Temporal and out-of-sample prediction analysis of motorcyclists injury severities

Abstract

Motorcycle crashes represent one of the most severe threats to road safety, with disproportionately high rates of fatalities and injuries compared to other road users. This study investigates the factors influencing motorcyclists’ injury severities in single-vehicle (SV) and multi-vehicle (MV) crashes, using the United Kingdom motorcycle crash data from 2016 to 2020. Motorcyclist injuries are categorized into minor, severe, and fatal. A random parameters multinomial logit model with a heterogeneity approach in means and variances is applied to model injury severities, addressing multiple layers of unobserved heterogeneities. To assess the temporal instability of significant factors, a series of likelihood ratio tests is conducted. The findings reveal transferability between SV and MV crashes, with significant temporal instability over the five years. The findings reveal substantial differences in determinants of SV and MV crashes: for example, motorcyclists aged 25–55 years involved in SV crashes had a 0.0292 higher probability of fatal injury, while elderly non-motorcycle drivers (over 65 years) significantly increased motorcyclists’ likelihood of sustaining fatal injuries in MV crashes. The out-of-sample prediction simulation highlights substantial differences in injury severity probabilities across accident types (SV and MV) and over time. This research underscores the importance of considering SV and MV crash transferability and temporal instability to capture unobserved effects influencing motorcyclist injury severity. The statistically significant variances between SV and MV crash injury severity models offer insights for distinct policy interventions targeting SV and MV motorcycle rider safety.

Introduction

The number of casualties from motorcycle crashes is on the rise globally. In 2016, motorcyclists accounted for nearly 28% of the 1.35 million traffic crash deaths¹. In the UK, motorcycle collision casualties surged by 16%². In the US, motorcyclists’ fatality rate per vehicle-miles-traveled is almost 27 times higher than that of passenger-car occupants³. A similar disparity is observed in the UK, where motorcyclists’ fatality rate per mile traveled is approximately fifty times higher than that of car drivers². Therefore, thoroughly investigating the interrelated determinants of motorcyclists’ crash-injury severities is crucial for devising effective measures to enhance motorcycle safety.

Numerous studies have examined the effects of multiple factors on injury severities of motorcyclists, including rider and vehicle attributes, roadway and environmental conditions, helmet usage, alcohol involvement and other related factors^{4,5,6,7,8,9,10,11}. Nevertheless, recent research focuses mainly on the effects of motorcyclists, neglecting other potential factors like elements of drivers and vehicles that collide with motorcycles. In addition to the individual attributes of motorcyclists, non-motorcyclist-related characteristics tend to influence the severity of injuries.

In addition, for the majority of research related to motorcycle crashes, the injury severities stemming from single-vehicle (SV) and multi-vehicle (MV) crashes have been either studied as a whole or regarded as an explanatory factor^11,12,13. Consequently, it is difficult to distinguish influential factors specifically for SV and MV motorcycle crashes. However, it is essential to do so because the mechanism of causing casualties is highly likely to be different if motorcycles crash with motor vehicles or other fixed objects. To the best of the authors’ knowledge, there exists limited studies within motorcycle crash analysis that distinctly differentiate between SV and MV crashes^14,15,16. Yet, traditional logit and probit models applied in these studies assume fixed estimated parameters for all observations, which could potentially result in biased parameter estimates or inaccurate inferences and conclusions¹⁷. To accommodate multiple layers of unobserved heterogeneities, we are motivated to delineate the analysis of injury severity between SV and MV crashes using random parameters in the means and variances heterogeneity approach^5,9,18. Such approach has been widely utilized because of its superiority in interpreting unobserved heterogeneity that may potentially cause biased parameter estimates^19,20,21,22.

Temporal instability has garnered significant attention from researchers. For instance, temporal issues arising from potential changes in riding experience, motorcycle performance, macroeconomic conditions, interactions with other road users, and variations in riders’ behaviors and skills over time have been identified⁵. Additionally, substantial temporal variation was highlighted in the marginal effects of factors influencing the injury severity of motorcyclists⁸. It was comprehensively discussed that neglecting such instability can lead to inaccurate estimation results, incorrect findings, and potentially counterproductive safety measures²³. Therefore, it is crucial to investigate temporal instability as a source of unobserved heterogeneity in the analysis of motorcycle crash injury severities.

Beyond employing pairwise likelihood ratio tests to evaluate how a model formulated using data from one period fits data from another time²⁴, recent investigations underscore the efficacy of out-of-sample prediction in discerning temporal instability^{25,26,27,28,29}. Out-of-sample projections calculate probability differences to explicitly reveal the non-transferability of parameters estimated through different categorical grouping datasets.

To comprehensively address the challenges and concerns above, this study makes three distinct contributions:

• (1) It rigorously examines the determinants of injury severities for motorcyclists in both SV and MV crashes, allowing for a direct comparison of transferability across crash types.

• (2) It extends prior work by jointly modeling multi-layer heterogeneity in both means and variances within the random parameters multinomial logit framework, thereby capturing unobserved effects more comprehensively than fixed-parameter or variance-only approaches.

• (3) It uses the likelihood ratio tests and out-of-sample simulations to systematically examine the temporal instability of key factors over a five-year UK crash dataset. These methodological and empirical contributions enable policymakers and related agencies to develop more targeted and generalizable countermeasures to reduce the severity of motorcyclist injuries.

The rest of this paper is structured as follows, indicated in Fig. 1. Section 2 presents a comprehensive literature review on the injury severities associated with motorcycle-involved crashes. Section 3 describes the data and the methodological framework. Section 3 explores the temporal instability and non-transferability, conducted using likelihood ratio tests. Section 4 presents the analysis and discussion of the estimated results, followed by the study conclusions and limitations in Sect. 5.

Fig. 1

Flow chart of current study.

Literature review

A comprehensive review of the existing literature focused on the injury severity resulting from motorcycle crashes is presented in this section. Initially, the key findings from studies that explore determinants of injury severity in such crashes are summarized. Then, an overview of the methodological paradigms used in the literature.

Influencing factors

Significantly, recent scholarly endeavors have undertaken a comprehensive analysis of the determinants influencing injury severity in motorcycle collisions^5,10,11. Nevertheless, the literature reviews above were presented in terms of the motorcyclist perspective, like features of motorcycles, demographic attributes and driving behaviors. As reported, the related factors concerning the driver and vehicle were confirmed to determine the behaviors of another driver involved in the same collision³⁰. Considering the SV crashes (hitting fixed objects) and MV crashes (collisions with other motor vehicles), the demographic attributes, behaviors and related elements of other vehicles have not been included. Thus, we summarized the differences in determinants between SV and two-vehicle crashes, along with the associated attributes of involved vehicles, in this part.

Motorcyclist and non-motorcycle driver attributes

Gender markedly influences the injury severities sustained by motorcyclists, with evident distinctions between SV and MV crashes. Concerning MV motorcycle crashes, it is found the male motorcyclists exhibit a higher risk of sustaining severe injuries and fatalities^31,32, while those female motorcyclists tend to suffer from severe injuries¹⁸. Regarding SV motorcycle crashes, it has been revealed that female motorcyclists are 20% more likely to be injured compared with male motorcyclists¹⁴. Similarly, it is also stated that female motorcyclists tend to suffer from severe injuries^15,33.

Regarding age attributes, many previous studies have yielded consistent results that the motorcyclists’ injury severities increased with age^14,32,34. In the MV motorcycle crashes, it is found that motorcyclists over 60 years old tend to sustain severe injuries⁵. Motorcyclists over 50 years old are more likely to be involved in fatalities^8,19. Moreover, motorcyclist age is observed to have the most significant effects on SV crashes: a 1% increase in age causes a 1.1% increase in fatality likelihood compared with MV motorcycle crashes¹⁵. Otherwise, three age groups (under 30, 30–49, and 50 and older) were analyzed for their impact on motorcyclists involved in SV crashes⁹. In addition, teenage motorists (up to 19 years old) face a heightened risk of fatal or serious injuries in angle-perpendicular crashes³⁴. Driver characteristics (gender, age, or alcohol drinking) have no significance in affecting the injury severities of motorcyclists¹⁸.

Moreover, risky behaviors like speeding^12,35,36,37, and alcohol involvement increase the injury severities in motorcycle crashes^12,15,38,39, Specifically, alcohol drinking increases the likelihood of male motorcyclists getting incapacitating injury and fatal injury by 21.3% and 58.9%, respectively¹⁵. Helmet utilization significantly reduces the probability of sustaining fatal or incapacitating injuries during motorcycle crashes^12,32,39. However, it is worth noting that helmeted riders tend to be fatally injured when hitting fixed objects, which could be explained in at least three ways⁴⁰. First, the physiological factors might be the key elements related to the increased fatal injury likelihood of helmeted motorcyclists hitting fixed objects. Second, helmeted motorcyclists are more likely to ride recklessly due to the sense of security gained from the helmets. Thirdly, motorcyclists who do not wear helmets may possess superior riding skills, potentially making them less susceptible to severe injuries in hitting-object crashes.

Motorcycle and non-motorcycle vehicle characteristics

Motorcycle crashes involving larger engine capacities have been consistently correlated with an elevated risk of more severe injuries^6,31,32,40.

Motorcycle age has a statistically significant correlation with injury severity. Particularly, newer motorcycle (less than 5 years) was positively related to no injury proportion in motorcycle crashes¹⁴. Conversely, when a motorcycle’s age ranges between 11 and 20 years, there’s a 2.7% heightened likelihood of the motorcyclist sustaining a KAB injury severity⁴¹. In the classification schema for injury severity in vehicular incidents, the categories are delineated as follows: Type K denotes fatal injuries, Type A represents incapacitating injuries, Type B indicates non-incapacitating injuries, Type C signifies potential injuries, and Type O corresponds to instances with no injury.

Roadway and environmental conditions

Rural roads are positively linked to higher injury levels^11,33. The injury severities in motorcycle crashes on urban roads. The effects of helmet-wearing on the injury levels of rural motorcyclists⁴². A comparative analysis of the injury severities in urban and rural motorcycle crashes, and considerable differences were found in the contributing factors affecting the injury severities¹⁰. The complicated environment in intersection area was positively related to the severities of SV motorcycle crashes. Recently, the complicated environment in the intersection areas made drivers of motor vehicles less likely to notice the motorcycles, causing more severe outcomes in two-vehicle involving motorcycles and other motor vehicles^8,11,13,16.

Wet surfaces have been associated with a heightened risk of motorcycle crashes without injuries^12,40. Conversely, dry pavements appear to elevate the risk of fatal or severe injuries resulting from motorcycle crashes^6,32,33. A direct correlation exists between higher speed limits and the severity of injuries sustained in motorcycle crashes, as evidenced by numerous studies^34,35,40.

Adverse weather conditions such as fog, rain, and snow have been reported to increase the risk for minor or non-injurious SV motorcycle crashes¹⁵. On the contrary, these conditions are highly associated with fatal and severe injury likelihood in motorcycle crashes. Clear weather, meanwhile, has been linked to a greater probability of severe injuries in motorcycle crashes^34,35,36, while the majority of rural motorcycle crashes under clear weather conditions result in non-fatal outcomes³⁸.

Daylight conditions are captured to amplify the severity of motorcycle-related injuries^5,15,43, but seemingly reduce the risk of fatal injury in motorcycle crashes^9,16,18. In contrast, conditions of darkness, especially in the absence of streetlights, significantly enhance the probability of severe injuries^{11,34,35,36,38}.

Crash characteristics

Fixed-object collisions were observed to increase the risk of fatality and incapacitating injury in motorcycle crashes^6,14,15. The motorcyclists involved in MV crashes are major safety concerns, showing varied crash features that differ considerably from those in SV crashes¹⁴. It should be noted that the type of vehicles that collided with the motorcycles significantly affected the injury severities of the motorcyclists. Specifically, hitting passenger cars is highly related to fatal or major injury severity of motorcycle crashes^11,18,32. Likewise, the involvement of trucks increased the fatal injury likelihood^12,16,44. A collision with a pick-up truck causes a lower no-injury likelihood by 4.7%¹⁸.

Head-on collisions greatly increased the fatality likelihood^7,14, while rear-end crashes tended to increase the minor injury likelihood^10,18.

Temporal characteristics

The time when accidents happen is demonstrated as a critical factor associated with the resulting injury severities. For instance, riding at midnight and early morning hours tends to increase the risk of serious injury^34,35,36, and motorcycle crashes during peak hours increase the fatal risk^13,20,44. A distinct pattern emerges during weekends, where motorcycle-related incidents correlate with severe injury severities¹². The SV crashes in April were 111% more likely to result in a fatality, while MV crashes in April were 64% less likely to result in a fatality compared to SV crashes¹⁴.

Methodological approaches

In the realm of modeling motorcyclist injury severities, the multinomial logit model framework has been extensively employed^12,13,40. However, a limitation intrinsic to fixed parameter models is their assumption of consistent parameter estimates across all observations, which may lead to potential biases in these estimates and result in inaccurate inferences due to the presence of unobserved heterogeneities¹⁷. To address this concern, various modeling approaches have been proposed in recent studies, including the random parameters¹⁸, latent class models^7,16,33.

Nevertheless, many of these studies operating on the random parameters approach assume a distribution of random parameters that is independent^17,45,46. Consequently, they often neglect the potential influence of explanatory factors on individual parameter estimations.

To address the aforementioned issues, this study employs a random parameter approach with heterogeneity in means and variances, which is adept at capturing unobserved heterogeneity at multiple levels⁴⁷. Recent research about motorcycle injury severities analyzed by combing SV and MV crashes or taking these two crash types as independent variables using random parameters with heterogeneity in means and variances^5,6,9,20. Yet, the existing literature has seldom examined the differences between SV and MV motorcycle crashes based on random parameters with heterogeneity in means and variances within a unified spatiotemporal dimension. As a novel contribution, this research implements a suite of random parameter logit models, incorporating heterogeneity in both means and variances.

To better contextualize the methodological advances in motorcycle crash injury severity analysis, Table 1 summarizes representative studies employing logit-based modeling approaches. Early applications primarily relied on fixed-parameter multinomial logit models, which did not account for unobserved heterogeneity. Subsequent research introduced random parameter logit models to allow variation across observations, and later latent class approaches to capture class-specific differences. More recent studies emphasized the importance of modeling heterogeneity not only in means but also in variances. Building on this progression, the present study employs a random parameters multinomial logit framework with heterogeneity in both means and variances, while also incorporating temporal instability tests to assess the transferability of model results across years.

Table 1 Summary of previous methodological approaches in motorcycle crash injury severity analysis.

Study methodology

Data description

The motorcycle crashes that occurred in the UK between 2016 and 2020 were collected in the official STATS19 dataset². Each record in this comprehensive dataset provides detailed information about the crash, including exact temporal data (year, month, date, hour) of the event, weather conditions, roadway, speed limits, type of road, and demographic details of the involved rider/driver, such as age and gender.

As visualized in Fig. 2, there is a clear depiction of injury severity distribution across SV and MV motorcycle crashes from 2016 to 2020. The analysis covers 2016–2020, as more recent STATS19 data were not yet fully released and quality-checked at the time of the study. The data contains 18,081 completed observations, of which 87.6% were MV crashes and 12.4% were SV crashes. Several critical patterns emerge. First, MV crashes consistently outnumber SV crashes, reflecting the greater exposure and interaction complexity in multi-vehicle environments. Second, the proportion of severe and fatal injuries is relatively higher in SV crashes compared to MV crashes, highlighting the increased vulnerability of riders when no other vehicle is involved. Third, the year-to-year variations in severity distribution suggest potential temporal instability, which provides motivation for the modeling framework applied later in this study. These descriptive findings not only illustrate the empirical foundation of the analysis but also justify the inclusion of SV/MV differentiation and temporal effects in the study design.

Fig. 2

SV and MV motorcycle crash injury severity over the years: 2016 − 2020.

The ‘injury-severity level’ is applied as the dependent variable in our study. Following the STATS19 injury classification, minor injury, severe injury, and fatal injury are considered⁴⁸. In terms of the distribution of observed injury severities, approximately 34.7% and 68.0% of minor injuries occurred in SV and MV crashes, respectively. Notably, the proportions of severe and fatal injuries are markedly elevated in SV motorcycle crashes (56.7% and 8.6%, respectively) in comparison to MV crashes (30.0% and 2.0%, respectively). Owing to these disparities, injury severities are modeled distinctly for SV and MV motorcycle crashes.

Table A1 and Table A2 present the descriptive statistics of the key variables in the proposed models for both SV and MV motorcycle crashes.

Analytical model

Although injury severity is an ordinal outcome, the multinomial logit framework was adopted because ordered models (e.g., ordered logit or probit) impose the proportional odds assumption, which is often violated in crash data. The multinomial logit model relaxes this constraint and allows the effects of explanatory factors to vary freely across different severity levels. Moreover, by incorporating random parameters with heterogeneity in means and variances, the chosen framework provides greater flexibility in capturing unobserved heterogeneity than conventional ordered models, making it more suitable for the present analysis.

Buiding on this rationale, the present research develops distinct models to elucidate the injury severities experienced by motorcyclists in both SV and MV crashes. These models employ the random parameters logit methodology, specifically incorporating heterogeneity in both means and variances, denoted as the RPLHMV approach. The injury-severity function $\:{Y}_{in}$ determines the motorcyclist injury-severity level $\:i$ in crash $\:n$, and is formulated as follows^24,49,50

$$\:{Y}_{in}={\varvec{\upbeta\:}}_{\mathbf{i}}{\mathbf{X}}_{\mathbf{i}\mathbf{n}}+{\epsilon\:}_{in}$$

(1)

where $\:\:{\varvec{X}}_{\varvec{i}\varvec{n}}$represent the vectors of explanatory variables that determine motorcyclist-injury severity level $\:i$ (minor injury - MI, severe injury – SI, or fatal injury - FI) in crash $\:n$. The vector $\:{\varvec{\beta\:}}_{\varvec{i}}$ represent the corresponding parameters. Additionally, $\:{\epsilon\:}_{in}$ signifies the error term that is assumed to follow an independent and identical distribution with zero mean and variance σ². To encompass latent heterogeneity, this study employed random parameters with heterogeneity in means and variances^17,51:

$$\:{\beta\:}_{in}={{\upbeta\:}}_{\text{i}}+{\varvec{\Theta\:}}_{\mathbf{i}\mathbf{n}}{\mathbf{Z}}_{\mathbf{i}\mathbf{n}}+{\sigma\:}_{in}EXP\left({\varvec{\uppsi\:}}_{\mathbf{i}\mathbf{n}}{\mathbf{W}}_{\mathbf{i}\mathbf{n}}\right)+{\upsilon\:}_{in}\:\:$$

(2)

where $\:{\beta\:}_{i}$ represent the average parameter estimate encompassing all crashes, the vector $\:{\varvec{Z}}_{\varvec{i}\varvec{n}}$ delineate explanatory variables that influence the mean, $\:{\varvec{\varTheta\:}}_{\varvec{i}\varvec{n}}$ are the corresponding estimable vectors. Additionally, $\:{\:\varvec{W}}_{\varvec{i}\varvec{n}}$ are vectors that elucidate the explanatory variables introducing heterogeneity in variances. The variance denoted by $\:{\sigma\:}_{in}$, and its associated vector of estimable parameters, $\:{\varvec{\psi\:}}_{\varvec{i}\varvec{n}}\:$, further contribute to the model. The term $\:{\upsilon\:}_{in}\:$acts as a disturbance factor within the model. Then, the outcome possibility of the RPLHMV model formulation can be expressed as²⁴

$$\:{P}_{n}\left(i\right|\phi\:)=\int\:\frac{\text{exp}\left({\varvec{\upbeta\:}}_{\mathbf{i}}{\mathbf{X}}_{\mathbf{i}\mathbf{n}}\right)}{\sum\:_{i\in\:I}\text{exp}\left({\varvec{\upbeta\:}}_{\mathbf{i}}{\mathbf{X}}_{\mathbf{i}\mathbf{n}}\right)}f\left({\varvec{\upbeta\:}}_{\mathbf{i}}\right|\varvec{\upphi\:})d{\varvec{\upbeta\:}}_{\mathbf{i}}$$

(3)

where$\:\:{P}_{n}\left(i\right|\phi\:)$ denotes the probability associated with a given injury severity level $\:i$, conditional upon $\:f\left({\varvec{\beta\:}}_{\varvec{i}}\right|\varvec{\phi\:})$. Here, $\:f\left({\varvec{\beta\:}}_{\varvec{i}}\right|\varvec{\phi\:})$ functions as the density function of $\:{\beta\:}_{i}$, where $\:\phi\:$ refers to a vector of parameters encompassing both means and variances.

The RPLHMV model is estimated with a simulated maximum likelihood method. To ensure robustness and stability in parameter estimates, a total of 1,000 Halton draws are implemented⁵². In terms of the distribution of the random parameters, the normal distribution is used to achieve the best goodness-of-fit^49,53,54.

While a comprehensive set of variables was initially included to capture potential determinants, the interpretation is exploratory rather than causal, consistent with prior crash severity modeling practices. This approach aims to maximize coverage of possible influencing factors, while acknowledging that causal inference is beyond the scope of the present analysis.

Likelihood ratio tests for transferability and Temporal stability

An extensive number of research efforts indicates that the factors determining injury severity can change over time^5,47,53, and that the factors determining injury severity might vary across different crash types^20,47. Thus, likelihood ratio tests are conducted for differences between SV and MV motorcycle crashes, followed by those for temporal instability.

In the beginning, for each year $\:t$ (2016, 2017, 2018, 2019, 2020), transferability tests were estimated to test the model instability across SV and MV motorcycle crashes, as follows⁴⁷

$$\:{\chi\:}_{g}^{2}=-2[LL\left({\beta\:}_{Full,t}\right)-LL\left({\beta\:}_{Single,t}\right)-LL\left({\beta\:}_{Multi,t}\right)]$$

(4)

where $\:LL\left({\beta\:}_{Full,t}\right)$ denotes the log-likelihood upon convergence of the model derived from the comprehensive containing the SV and MV motorcycle crashes in the year $\:t$. Conversely, $\:LL\left({\beta\:}_{Single,t}\right)$ and ($\:LL\left({\beta\:}_{Multi,t}\right)$ indicate the log-likelihood at the convergence for models specific to SV and MV motorcycle models in year $\:t$. It is pivotal to acknowledge that the degrees of freedom equate to the aggregate of statistically significant parameters in each separate model, discounted by the number of such parameters in the combined model²⁴. For the years 2016, 2017, 2018, 2019, and 2020, the random parameter model estimates give $\:{\chi\:}^{2}$ values of 56.32, 84.32, 124.62, 63.62 and 41.62 with 16, 13, 25, 18 and 13 degrees of freedom, respectively. These empirical results compellingly suggest that the null hypothesis, postulating the equivalency of SV and MV motorcycle models, can be refuted with a confidence exceeding 99.99%. These findings indicated that the null hypothesis that SV and MV motorcycle models are the same should be rejected with > 99.99% confidence.

Following this, a bifurcated series of likelihood ratio tests is conducted to probe the temporal variability in the impacts of determinants on injury severity outcomes from motorcycle crashes. The pairwise tests are geared towards juxtaposing models associated with two distinct years, aiming to discern the stability and potential transferability of the estimated parameters across these temporal milestones. The likelihood ratio chi-square test statistic, $\:{\chi\:}_{{t}_{1}}^{2}$, is given by²⁴

$$\:{\chi\:}_{{t}_{1}}^{2}=-2[LL\left({\beta\:}_{{y}_{1}{y}_{2}}\right)-LL\left({\beta\:}_{{y}_{1}}\right)]$$

(5)

where $\:LL\left({\beta\:}_{{y}_{1}{y}_{2}}\right)$ denotes the log-likelihood at the convergence of the model estimating parameters from subgroup year $\:{y}_{2}$ while using data from subgroup year $\:{y}_{1}$, and $\:LL\left({\beta\:}_{{y}_{1}}\right)$ denotes the log-likelihood at the convergence of the model using the data subgroup $\:{y}_{1}$. This test is also conducted with year-$\:{y}_{1}$ subgroup and year-$\:{y}_{2}$ subgroup being reversed to obtain two test results for each model. Results pertinent to these tests, ascertaining the consistency of parameter stability across biennial intervals, are elucidated in Tables 2 and 3. A critical observation from these tables reveals that the null hypothesis, postulating parameter stability across the specified time frames, can be dismissed with a confidence level exceeding 99%. This suggests a pronounced temporal variability in the estimated parameters for the years spanning 2016 to 2020.

Table 2 Likelihood ratio test outcomes for SV motorcycle models: analysis across Temporal intervals using random parameters (degrees of freedom and confidence levels noted).

Table 3 Likelihood ratio test outcomes for MV motorcycle models: analysis across Temporal intervals using random parameters (degrees of freedom and confidence levels noted).

Conclusively, subsequent pairwise tests have been conducted to assess the temporal stability between the integrated model and its constituent models⁵:

$$\:{\chi\:}_{{t}_{2}}^{2}=-2[LL\left({\beta\:}_{2016-2020,g}\right)-{\sum\:}_{2016}^{2020}{LL(\beta\:}_{t,g})]$$

(6)

where $\:LL\left({\beta\:}_{2016-2020,g}\right)$ denotes the log-likelihood at the convergence of the model for crash group $\:g$ (SV and MV) in the five years (2016–2020), while $\:LL\left({\beta\:}_{t,g}\right)$ expresses the log-likelihood at the convergence of the models for crash group $\:g$ using one specific year $\:t$ data. The model estimate gained from the test gave an $\:{\chi\:}^{2}$ values of 272.81 and 349.67 with 42 and 85 degrees of freedom, respectively, for SV and MV motorcycle crashes based on random parameters models. The modeling methodology posits a null hypothesis: the stability of statistically significant parameters within discrete SV and MV motorcycle models can be rejected at a 99.99% confidence level.

Notably, year-to-year variations in significance likely reflect changes in behavioral patterns, enforcement, or contextual traffic conditions rather than statistical artifacts, as confirmed by correlation checks. Accordingly, the interpretations remain exploratory and should be viewed as indicative rather than causal, consistent with prior temporal instability studies.

Model results discussion

To assess the injury severities stemming from motorcycle-involved incidents, we employ the random parameters multinomial logit method, incorporating heterogeneity in both means and variances. The efficacy and appropriateness of the models are assessed using a trio of statistical criteria: the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), the McFadden R-Squared, and the log-likelihood value upon convergence. All model estimations were conducted at a 90% confidence level, a threshold commonly adopted in exploratory traffic safety studies to balance statistical rigor with the need to capture meaningful effects under high variability. Akaike Information Criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Bayesian Information Criterion (BIC) is employed to choose the best model among multiple candidate models, particularly when balancing between model complexity and data fitting. McFadden R-squared is used to compare the log likelihood of the full model (L) to the log likelihood of the model with just the intercept (L0, the null model). Log-likelihood is typically used to derive the maximum likelihood estimator of the parameter. An optimal model estimation is suggested by lower AIC values, augmented McFadden R-Squared figures, and elevated log-likelihood values at the point of convergence²⁴. As the goodness-of-fit measures indicate in Tables A3 and A4, the applied modeling approach statistically outperforms the fixed parameter multinomial logit approach and the random parameters multinomial logit approach for all analysis scenarios. The discussion of the model estimation results is presented below, while the corresponding marginal effects are shown in Tables A5 and A6.

Beyond confirming the statistical differences between SV and MV crashes, our findings highlight distinct underlying mechanisms. SV crashes are more strongly influenced by rider-related vulnerabilities, such as age and maneuvering behavior, while MV crashes are shaped by the characteristics of other involved drivers and roadway environments, such as male or elderly drivers and speed limits. These distinctions indicate that SV interventions should prioritize rider protection and behavioral training, whereas MV interventions should emphasize driver awareness, enforcement, and infrastructure measures.

Heterogeneity in means and variances

In the SV crashes, random parameter variables were identified in the models only for 2016 and 2019, with no such variables detected in other years. In the 2016 model, the only random parameter was the constant term associated with severe injury. In contrast, the 2019 model featured one statistically significant random parameter, the “straight indicator,” which indicated a decreased likelihood of sustaining minor injuries for approximately 79.0% of the observations.

The model fit results for MV crashes are presented in Table A4. In the 2016 model, two variables were statistically significant as random parameters: the constant term and the indicator for younger motorcyclists (under 25 years old). The constant term linked to severe injury exhibited marked heterogeneity, particularly for incidents on single carriageways. The young motorcyclist indicator showed a dichotomy under minor injury outcomes: 83.8% of accidents indicated an increased probability of minor injuries, while the remaining showed a decrease. Notably, the variance of this indicator in minor injury severity was influenced by the age of the vehicle involved, specifically those not between 6 and 11 years old, leading to a more uniform distribution of the betas by broadening the parameter density function’s tail.

In the 2017 model, only the constant term associated with severe injury was recognized as a random parameter, with no statistically significant heterogeneity observed in its mean and variance. The 2018 model identified one statistically significant random parameter: the 30-mph speed limit indicator, which suggested a reduced probability of severe injuries for 92.3% of the observations. The presence of the single carriageway, urban locale, and straight path indicators increased the average value of the 30-mph speed limit indicator, thereby heightening the likelihood of severe injuries.

For the 2019 model, two statistically significant random parameters were found: the constant term and the Wednesday indicator. The constant term associated with minor injuries displayed variance affected by the age of the motorized vehicle, particularly if the vehicle was younger than 6 years or older than 11 years. The Wednesday indicator was significant for minor injuries, with 88.0% of crashes showing an increased probability of minor injury. This suggests that mid-week commuting patterns or fatigue accumulation may influence rider risk. In practice, such findings highlight the value of targeted mid-week enforcement campaigns and awareness initiatives. The variance of the Wednesday indicator was further influenced by fine weather conditions, reflecting lower variability. In the 2020 model, the only random parameter identified was the constant term specific to severe injury.

These statistically significant variances reinforce that the impacts of key factors on motorcyclist injury severity are not uniform across all crashes. Instead, their influence varies depending on rider, vehicle, and environmental contexts, underscoring the importance of accommodating unobserved heterogeneity. For example, variance in rider-related parameters likely reflects differences in individual risk perception and protective behavior, while roadway-related variances may be shaped by enforcement intensity or traffic composition. Hence, the identification of significant variances provides not only statistical improvements in model fit but also meaningful behavioral and policy insights, highlighting contexts where targeted interventions may be most effective.

Rider-related characteristics

Among rider-associated variables, certain demographics, such as male riders, young riders (below 25 years old), and middle-aged riders (25 to 55 years old) from urban areas, exhibit statistically significant impacts on SV and MV motorcycle crashes. Conversely, riders aged over 55 years show statistical significance only in the MV crash model.

Specifically, the male rider variable is significant in MV motorcycle models for 2017, 2018, and 2020, and in the 2020 model for SV motorcycle crashes. This variable decreases the probability of minor injuries but increases the likelihood of severe and fatal injuries. These findings align with previous studies^32,36, suggesting that male motorcyclists are more prone to aggressive driving than their female counterparts¹¹. This underscores the necessity of enhancing safety education and imposing effective penalties.

In MV motorcycle crashes, the young motorcyclist variable shows significant temporal heterogeneities. The probability of severe injuries increases in the 2016 model, while the likelihood of fatalities decreases in the 2017 model. Additionally, the probability of minor injuries rises in both the 2018 and 2020 models. For SV crashes, the young motorcyclist variable is significant in the 2016, 2019, and 2020 models, increasing the probability of minor injuries by 0.0287 − 0.0208. The middle-aged motorcyclist variable (25 to 55 years old) positively influences the likelihood of minor accidents in MV crashes, while it increases the probability of fatal injuries in SV crashes by 0.0292 in the 2018 data model. While some of these estimated effects, such as the marginal increases of 0.0208–0.0287 in the probability of minor injuries, are statistically significant but small in magnitude, they should be interpreted as supplementary evidence. In contrast, more substantive effects, such as the elevated fatal risk among middle-aged riders in SV crashes, provide stronger guidance for practical interventions.

The elder motorcyclist variable positively influences the probability of fatal injuries in the 2016 model. These findings indicate that injury severity tends to increase with the rider’s age, likely due to physiological degeneration, such as reduced physical capabilities and slower reaction times^14,15. It is also noted that rider age has the most significant impact in SV crashes¹⁵.

Furthermore, results from the SV model of 2018 and the MV model of 2016 suggest that urban motorcyclists are more likely to experience minor injuries, but less likely to be involved in fatal accidents.

These results underscore the importance of tailoring safety interventions to specific rider groups. Male riders require stricter enforcement and targeted education to address aggressive riding behaviors. Younger riders would benefit from graduated licensing systems and advanced training programs, while older riders may require refresher courses and age-sensitive infrastructure design to account for slower reaction times. Urban-focused measures, such as motorcycle-exclusive lanes, could further reduce minor crash risks, whereas improving emergency response capacity in rural areas remains critical to lowering fatalities.

Driver-related characteristics

This section examines the impact of non-motorcycle drivers’ characteristics on motorcyclists’ injury severity. According to the model estimation results, non-motorcycle drivers who are male, young (under 25 years old), or elderly (over 65 years old) exhibit statistically significant relationships with the injury severities of motorcyclists. Specifically, male drivers are less likely to sustain minor injuries but more likely to be involved in severe and fatal accidents. This finding suggests that male drivers pose greater threats to other road users¹⁵.

Regarding age, the models indicate that young drivers (under 25 years old) and elderly drivers (over 65 years old) increase the likelihood of accidents resulting in minor injuries, supported by the 2019 and 2018 models, respectively. Additionally, the 2016 model shows that elderly drivers also increase the probability of fatal accidents, suggesting that motorcyclists are more likely to sustain fatal injuries in collisions with vehicles driven by older individuals. These insights align with recent studies³⁴, which highlights the risks posed by elderly drivers due to their diminished physical capabilities and delayed reaction times in critical situations.

Male and young drivers require stricter enforcement and enhanced driver education programs to mitigate risky driving behaviors that endanger motorcyclists. For elderly drivers, periodic driving assessments and the adoption of advanced driver-assistance technologies may reduce crash severity outcomes. Collectively, these measures could substantially improve motorcycle safety in mixed traffic environments.

Roadway and environmental conditions

Among the road and environment-related variables, weather, light conditions, speed limits, and road types significantly impact the severity of SV and MV accidents. However, the road grade variable significantly influences only MV accidents.

For MV accidents, the 2017 and 2019 models indicate that clear weather conditions reduce the probability of minor injuries by 0.0191 and 0.0220, respectively, whereas the 2018 model suggests an increased probability of severe crashes by 0.0026. Previous studies support this finding^34,35,36. Motorcyclists may ride faster and more aggressively with lower vigilance in clear weather compared to adverse conditions (e.g., rain, snow, fog), thereby increasing the likelihood of severe injuries in accidents³².

The likelihood of fatal accidents for motorcyclists increases when driving in darkness on unlit streets (2017 model). Conversely, the 2019 model indicates a reduced probability of fatal accidents during daylight³², who highlighted the crucial role of visibility. Human perception and response capabilities are diminished at night due to physiological limits. Therefore, effective illumination systems should be implemented in areas frequently used by motorcyclists to prevent severe nighttime accidents.

Speed limits also play a crucial role in accident severity. The 2016 and 2020 models show that road sections with a 30 mph speed limit increase the probability of minor injuries, while the 2017, 2019, and 2020 models indicate a reduced probability of severe or fatal injuries at this speed limit. Conversely, a 60 mph speed limit reduces the likelihood of minor injuries (2019 model) but significantly increases the probability of fatal accidents (2020 model). This finding aligns with previous studies^18,34,35,36, suggesting that higher speed limits exacerbate the severity of motorcycle-involved accidents. Interestingly, the 2018 SV crash model indicates a reduced likelihood of fatal accidents under a 60 mph speed limit, likely due to motorcyclists’ ability to slow down when colliding with a static object, which results in lower momentum. However, collisions involving other motor vehicles at this speed tend to result in more severe and fatal crashes.

Instead of the number of lanes, the presence of a central reservation significantly affects injury severities. The 2018 model shows that single carriageways (without separation from oncoming traffic) reduce the likelihood of minor injuries in MV crashes. However, the likelihood of severe (2020 model) and fatal accidents (2016, 2019, and 2020 models) increases on single carriageways. The 2016 and 2017 SV accident models imply that the likelihood of fatal injuries is higher on both single and dual carriageways. Notably, the dual carriageway indicator has a higher marginal effect (0.0815) on causing fatal crashes than single carriageways (0.0129), likely due to the physical barriers separating traffic directions. Improper design configurations of traffic barriers, especially their end treatments, may contribute to serious injuries by increasing rollover crash risks⁵⁵. Therefore, road authorities should address these limitations by implementing appropriate measures, such as using blunt and turned-down end terminals for traffic barriers.

The urban area indicator consistently shows across models from 2016 to 2020 that MV accidents in urban areas are more likely to result in minor injuries. This finding may be attributed to slower speeds and the accessibility of medical services within urban⁷.

Motorcycle and non-motorcycle vehicle characteristics

Based on model estimation results, if motorcycles are involved in MV collisions while driving straight prior to the collision, the 2017, 2019, and 2020 models suggest a reduced likelihood of minor accidents by 0.0065–0.0126, but the 2018 model indicates an increased probability of fatal accidents by 0.0134. Similarly, in SV accidents, the 2018 and 2020 models suggest a reduced likelihood of minor injuries if motorcycles collide with non-vehicle objects. Conversely, the 2019 SV accident model indicates that driving straight prior to the collision decreases the likelihood of fatal accidents, as motorcycles can be more easily controlled and decelerated.

In MV accidents, the movement status of the opposing vehicles significantly influences the outcome. Specifically, opposing vehicles driving straight prior to the collision reduce the likelihood of minor accidents (according to the 2016, 2017, and 2018 models) but increase the likelihood of severe and fatal accidents (according to the 2019 and 2020 models), due to the high relative speed between motorcycles and other vehicles.

For MV accidents, riding a new motorcycle (less than 6 years old) increases the likelihood of minor accidents (2020 model) and decreases the likelihood of fatal accidents (2019 model). This pattern is also supported by the 2017 and 2018 SV accident models. The newer motorcycles (less than 5 years old) result in a higher likelihood of no injury in motorcycle crashes¹⁴. Therefore, regular maintenance and inspection of motorcycles, such as checking chains, tires, and turn indicators, are necessary to mitigate unexpected crash risks.

The age of the vehicles involved in collisions significantly impacts the injury severity for motorcyclists. Middle-aged vehicles (6–11 years old) and older vehicles (over 11 years old) reduce the likelihood of minor injuries (2016 model) but increase the likelihood of severe injuries (2016 and 2019 models). Unlike new motorcycles, the 2017 model indicates that new vehicles (less than 6 years old) increase the probability of causing motorcyclist fatalities. This may be due to less experienced drivers or unfamiliarity with new vehicles, coupled with aggressive driving behavior.

Additionally, the type of vehicle involved in the collision significantly affects the injury levels of motorcyclists. For instance, if motorcycles collide with passenger vehicles, the 2017 model shows an increased likelihood of minor and severe accidents, while the 2019 model indicates a decreased likelihood of fatal accidents.

Thus, improving road lighting in high-risk areas, reassessing speed limit policies, and adopting motorcycle-friendly traffic barrier designs could mitigate severe and fatal injuries. Additionally, urban traffic management strategies, such as creating safer intersections and designated motorcycle facilities, may further reduce injury risk for motorcyclists in dense traffic environments.

Temporal-related characteristics

In MV accidents, the 2019 model indicates that the likelihood of minor accidents increases during the morning peak but decreases at night or dawn. Riding motorcycles at night does not increase the likelihood of accidents according to the 2016 and 2020 models; however, the absence of illumination on road sections poses hidden dangers, as previously discussed.

For MV accidents occurring on Mondays, the 2016 model shows a decreased likelihood of minor accidents, while the 2018 model indicates an increased probability of severe accidents. The 2016 and 2019 models suggest that accidents on Thursdays decrease the likelihood of fatal accidents. In SV accidents, the 2019 model suggests that Wednesdays increase the probability of minor accidents. Notably, our study found that Saturdays reduce the likelihood of severe or fatal MV accidents. This finding contradicts previous studies, which may be due to regional differences in lifestyles, driving behaviors, and travel purposes. Further exploration is needed to understand how weekends affect the severity of motorcycle-involved accidents.

Seasonal variations also influence accident severity. In MV accidents, the 2018 model indicates that summer increases the likelihood of minor and severe injuries, consistent with existing studies^{12,20,34,35,36}. However, the 2016 model suggests a reduced likelihood of fatal accidents in summer. For SV accidents, the 2016 model indicates an increased likelihood of minor accidents in winter, whereas spring reduces the probability of fatal accidents. Although lacking yearly data, a 111% increased likelihood of fatalities in single crashes occurring in April, possibly due to motorcyclists reacquainting themselves with riding skills after winter¹⁴. Conversely, April showed a 64% reduced fatality probability in MV crashes. These contradictory findings may arise from differences in the mechanisms of SV and MV crashes. Further research into motorcyclist proficiency, especially after extended periods of inactivity (such as winter), presents a promising avenue for future studies.

Crash-related characteristics

Among MV accidents, crash types significantly influence motorcyclists’ injury severities. Head-on collisions reduce the probability of minor injuries (in 2016, 2017, and 2018) and severe injuries (in 2016 and 2017). Similarly, rear-end collisions decrease the likelihood of minor and severe injuries according to the 2016 model and the 2016 and 2018 models, respectively. However, these findings contrast with existing studies. Chang et al. (2021) argued that the increased energy dissipation from vehicles moving in opposite directions can heighten injury severity. Particularly, sideswipe crashes escalate the severity of injuries in the 2018 model, consistent with previous studies^11,31. This may be due to lateral impacts, indicating inattention to oncoming traffic by at least one driver, thus high-speed collisions in such scenarios are more likely to result in severe injuries.

Heterogeneity is also observed in SV accidents involving different stationary objects. According to model estimations, when motorcycles crash into road signs, the likelihood of minor injuries decreases in the 2019 model, but fatal injuries increase in the 2020 model. This may be due to increased speeding during the COVID-19 pandemic due to reduced traffic volumes⁵⁶, leading to higher crash risks and severity outcomes²⁰. Crashing into roadside trees or bus stops significantly increases the probability of fatal injuries, as shown in the 2017, 2018, 2019, and 2020 models. Additionally, hitting roadside barriers reduces the likelihood of minor injuries according to the 2017 and 2018 models. Collisions with walls or fences decrease the probability of minor injuries in the 2020 model but increase the likelihood of fatal injuries in the 2019 model.

Evaluation of transferability and Temporal instability

The results indicate that the influencing factors of motorcyclists’ injury severity are transferable between SV and MV crashes and are temporally unstable over the five-year study period. To further assess the transferability and temporal variability of influencing factors, this study employs a cross-validation approach. Specifically, it utilizes a SV motorcycle model to forecast MV motorcycle data and leverages parameters from the prior year’s SV/MV model to predict subsequent year injury severity outcomes. Then the prediction accuracy is finally obtained by comparing the difference with the predicted probability of their influencing factors. The cross-validation method described above is called an out-of-sample. It is worth noting that the mean of the random parameters cannot be taken into account when using this method, which leads to biased estimation. See recent studies for more details^25,26,27,28.

Firstly, we used the SV model to predict MV data and used the MV model to predict SV data. The results are shown in Table 4. Of particular note is, when using SV to predict MV crashes, the severe injury predictions are overestimated by 0.0007 only in 2018, and all the other years have a stable difference. It seems that the influence factors of severe injury of motorcyclists in SV motorcycle crashes model can be used to predict MV motorcycle crashes. Our analysis revealed significant variability in prediction precision among individuals. Specifically, the average prediction accuracy balances overestimations and underestimations in individual predictions. Relying solely on the forecast’s mean value to gauge the impact of influencing factors may lead to oversight. To better visualize individual disparities during the forecasting process, we’ve charted a frequency distribution map, highlighting individual prediction accuracies. Refer to the accompanying Figs. 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 for a detailed view.

Table 4 Difference in probabilities by transferability.

Fig. 3

SV motorcycle predicts MV motorcycle crashes in 2016.

Fig. 4

MV motorcycle predicts SV motorcycle crashes in 2016.

Fig. 5

SV motorcycle predict MV motorcycle crashes in 2017.

Fig. 6

MV motorcycle predicts SV motorcycle crashes in 2017.

Fig. 7

SV motorcycle predict MV motorcycle crashes in 2018.

Fig. 8

MV motorcycle predicts SV motorcycle crashes in 2018.

Fig. 9

SV motorcycle predict MV motorcycle crashes in 2019.

Fig. 10

MV motorcycle predicts SV motorcycle crashes in 2019.

Fig. 11

SV motorcycle predict MV motorcycle crashes in 2020.

Fig. 12

MV motorcycle predicts SV motorcycle crashes in 2020.

By contrast, the predictions of minor and fatal injuries show a slightly large difference. Specifically, minor injury predictions are overestimated in 2016, 2017, and 2019 by 0.0002, 0.0005, and 0.0007, respectively, but underestimated in 2018 and 2020 by 0.0013 and 0.0002. Fatal injury predictions were overestimated in 2018 and 2020 by 0.0006 and 0.0002 and underestimated in 2016, 2017, and 2019 by 0.0002, 0.0005, and 0.0008, respectively. When using MV crash models to predict SV injury severity, minor injury predictions are overestimated in 2017, 2018, and 2020 by 0.0003, 0.0005, and 0.0006, respectively, but underestimated in 2016 by 0.0009. Fatal injury predictions were overestimated in 2016, 2017, and 2019 by 0.0027, 0.0002, and 0.0010, respectively, but underestimated in 2018 and 2020 by 0.0005 and 0.0005.

Secondly, we used the previous year’s SV/MV model parameters to predict the following year’s injury severity outcomes. The results are shown in Tables 5 and 6. For SV crashes, we find that the 2016 model underestimated minor injuries in 2018 crashes by 0.0003 and underestimated severe injuries in 2019 crashes by 0.0007. The 2018 model underestimated fatal injuries in 2020 crashes by 0.0042. However, the 2019 model overestimated fatal injuries in 2020 crashes by 0.0013.

Table 5 Difference in probabilities by Temporal instability for SV motorcycle crashes [minor injury - MI, severe injury – SI, or fatal injury - FI].

Table 6 Difference in probabilities by Temporal instability for MV motorcycle crashes [minor injury - MI, severe injury – SI, or fatal injury - FI].

For MV crashes, the 2016 model underestimated fatal injuries in 2019 crashes by 0.0004 and minor injuries in 2020 crashes by 0.0011, while overestimated minor injuries in 2017 crashes by 0.0006. The 2017 model underestimated fatal injury in 2019 crashes by 0.0009 and overestimated severe injury in 2018 crashes by 0.0006. The 2018 model underestimated fatal injury in 2019 m crashes by 0.0009 and overestimated fatal injury in 2020 crashes by 0.0003. The 2019 model overestimated minor injuries in 2020 crashes by 0.0003.

It is worth noting that, similar to the study by Yan et al.²⁹, the predictive deviation observed in this study remains modest when utilizing random parameter models. However, various other scholarly investigations have documented noteworthy instances of both underestimation and overestimation in out-of-sample predictions^22,25.

Concluding remarks

To investigate the mechanism causing different levels of injuries (minor, severe and fatal) in motorcycle-involved crashes for SV and MV crashes, this study estimated random parameter multinomial logit models with heterogeneity in means and variances based on data from the UK during 2016–2020. The analysis examined a series of determinants observed to exert a statistically significant influence on injury outcomes. These determinants encompass rider/driver attributes, vehicle characteristics, roadway conditions, environmental conditions, specific crash details, and temporal considerations. Based on this study, the following comments are offered:

• 1. The employed random parameter multinomial logit model, distinguished by its inherent heterogeneity in means and variances, presents distinct methodological advantages. Firstly, the random parameters logit with heterogeneity in the means and variances model provides a superior statistical fit compared to the traditional lower-order logit model counterparts. Secondly, the approach provides enhanced insights by accommodating the heterogeneity of explanatory variables across observations. By considering factors that influence the means and variances of the parameter density functions of the random parameters, we can more rigorously identify factors that potentially affect the magnitude of a parameter’s effect on injury severity. This results in a more nuanced and comprehensive understanding of the determinants.

• 2. Building on our exhaustive analytical framework, we determined that the mechanisms influencing the severity of injuries in SV and MV motorcycle collisions exhibit distinct differences. Several variables with temporal instability also showed positive effects on the likelihood of fatal injuries in both SV and MV crashes. For instance, data from 2020 shows a notable incidence of single motorcycle crashes involving collisions with bus stops and walls or fences. It is suggested that the visibility of bus stops and roadside walls or fences be improved, and more protective barriers or bollards be installed. Additionally, more fatal injuries occurred in two-vehicle motorcycle crashes when the movement preceding the collision was straight in 2019 and 2020. Enforcing speed limits should be prioritized to mitigate the severity of injuries.

• 3. For SV motorcycle crashes, the results show that motorcyclists between 25 and 55 years old are highly likely to get killed once they are involved in SV motorcycle crashes. Therefore, we must carefully monitor traffic in road sections with more active motorcyclists in this age group to discourage them from riding motorcycles.

• 4. In MV motorcycle crashes, male and elderly drivers who collide with motorcycles pose significant threats to motorcyclists. Therefore, targeted enforcement and education programs for male and elderly drivers are essential. Additionally, higher speed limits have been directly correlated with increased injury severity in motorcycle-involved crashes. To mitigate this risk, motorcyclists frequently traveling on roads with higher speed limits should be required to wear protective gear and maintain greater distances from surrounding vehicles. Furthermore, particular attention should be given to areas prone to side-impact collisions, such as during lane changes when a vehicle might inadvertently strike the side of a motorcycle. It is advisable for manufacturers to incorporate advanced systems like Lane Change Alert with Side Blind Zone Alert into their vehicle designs. However, due to temporal inconsistency, these coefficients should be interpreted cautiously as exploratory rather than definitive, though they still indicate potential value for targeted enforcement and education, to be validated in future research with pooled datasets.

• 5. Exploring potential spatial instability is an intriguing area for future research. Such an investigation would offer a deep understanding of the disparities in motorcycle crash-injury severities across various regions. While temporal instability tests revealed that some effects vary across years, this does not diminish the overall value of the analysis. Instead, these tests highlight which factors remain consistently influential (e.g., rider age and speed-related variables), providing policymakers with reliable targets for intervention. The temporal variations further indicate where adaptive, year-specific safety strategies may be warranted. These implications align with the Safe System framework, emphasizing safer people, vehicles, roads, and speeds, thereby enhancing the policy relevance of this study.

• 6. This study has several limitations. First, the analysis relies solely on police-reported motorcycle crash data from the United Kingdom, which may restrict the generalizability of the findings to other contexts. Second, potential misclassification of injury severities in police records could introduce bias into the results. Finally, unobserved factors such as rider behavior or medical response were not captured in the dataset. These limitations suggest that the conclusions should be interpreted with caution, and future research could benefit from incorporating multi-source or multi-country data.