S* | N/S | N/S | N/S | N/S | N/S | N/S | N/S | N/S | | | Posted Speed Limit (≥55
mph) | − 0.816 | 0.138 | <0.001 | − 0.730 | 0.144 | <0.001 | − 0.632 | 0.263 | 0.016 | − 0.596 | 0.289 | 0.040 | | | Right Shoulder Width | 0.030 | 0.014 | 0.036 | 0.137 | 0.025 | <0.001 | 0.046 | 0.026 | 0.081 | 0.092 | 0.029 | 0.001 | | | Presence of Horizontal Curve | 0.186 | 0.104 | 0.072 | 0.233 | 0.104 | 0.025 | N/S | N/S | N/S | 1.256 | 0.355 | <0.001 | | | Presence of Roadside
Guardrails | − 0.602 | 0.123 | <0.001 | − 1.780 | 0.212 | <0.001 | − 0.964 | 0.227 | <0.001 | − 1.746 | 0.315 | <0.001 | | | Median Barrier: Cable | − 1.368 | 0.253 | <0.001 | N/S | N/S | N/S | − 1.201 | 0.473 | 0.011 | N/S | N/S | N/S | | | Median Barrier: Concrete | − 0.687 | 0.233 | 0.003 | − 0.664 | 0.217 | 0.002 | − 0.972 | 0.365 | 0.008 | N/S | N/S | N/S | | | Dispersion Part | | | | | | | | | | | | | | | Constant | 0.798 | 0.050 | <0.001 | 0.937 | 0.086 | <0.001 | 1.423 | 0.064 | <0.001 | 4.843 | 1.381 | <0.001 | | | Principal Arterial | na** | na | na | − 0.312 | 0.058 | <0.001 | na | na | na | N/S | N/S | N/S | | | Posted Speed Limit (≤35
mph) | na | na | na | N/S | N/S | N/S | na | na | na | − 0.455 | 0.110 | <0.001 | | | Right Shoulder Width | na | na | na | 0.053 | 0.010 | <0.001 | na | na | na | N/S | N/S | N/S | | | Presence of Horizontal Curve | na | na | na | N/S | N/S | N/S | na | na | na | 0.450 | 0.127 | <0.001 | | | Terrain Type: Flat | na | na | na | − 0.151 | 0.044 | 0.001 | na | na | na | − 0.234 | 0.077 | 0.002 | | | Presence of Roadside
Guardrails | na | na | na | − 0.766 | 0.128 | <0.001 | na | na | na | − 0.587 | 0.169 | 0.001 | | | Median Barrier: Cable | na | na | na | 0.524 | 0.091 | <0.001 | na | na | na | 0.464 | 0.180 | 0.010 | | | Median Barrier: Concrete | na | na | na | N/S | N/S | N/S | na | na | na | 0.386 | 0.178 | 0.030 | | | Ln(AADT) | na | na | na | N/S | N/S | N/S | na | na | na | − 0.325 | 0.138 | 0.019 | | | Fixed Disp. Parameter | 2.221 | 0.111 | <0.001 | na | na | na | 4.150 | 0.267 | <0.001 | na | na | na | |

Pre-Pandemic (2015–2019) Post-Pandemic (2020–2022)
CMP Model HTCMP Model CMP Model HTCMP Model
Goodness-of-Fit (GOF) Statistics
Number of observations 634 634 363 363
Number of parameters 10 13 8 14
Log-likelihood at convergence (LLβ) − 838.30 − 806.27 − 357.07 − 334.29
Log-likelihood at zero (LL0) − 954.93 − 954.93 − 396.64 − 396.64
Deviance (D) = (2*(LLβ − LL0)) 233.26 297.32 79.14 124.70
(df = 8, P-Value < 0.001) (df = 11, P-Value < 0.001) (df = 6, P-Value < 0.001) (df = 12, P-Value < 0.001)
LRT (HTCMP vs CMP) 64.06 45.56
(df = 3, P-Value < 0.001) (df = 6, P-Value < 0.001)
McFadden pseudo R2 0.122 0.156 0.100 0.157
AIC (Akaike Information Criterion) 1696.59 1638.53 730.14 696.59
BIC (Bayesian Information Criterion) 1741.11 1696.41 761.30 751.11
MAD (Mean Absolute Deviance) 0.842 0.832 0.610 0.562
MSPE (Mean Square Prediction Error) 1.306 1.278 0.856 0.775

* N/S = not statistically significant at 10% significance level.

8. Conclusions

Limited studies have developed motorcycle crash-specific SPFs in the United States, especially along urban roadway segments and for each of the pre-pandemic and post-pandemic periods separately. This study took the initiative and developed motorcycle SPFs along urban two-lane undivided and multilane segments in Kentucky separately in each of the pre-pandemic (2015–2019) and post-pandemic (2020–2022) periods. For both pre- and post-pandemic periods, CMP and HTCMP models were developed and compared for each urban segment facility while accounting for motorcycle crash under-dispersion. For both urban two-lane undivided and multilane segment facilities, the HTCMP models outperformed their CMP counterparts pre- and post-pandemic, based on GOF statistics and prediction performance. The superiority of the HTCMP model suggests that the varying dispersion parameter could efficiently handle the motorcycle crash under-dispersion by incorporating site-specific variables in the dispersion part of the model.

From the developed SPFs, higher AADT and presence of horizontal

curve were associated with increased motorcycle crash frequency, while the presence of roadside steel strong-post W-beam guardrail significantly reduced motorcycle crash frequency along all urban segments, both pre- and post-pandemic. Furthermore, posted speed limits (≥55 mph) were significantly associated with reduced motorcycle crash frequency along urban multilane segments, while collector and local road types were associated with reduced motorcycle crash frequency along urban two-lane segments.

The results of the HTCMP models (for both urban two-lane and multilane) were then used to rank the top 10 motorcycle-specific highcrash segments in each of the pre- and post-pandemic periods using the EB method. An in-depth investigation of motorcycle crashes at the identified high-crash locations was also performed. Based on the study findings, several countermeasures were proposed to enhance motorcyclists' safety along both urban two-lane and multilane segments (e.g., installing chevrons and roadside guardrails at curved sections). Along urban multilane segments, it is recommended to provide right shoulders between 3 and 9 feet (since a significant increase in motorcycle crashes

** na = not applicable.

Fig. 5. Average Lane Widths at Urban Multilane Segments vs. Posted Speed Limits.

Fig. 6. Normalized Motorcycle Crash Frequency at Urban Multilane Segments vs. Right Shoulder Widths.

Table 5 Top 10 High Motorcycle-Crash Urban Multilane Segments.

| | Pre-Pandemic (2015–2019) | | | | | Post-Pandemic (2020–2022) | | | | | | | |------|--------------------------|-------|-------|-----------------|--------------|---------------------------|----------|-------|------------------|--------------|--|--| | Rank | Nobs.* | Np* | EB* | EEC*
(EB-Np) | Segment AADT | Nobs.** |
Np | EB | EEC**
(EB-Np) | Segment AADT | | | | 1 | 10 | 3.611 | 9.061 | 5.450 | 16,311 | 6 | 1.704 | 5.306 | 3.602 | 23,881 | | | | 2 | 9 | 2.254 | 7.438 | 5.185 | 81,002 | 6 | 2.080 | 5.488 | 3.408 | 40,523 | | | | 3 | 8 | 2.435 | 6.997 | 4.563 | 32,638 | 5 | 2.185 | 4.702 | 2.517 | 153,657 | | | | 4 | 8 | 3.220 | 7.463 | 4.242 | 13,144 | 4 | 1.283 | 3.498 | 2.215 | 16,486 | | | | 5 | 6 | 2.012 | 5.325 | 3.313 | 15,684 | 5 | 2.467 | 4.653 | 2.185 | 20,130 | | | | 6 | 8 | 4.622 | 7.763 | 3.141 | 29,531 | 4 | 1.508 | 3.510 | 2.001 | 95,740 | | | | 7 | 6 | 2.243 | 5.127 | 2.884 | 38,814 | 4 | 1.797 | 3.768 | 1.971 | 51,078 | | | | 8 | 5 | 1.201 | 3.955 | 2.754 | 14,586 | 4 | 1.861 | 3.762 | 1.900 | 16,311 | | | | 9 | 5 | 1.107 | 3.846 | 2.739 | 15,447 | 3 | 1.029 | 2.801 | 1.771 | 15,708 | | | | 10 | 7 | 3.887 | 6.590 | 2.703 | 56,997 | 3 | 0.813 | 2.578 | 1.766 | 9,375 | | |

* Unit of "crashes in five years" (Note: Nobs. = Observed crashes; Np = Predicted crashes). ** Unit of "crashes in three years" (Note: Nobs. = Observed crashes; Np = Predicted crashes).

Fig. 7. Most Frequent Crash Characteristics within Top Ten Motorcycle-Specific High-Crash Urban Multilane Segments.

was observed on road segments with right shoulder widths less than 3 ft and greater than 9 ft).

It is important to note that the findings from the motorcycle-specific SPFs along urban segments in this study are specifically based on motorcycle crashes in Kentucky. The study results can be transferable to other states with similar motorcycle crash and traffic characteristics/ demographics as those in Kentucky. To build upon this study, future studies can compare the SPF model results along urban segment facilities in other states, which would help assess how these study findings can be transferred or generalized. Other potential research avenues include development of motorcycle crash-specific SPFs along other facilities, such as intersections and ramps, as well as along urban segments with raised medians and flushed medians separately (given that enough site and crash sample sizes exist).

CRediT authorship contribution statement

Bharat Kumar Pathivada: Data curation, Formal analysis, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing. Arunabha Banerjee: Data curation, Writing – review & editing. Kirolos Haleem: Conceptualization, Funding acquisition, Validation, Writing – original draft, Writing – review & editing.

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.

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