
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12586-8
10.1016/j.heliyon.2024.e36555
e36555
Research Article
Examining drivers injury severity for manual and automatic transmission vehicles-involved crashes: Random parameter mixed logit model with heterogeneity in means and variances
Atombo Charles catombo@htu.edu.gh

Department of Mechanical Engineering, Department of Civil Engineering, Ho Technical University, P.O. Box HP217, Ho, Ghana
19 8 2024
30 8 2024
19 8 2024
10 16 e365556 6 2023
16 8 2024
19 8 2024
© 2024 The Author
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
The effect of vehicle transmission type on driver injury severities have not been thoroughly studied. The study used four-year historical crash data that occurred between the year 2019 and 2022 in Ghana. The data shows 1856 and 2272 crashes for automatic and manual transmission, respectively. The study examined the factors influencing driver injury severity in crashes involving vehicles with manual and automatic transmissions, using Random Parameter Mixed Logit Model to account for heterogeneity in the dataset. It was observed that use of manual transmission is related to a higher risk of incapacitating and fatal injuries compared to automatic transmission. Specifically, for automatic transmission vehicle-involved crashes, factors related to fatal injury were overaged vehicles, public transport, morning and evening peak hours, head-on and rollover crashes. Crashes involving saloon cars and low age cars were associated with incapacitating injury whiles rainy weather condition was related to both fatal and incapacitant injuries. Regarding manual transmission, fatal injury was associated with crashes involving male and novice drivers, cars, pickup trucks, HGV, public transports, morning and evening peak hours, rainy weather conditions and curved roads. Also, buses, private cars and trip distance were related to incapacitating injury. The rollover crashes and overaged vehicles were also associated with both fatal and incapacitating injuries. Four random parameters demonstrated heterogeneity in means, with two factors influencing the variances of two parameters for automatic transmission model. For the manual transmission model, five random parameters showed heterogeneity in means, with four variables influencing the variances of three parameters. These findings are valuable for policymakers, manufacturers, and drivers in implementing targeted interventions and safety measures to promote road safety.

Keywords

Automatic transmission
Manual transmission
Driver injury severity
Mixed logit model
Random parameter
==== Body
pmc1 Introduction

Safety of vehicular occupants has been a significant concern to all road traffic safety stakeholders for many years. In order to provide directions for safety countermeasures, several efforts have been made to better understand the factors affecting crash-injury severity regarding the use of motor vehicles. Despite the efforts, crash related injuries involving drivers and passengers is still a concern as road traffic injuries have been recorded to be eighth leading cause of death worldwide, with an estimated 1.35 million fatalities annually [1]. The road traffic crashes that resulted in fatalities or permanent disabilities have detrimental effects on socioeconomic well-being of peoples, especially in the developing countries [2,3]. Over the years, road traffic crashes have been on the rise in developing countries. A large number of persons involved in motor vehicle crashes surfers’ permanent injuries and incapacitation [4,5]. Vehicle crashes occur for several reasons, such as driver error, environmental factors, and vehicle design. One of the factors related to vehicle design that may affect crash injury severity is the type of transmission used in the vehicle.

Vehicles can have either a manual or automatic transmission. The manual transmission system, often referred to as “stick shift” was the first type of vehicle transmission, which required the driver to disengage, shift, and then re-engages the transmission. The benefits associated with the use of vehicles with manual transmissions include greater driver control in challenging driving conditions and less distraction than the automatic transmission [6].

Nowadays, most of the vehicles on the road are using the automatic transmission system where gear change is automatically performed in relation to the speed of the vehicle. Vehicles with automatic transmission allow drivers to keep their hands and feet on the steering wheels and pedals respectively, while driving the vehicle, which may enhance drivers’ reaction time to situations. Among the reasons for introducing the automatic transmission system was to improve vehicle safety and driving performance [7]. Automatic transmission vehicles are becoming increasingly popular in both developed and developing countries.

Manual and automatic transmission vehicles have different characteristics such as acceleration and control over the vehicle that may affect crash outcomes. The crash injury severity associated with transmission type may also depend on several factors such as driver characteristics, vehicle type, travelling distance, time of day, crash type, weather condition and road type and the interactions among these factors.

Studies have used traditional regression models to predict crashes involving manual and automatic transmission vehicles [6,[8], [9], [10], [11]]. Some of these studies have indicated that drivers who drive manual transmission vehicles may be more aware of their surroundings and therefore less susceptible to be involved in crashes. For instance, studies have indicated that manual transmissions are safer and lead to fewer crashes [8,12]. This argument was supported with the fact that manual transmission keeps drivers focused when driving. In addition, this type of transmission involves listening to the vehicle and carefully observing other cars around. Hence, drivers are less likely to engage in other distracting activities and as a result have more control over their vehicles, which can be useful in hazardous situations such as high traffic periods and poor weather conditions.

On the contrary, some studies found that manual transmission may face challenges when shifting gears and therefore drivers must have better driving skills and be more alert and better coordinate traffic situations while driving. The study of Warshawsky-Livne and Shinar [9] measured brake reaction and movement times in a driving simulator under both manual and automatic gear conditions. They found that reaction times increased with age and that manual gear shifting takes a longer movement time compared with automatic transmission. Their result implies that automatic gear shifting may improve driving performance compared to manual transmission. Additionally, considering the multitasking (extra pedal and stick shift) in the use of manual transmissions, it could be distracting to some drivers, especially inexperienced and older drivers. This category of drivers having multitasking activities (pedal and gear shift) at the same time can make them commit mistakes while driving which may affect crash rate and injury severity.

In the case of automatic transmission, M.S. Akple et al. [6] indicated that vehicles with automatic transmission are easier to operate, particularly for drivers with less experience. Furthermore, they indicated that in automatic transmission, the automatic gear shifting eliminates the need for frequent gear changes, which can be challenging for new and inexperienced drivers, particularly in congested traffic situations. This implies that vehicles with automatic transmission require less focus and attention from the driver, as the system automatically changes gears when it detects a need for a gear change.

Because of the complex nature of the road environment coupled with internal and external factors, a study indicated that drivers of automatic transmission are safer drivers than those on manual transmission [10]. The study of Selander et al. [11] investigated whether driving behaviour in older drivers improves when using an automatic transmission compared to a manual transmission. They observed that the older drivers demonstrated acceptable driving behaviours when driving vehicles with an automatic transmission. The study also revealed that older drivers who used automatic transmission demonstrated safer adjustments to speed in urban areas, maintained safer lane positioning, exhibited greater manoeuvring skills, and adhered more closely to speed regulations. The study concluded that vehicles with automatic transmission are safer for older drivers. Another study examined how young novice drivers and experienced drivers detect signs while driving manual and automatic gear shifts [13]. The study findings indicated that novice drivers had a higher rate of missed signs when driving with a manual gear compared to an automatic gear. However, the difference was not observed among the experienced driver group, suggesting that young drivers might gain advantages from using vehicles with automatic transmissions.

On the other hand, a study of Washino [8] discovered that when considering all factors related to crashes, vehicles equipped with automatic transmission (AT) have crash rates that are double compared to those with manual transmission (MT), except in the case of head-on collisions. However, their study indicated that in fatal crashes, the crash rates for both vehicle transmission types are approximately equal. The study further indicated that the causes of traffic crashes are not solely attributed to poor driving skills among AT vehicle drivers. Instead, AT vehicles are found to induce a certain level of emotional effect.

Besides, studies have employed random parameters models incorporating unobserved heterogeneity to evaluate injury severity outcomes [[14], [15], [16]]. These studies have shown that the random parameters model is an effective approach for capturing the complex interactions between various factors contributing to injury severity. Moreover, this model can account for unobserved heterogeneity in both means and variances within the data.

Though previous related studies have considerably added to the comprehension of factors associated with traffic crashes, the majority of these studies examine driving performance, driving behaviour and crash rates, particularly among novice, older, and young drivers using automatic and manual transmission vehicles. There is no study that used real crash data and random parameters to examine factors impacting injury severity outcomes specifically in crashes concerning manual and automatic transmission vehicles. Furthermore, the previous related studies focused on crash rates without considering the injury severity to the drivers. In addition, studies have indicated that driver skill, experience, and attentiveness is key in traffic safety [7,8,11,12]. Other factors such as driver and vehicle characteristics, crash type, road conditions, environmental factors, and temporal characteristics as well as the interaction between these factors also come into play. These underlying factors influencing crash-injury severity are complex and unobserved which can possibly lead to potentially biases and erroneous crash estimates [17]. Yet, previous related studies did not account for unobserved heterogeneity in means and variances using random parameters in their analysis to make definite conclusions. Therefore, this study employed random parameters models to account for unobserved heterogeneity in the means and variances within the crash dataset, to estimate factors influencing injury severity among drivers involved in crashes with manual and automatic transmission vehicles. Notably, this is the first study that specifically examines the impact of factors on the driver's injury severity, with a particular emphasis on crashes involving manual and automatic transmission vehicles.

2 Methodology

Studies have employed random parameter methods for accounting for the unobserved heterogeneity [14,15]. This study employed a random parameter mixed logit model, which considers heterogeneity in both means and variances, to estimate the severity of drivers’ injuries in crashes involving vehicles with either automatic or manual transmissions. The modelling method commences by defining an injury severity function Skn which represent the likelihood that drivers sustain a specific injury severity outcome k (minor injury, incapacitating injury and fatal injury) in crash n as stated in Eq. (1) [18].(1) Skn=βkXkn+εkn

The injury severity function, denoted as Skn determines the likelihood of different injury severity outcomes k in crash n. The vector βk corresponds to the coefficients that are estimated for this function. Xkn represents the vector of predictor variables (driver and vehicle attributes, travelling distance, time of day, crash type, weather condition and road type), that affect the severity of driver injuries. The error term εkn is assumed to follow an independent and identical distribution. Additionally, the study account for unobserved heterogeneity across observations and used βk as a vector of parameters that is estimated, as specified in Eq. (2).(2) βk=a+ψZk+φk

where a represent the mean parameter, Zk is a vector of predictor variables from crash n,ψ is a vector of parameters that is estimated, and φk is a randomly distributed term that accounts for unobserved heterogeneity. The unobserved heterogeneity in the means and variances of the random parameters, as described in Eq. (3) is denoted by βkn which represent a vector of estimable parameters.(3) βkn=β+ψknZkn+σknexp(ωknWin)vkn

where β is mean parameter ,Zkn represent a vector of predictor variables that measures the heterogeneity in the mean, impacting severity of injury i.ψkn is a corresponding vector of parameter estimates, while Wkn denote a vector of distinct crash predictor variables that defines the heterogeneity in the standard deviation σkn with matching parameter vector ωkn. In addition, vkn refer to a randomly dispersed variable that measures unobserved heterogeneity across crashes.

The probability of a driver sustaining injury severity i in crash n, denoted as Pn(k)statedinEq.4, can be expressed by assigning a continuous density function to the vector βkn, such that Pro(βkn=β)=f(φ):.(4) Pn(k)=∫EXP(βkXkn)∑∀IEXP(βkXkn)f(β|φ)dβ

The function f(β|φ) represents the density of β, where φ denotes the vector of parameters, including mean and variance, associated with that density function, while all other terms retain their previous definitions.

“The model was estimated using simulated maximum likelihood with 1000 Halton draw” [19]. Distributions for the random parameter were examined, with the normal distribution providing the best statistical fit, as noted in the previous study [20]. Besides, marginal effects were calculated to provide further understanding into the estimated results, as they allow for the examination of how different parameter estimates impact the model outcomes [18]. The marginal effects in this study indicate how the likelihood of an injury severity outcome changes with a one-unit change in the predictor variable, assuming all other variables remain constant.

2.1 Data description

Historical crash data from 2019 to 2022 were obtained from a road traffic crash report of the National Road Safety Authority (NRSA), Insurance Companies, and Driver and Vehicle Licensing Authority (DVLA) in Ghana. Data included crashes involving transmission types (automatic and manual transmission vehicles). The data used included 4128 crashes, out of which automatic and manual transmission vehicles recorded 1856 and 2272 crashes respectively. The dataset contained comprehensive information on injury severity outcomes: minor injury (injury which require first-aid only), incapacitating injury (injury preventing a person from performing activities they could before the injury), and fatal injury (injury resulting in death within thirty days of the crash), driver characteristics (sex and driving experience), vehicle type, vehicle age, transport type, trip distance, time of day, crash type, weather condition and roadway type. The origin and destination of the vehicles were used to determine the distance vehicles were expected to cover before the crash and named as ‘trip distance’. The registration numbers of the vehicles were documented and utilised as indicators to prevent data duplication.

Fig. 1 displays the injury severity distribution for crashes involving automatic and manual transmission vehicles. The analysis specifically showed significant differences in the number of crashes between the two vehicle transmission types, with automatic transmissions recording a higher number of crash-injury severity compared to manual transmission vehicles.Fig. 1 Injury severities distribution for automatic and manual transmission vehicle.

Fig. 1

2.2 Descriptive statistics

The variables were coded 1 and 0, where 1 indicates that the variable statement is true and 0 indicates it is false as presented in Table 1. The results in Table 1 show the descriptive statistics for the variables that had a significant impact on injury severity in both automatic and manual transmission vehicle-involved crashes. The results showed that 23 variables were significantly associated with injury severity in the automatic transmission model, while the manual transmission model identified 27 variables with a significant impact on injury severity outcomes. It is widely acknowledged that traffic crashes are influenced by various factors, including vehicle, driver, road, and environmental factors as well as the interaction between these factors [21,22]. Along with this understanding, the present study focuses on these factors to gain insights into their impact on injury severity in the context of Ghana.Table 1 Descriptive statistics: Automatic and manual transmission.

Table 1Variable	Automatic transmission (N = 1856)	Manual transmission (N = 2272)	
Mean	Standard deviation	Mean	Standard deviation	
Driver's sex	
Sex (1 if male driver, 0 otherwise)	0.491	0.500	0.310	0.392	
Sex (1 if female driver, 0 otherwise)	0.510	0.500	0.466	0.499	
Driving experience	
Driving experience (1 if young novice, 0 otherwise)	0.620	0.485	0.880	0.325	
Driving experience (1 if experience, 0 otherwise)	0.462	0.499	0.056	0.231	
Vehicle type	
Vehicle type (1 if saloon car, 0 otherwise)	0.750	0.433	0.303	0.460	
Vehicle type (1 if pickup, 0 otherwise)	0.043	0.203	0.204	0.403	
Vehicle type (1 if buses, 0 otherwise)	–	–	0.169	0.375	
Vehicle type (1 if HGV, 0 otherwise)	0.151	0.358	0.194	0.395	
Vehicle age	
Vehicle age (1 if 1 to 10 old, 0 otherwise)	0.595	0.491	0.430	0.495	
Vehicle age (1 if 11to 20 old, 0 otherwise)	0.353	0.478	0.472	0.499	
Transport type	
Transport type (1 if private car, 0 otherwise)	0.323	0.468	0.542	0.439	
Transport type (1 if public transport, 0 otherwise)	0.217	0.431	0.310	0.442	
Trip Distance	
Trip distance ((1 if 1–100 km, 0 otherwise)	0.741	0.438	0.691	0.463	
Trip distance (1 if 101–200 km, 0 otherwise)	0.224	0.417	0.240	0.427	
Trip distance (1 if 201–300 km, 0 otherwise)	0.017	0.130	0.057	0.231	
Time of day	
Crash time (1 if 6–9am, 0 otherwise)	0.216	0.411	0.127	0.333	
Crash time (1 if 9am to 12noon, 0 otherwise)	0.172	0.378	0.218	0.413	
Crash time (1 if 12noon to 4pm, 0 otherwise)	0.207	0.405	0.296	0.456	
Crash time (1 if 4pm to 6:00pm, 0 otherwise)	0.257	0.489	0.301	0.413	
Crash type	
Crash type (1 if head-to-head crash, 0 otherwise)	0.267	0.443	0.246	0.431	
Crash type (1 if head-to-rear crash, 0 otherwise)	0.397	0.489	0.282	0.450	
Crash type (1 if rollover crash, 0 otherwise)	0.086	0.281	0.148	0.355	
Crash type (1 if side hit, 0 otherwise)	–	–	0.254	0.435	
Weather condition	
Weather condition (1 if rainy weather, 0 otherwise)	0.547	0.498	0.486	0.501	
Weather condition (1 if dusty weather, 0 otherwise)	0.451	0.503	0.556	0.497	
Roadway type	
Roadway type (1 if straight road, 0 otherwise)	0.483	0.500	0.514	0.500	
Roadway type (1 if curve road, 0 otherwise)	–	–	0.606	0.489	
Note: parameter coefficient insignificant.

2.2.1 Transferability tests

A series of likelihood ratio tests were conducted to determine whether automatic and manual transmission vehicle models are acceptable separately. The likelihood ratio test is expressed in Eq. (5) as:(5) χ2=−2[LL(βHolistic)−LL(βAT)−LL(βMT)]

where LL(βHolistic),LL(βAT), and LL(βMT) are the log-likelihoods at the convergence of the holistic model (Automatic and Manual transmission model). The log-likelihood ratio tests were conducted to determine the significance of the holistic model compared to the separate models (automatic and manual transmission models). The associated chi-square value was found to be 1521.55 with 25 degrees of freedom. This result indicates a confidence level exceeding 99.9 %. This implies that separately modelling crashes involving automatic and manual transmission vehicles is likely to produce a better fit than using a combined data.

A further likelihood test was performed to evaluate the similarity of parameter values between the model for crashes involving automatic and manual transmission, using the test statistics as expressed in Eq. (6).(6) x2=−2[LL(βt2t1)−LL(βt1)]

where LL(βt2t1) denotes the log-likelihood at convergence for the parameters of model t2, based on the data from models t1. LL(βt1) represents the log-likelihood at convergence for the parameters of model t1, which uses the same explanatory variables but allows the parameters to be unrestricted compared to the parameters of model t2. Additionally, the likelihood ratio test is applied in a reverse way [16]. The chi-square (x2) test was utilised to assess the confidence level and determine if the null hypothesis that the parameters in model t1 and t2 are the same can be rejected or accepted [17,23]. The result in Table 2 includes the coefficients of χ2 with their corresponding degrees of freedom for the models, showing that the null hypothesis that crashes involving automatic and manual transmission vehicles are the same can be rejected with over 99 % confidence.Table 2 Likelihood ratio test results between Automatic and Manual transmission.

Table 2t1	t2	
Automatic transmission (Model)	Manual transmission (Model)	
Automatic transmission	–	1689.28 (df=50)	
	[>99.99 %]	
Manual transmission	683.55 (df=32)	–	
[>99.99 %]		
Note: df-degrees of freedom, confidence level in brackets.

3 Results and discussion

The crash injury severities for automatic and manual transmission vehicles were estimated using the Mixed Logit model, accounting for heterogeneity in the means and variances as detailed in Table 3, Table 4, respectively. The estimation of each significant parameter in the model, together with their respective marginal effect estimations, is provided. The marginal effect estimates explain how a one-unit change in the independent variable impacts the severity of the injury outcomes. It further shows how the predicting variables affect the likelihood of injury severity as it varies from zero to one. This enhances the understanding of the extent to which predicting variables impact the severity of injuries [23]. A positive coefficient suggests that the severity outcome tends to increase, while a negative coefficient shows that injury severity outcome tends to decrease, assuming all other variables remain the same. The significant variables in the models were used to calculate the McFadden Pseudo R-squared values. The model with heterogeneity in means and variances had a satisfactory fit. The random parameter models for vehicles with automatic and manual transmissions, which account for heterogeneity in means and variances had McFadden Pseudo R-squared values of 0.167 and 0.257, respectively, indicating acceptable goodness-of-fit. The results of the estimation are presented and discussed.Table 3 Mixed Logit with heterogeneity in means and variances for automatic transmission.

Table 3Factors	Parameter estimate	t-value	Marginal effect	
Minor injury	Incapacitating injury	Fatal injury	
Constant [MI]	1.681	49.41				
Constant [II]	9.786	50.01				
Constant [FI]	1.160	35.11				
Driver's sex	
Sex (1 if female driver, 0 otherwise) [MI]	0.301	1.99	0.0095	−0.0034	−0.0012	
Standard deviation, Normally Distribution	1.046	3.81				
Sex (1 if female driver, 0 otherwise) [FI]	−0.474	−3.64	0.0037	0.0036	−0.0141	
Sex (1 if male driver, 0 otherwise) [II]	−1.824	−1.99	0.0037	−0.0044	0.0007	
Driving experience	
Experience (1 if young novice, 0 otherwise) [FI]	−1.125	−7.35	0.0048	0.0146	−0.0209	
Experience (1 if old experience, 0 otherwise) [FI]	−0.260	−1.96	0.0240	0.0190	−0.0122	
Vehicle type	
Vehicle type (1 if saloon car, 0 otherwise) [II]	3.744	3.46	−0.0032	0.0147	−0.0092	
Standard deviation, Normally Distribution	3.350	3.70				
Vehicle type (1 if pickup, 0 otherwise) [MI]	−0.996	−4.06	−0.0248	0.0074	0.0139	
Vehicle type (1 if Heavy good vehicle, 0 otherwise) [II]	−2.272	−3.54	0.0037	−0.0096	0.0035	
Standard deviation, Normally Distribution	4.597	6.12				
Vehicle age	
Vehicle age (1 if 1 to 10 old, 0 otherwise) [II]	−1.828	−1.80	0.0007	−0.0090	0.0062	
Vehicle age (1 if 1 to 10 old, 0 otherwise) [FI]	−0.483	−3.36	0.0003	0.0006	−0.0135	
Vehicle age (1 if 11 to 20 old, 0 otherwise) [FI]	0.638	4.32	−0.0045	−0.0063	0.0233	
Transport type	
Transport type (1 if private car, 0 otherwise) [MI]	−0.213	−1.96	−0.0059	0.0042	−0.0001	
Transport type (1 if public transport, 0 otherwise) [FI]	0.876	5.69	−0.0008	−0.0004	0.0332	
Trip distance	
Trip distance (1 if 1–200 km, 0 otherwise) [MI]	1.803	5.94	0.0378	−0.0019	−0.0096	
Trip distance (1 if 201–400 km, 0 otherwise) [MI]	2.104	6.94	0.0435	−0.0012	−0.0064	
Trip distance (1 if 401–600 km, 0 otherwise) [MI]	2.268	5.55	0.0051	−0.0141	−0.0103	
Time of day	
Crash time (1 if 6am–9am, 0 otherwise) [FI]	0.197	2.55	−0.0034	−0.0023	0.0005	
Crash time (1 if 9am to12noon, 0 otherwise) [MI]	−0.437	−4.52	−0.0120	0.0037	0.0010	
Crash time (1 if 12noon to 4pm, 0 otherwise) [MI]	−0.256	−2.97	−0.0067	0.0016	0.0014	
Crash time (1 if 4pm–6pm, 0 otherwise) [FI]	0.497	6.93	−0.0029	−0.0032	0.0215	
Crash type	
Crash type (1 if head-to-head crash, 0 otherwise) [MI]	1.099	9.97	0.0270	−0.0002	−0.0007	
Crash type (1 if head-to-head crash, 0 otherwise) [FI]	0.998	10.90	−0.0140	−0.0211	0.0321	
Standard deviation, Normally Distribution	1.902	2.12				
Crash type (1 if head-to-rear crash, 0 otherwise) [MI]	−0.411	−4.52	−0.0088	0.0040	0.0028	
Crash type (1 if head-to-rear crash, 0 otherwise) [II]	−1.337	−2.51	0.0026	−0.0084	−0.0039	
Crash type (1 if rollover crash, 0 otherwise) [MI]	−0.425	−3.39	−0.0104	0.0021	0.0039	
Crash type (1 if rollover crash, 0 otherwise) [FI]	2.672	25.61	−0.0170	−0.0224	0.0818	
Weather condition	
Weather (1 if rainy weather condition, 0 otherwise) [FI]	0.407	3.83	−0.0012	−0.0019	0.0092	
Weather (1 if rainy weather condition, 0 otherwise) [II]	3.246	5.22	−0.0067	0.0136	−0.0070	
Weather (1 if dusty environment, 0 otherwise) [MI]	0.336	3.51	0.0078	−0.0005	−0.0008	
Roadway description	
Roadway (1 if straight road, 0 otherwise) [MI]	0.745	4.87	0.0163	−0.0083	−0.0014	
Roadway (1 if straight road, 0 otherwise) [II]	4.128	4.61	−0.0022	0.0092	−0.0052	
Roadway (1 if straight road, 0 otherwise) [FI]	0.816	6.42	−0.0112	−0.0048	0.0154	
Heterogeneity in the mean	
Female driver [MI]: Crash time (1 if 12noon to 4pm, 0 otherwise)	−0.302	−1.97	–	–	–	
Heavy good vehicle [II]: Crash type (1 if head-to-rear crash, 0 otherwise)	2.504	2.27	–	–	–	
Saloon car [II]: Vehicle age (1 if 11 to 20 old, 0 otherwise)	1.784	2.04	–	–	–	
Saloon car [II]: Crash type (1 if head-to-rear crash, 0 otherwise)	−2.187	−3.11	–	–	–	
head-to-head crash [FI]: Crash time (1 if 4pm–6pm, 0 otherwise)	0.578	3.28	–	–	–	
Heterogeneity in the variance			–	–	–	
Female driver [MI]: Crash type (1 if head-to-rear crash, 0 otherwise)	−0.472	−3.47	–	–	–	
Saloon car [II]: Crash type (1 if head-to-rear crash, 0 otherwise)	−0.356	−2.47	–	–	–	
Saloon car [II]: Weather (1 if rainy weather, 0 otherwise)	1.121	2.26	–	–	–	
Log-likelihood at convergence	−3086.38					
Log-likelihood with constants	−3343.15				
McFadden Pseudo R-squared	0.167					
AIC	6224.76					
BIC	6368.44					
Number of observations	1856					

Table 4 Mixed Logit with heterogeneity in means and variances for manual transmission.

Table 4Factors	Parameter estimate	t-value	Marginal effect	
Minor injury	Incapacitating injury	Fatal injury	
Constant [MI]	1.570	67.86				
Constant [II]	12.462	70.09				
Constant [FI]	1.059	36.65				
Driver's sex	
Sex (1 if male driver, 0 otherwise) [MI]	0.532	10.52	0.0117	−0.0030	−0.0010	
Sex (1 if male driver, 0 otherwise) [MI]	−0.114	−3.36	−0.0018	0.0009	0.0030	
Sex (1 if male driver, 0 otherwise) [II]	−1.338	−2.46	0.0005	−0.0046	0.0007	
Sex (1 if female driver, 0 otherwise) [II]	−1.517	−4.16	0.0019	−0.0058	0.0051	
Sex (1 if male driver, 0 otherwise) [FI]	0.265	3.11	−0.0045	−0.0034	0.0092	
Standard deviation, Normally Distribution	2.934	3.15				
Driving experience	
Experience (1 if young novice, 0 otherwise) [FI]	0.588	2.42	−0.0055	−0.0016	0.0121	
Experience (1 if old experience, 0 otherwise) [MI]	−0.553	−7.72	−0.0015	0.0020	0.0056	
Vehicle type	
Vehicle type (1 if saloon car, 0 otherwise) [MI]	0.463	8.30	0.0121	−0.0008	−0.0005	
Vehicle type (1 if saloon car, 0 otherwise) [FI]	0.318	3.37	−0.0036	−0.0016	0.0141	
Vehicle type (1 if pickup, 0 otherwise) [MI]	0.396	7.36	0.0087	−0.0032	−0.0010	
Vehicle type (1 if pickup, 0 otherwise) [FI]	0.328	3.61	−0.0008	−0.0004	0.0159	
Vehicle type (1 if buses, 0 otherwise) [MI]	0.956	18.46	0.0203	−0.0061	−0.0002	
Standard deviation, Normally Distribution	4.149	5.07				
Vehicle type (1 if buses, 0 otherwise) [II]	2.079	3.72	−0.0016	0.0062	−0.0026	
Vehicle type (1 if heavy goods vehicle., 0 otherwise) [FI]	0.380	5.02	−0.0007	−0.0011	0.0126	
Vehicle age	
Vehicle age (1 if 1 to 10 old, 0 otherwise) [II]	−2.682	−3.47	0.0018	−0.0093	0.0035	
Vehicle age (1 if 1 to 10 old, 0 otherwise) [FI]	−0.401	−3.31	0.0006	0.0017	−0.0129	
Vehicle age (1 if 11 to 20 old, 0 otherwise) [MI]	0.143	2.26	0.0034	−0.0003	−0.0001	
Vehicle age (1 if 11 to 20 old, 0 otherwise) [II]	2.309	3.39	−0.0058	0.0079	−0.0021	
Vehicle age (1 if 11 to 20 old, 0 otherwise) [FI]	0.285	2.68	−0.0002	−0.0012	0.0105	
Transport type	
transport type (1 if private car, 0 otherwise) [II]	2.108	3.51	−0.0043	0.0072	−0.0028	
Transport type (1 if public transport, 0 otherwise) [FI	0.302	3.45	−0.0015	−0.0011	0.0138	
Trip distance	
Trip distance (1 if 1–200 km, 0 otherwise) [II]	5.754	3.66	−0.0043	0.0213	−0.0010	
Trip distance (1 if 201–400 km, 0 otherwise) [MI]	0.762	5.30	0.0143	−0.0023	−0.0037	
Trip distance (1 if 201–400 km, 0 otherwise) [II]	8.768	5.65	−0.0041	0.0310	−0.0006	
Trip distance (1 if 401–600 km, 0 otherwise) [MI]	0.412	2.49	0.0073	−0.0033	−0.0014	
Trip distance (1 if 401–600 km, 0 otherwise) [II]	11.373	6.38	−0.0028	0.0381	−0.0032	
Temporal characteristics	
Crash time (1 if 6–9am, 0 otherwise) [FI]	0.264	2.79	−0.0051	−0.0021	0.0082	
Crash time (1 if 9am to 12noon, 0 otherwise) [MI]	0.405	8.82	0.0098	−0.0008	−0.0017	
Crash time (1 if 9am to 12noon, 0 otherwise)) [II]	−2.493	−5.03	0.0065	−0.0078	0.0042	
Crash time (1 if 9am to 12noon, 0 otherwise)) [FI]	−0.255	−3.28	0.0019	0.0024	−0.0084	
Crash time (1 if 12noon to 4pm, 0 otherwise) [MI]	0.130	3.14	0.0039	−0.0005	−0.0009	
Crash time (1 if 4pm–6pm, 0 otherwise) [FI]	0.330	4.72	−0.0003	−0.0007	0.0107	
Crash type	
Crash type (1 if head-to-head crash, 0 otherwise) [MI]	1.990	32.21	0.0431	−0.0031	−0.0122	
Standard deviation, Normally Distribution	2.520	2.36				
Crash type (1 if head-to-rear crash, 0 otherwise) [MI]	0.409	7.23	0.0090	−0.0033	−0.0046	
Standard deviation, Normally Distribution	1.817	2.53				
Crash type (1 if head-to-rear crash, 0 otherwise) [II]	−1.605	−2.63	0.0027	−0.0052	0.0035	
Crash type (1 if head-to-rear crash, 0 otherwise) [FI]	−0.259	−2.71	0.0009	0.0011	−0.0129	
Crash type (1 if rollover crash, 0 otherwise) [MI]	0.512	8.61	0.0138	−0.0006	−0.0030	
Crash type (1 if rollover crash, 0 otherwise) [II]	3.161	4.92	−0.0036	0.0103	−0.0013	
Crash type (1 if rollover crash, 0 otherwise) [FI]	0.670	6.66	−0.0014	−0.0019	0.0145	
Standard deviation, Normally Distribution	4.663	6.20				
Crash type (1 if side hit, 0 otherwise) [MI]	0.472	9.91	0.0107	−0.0006	−0.0009	
Crash type (1 if side hit, 0 otherwise) [FI]	0.724	8.99	−0.0018	−0.0015	0.0272	
Weather condition	
Weather (1 if rainy weather condition, 0 otherwise) [FI]	0.392	6.21	−0.0016	−0.0037	0.0079	
Weather (1 if rainy weather condition, 0 otherwise) [II]	−4.776	−7.02	0.0042	−0.0152	0.0013	
Weather (1 if dusty environment, 0 otherwise) [MI]	0.292	5.84	0.0059	−0.0039	−0.0026	
Weather (1 if dusty environment, 0 otherwise) [II]	−1.053	−1.96	0.0020	−0.0033	0.0008	
Weather (1 if dusty environment, 0 otherwise) [FI]	−0.169	−2.00	0.0004	0.0007	−0.0036	
Roadway description	
Roadway (1 if straight road, 0 otherwise) [MI]	0.658	6.04	0.0208	−0.0055	−0.0132	
Roadway (1 if straight road, 0 otherwise) [II]	−4.860	−4.13	0.0134	−0.0016	0.0014	
Roadway (1 if curve road, 0 otherwise) [MI]	0.379	3.78	0.0071	−0.0018	−0.0014	
Roadway (1 if curved road, 0 otherwise) [FI]	2.899	2.68	−0.0050	−0.0039	0.0093	
Heterogeneity in the mean	
Buses [MI[:Crash type (1 if side hit, 0 otherwise)	0.877	6.94				
Head-to-rear [MI]: Weather (1 if rainy weather condition, 0 otherwise)	0.441	2.28				
Head-to-rear [MI]: Weather (1 if dusty environment, 0 otherwise)	1.017	5.12				
Head-to-head [MI]: Roadway (1 if curve road, 0 otherwise)	0.814	6.05				
Male driver [FI]: Vehicle type (1 if saloon car, 0 otherwise)	0.359	2.35				
Rollover [FI]: Vehicle type (1 if saloon car, 0 otherwise)	0.592	3.64				
Heterogeneity in the variance	
Male driver [FI]: Crash type (1 if side hit, 0 otherwise)	0.429	1.99				
Head-to-head [MI]: Weather (1 if dusty environment, 0 otherwise)	0.300	2.26				
Rollover [FI]: Weather (1 if dusty environment, 0 otherwise)	−1.519	−9.47				
Rollover [FI]: Roadway (1 if curve road, 0 otherwise)	0.337	2.05				
Log-likelihood at convergence	−2548.168					
Log-likelihood with constants	−3446.8062					
McFadden Pseudo R-squared	0.257					
AIC	5150.336					
BIC	5305.003					
Number of observations	2272					

3.1 Driver's sex

The result shows that female drivers increase the probability of minor injuries by 0.0095, and decrease fatal injuries by −0.0141 while driving automatic transmission vehicles. These findings contradict the study conducted by Kahane [24], which found that female drivers were more likely to be killed or injured than males in crashes of equal severity. The finding suggests that driving automatic transmission vehicles may be safer for females. This could be attributed to the ease of operation associated with automatic vehicles [6,25], which make them more accessible to female drivers. However, it is imperative that female drivers may still face challenges in controlling their vehicles, particularly in challenging road conditions. Therefore, female drivers with less driving experience may have a higher probability of being involved in minor crashes and sustaining minor injuries. Additionally, it is worth considering that the majority of females tend to drive smaller and lighter cars [26]. These types of vehicles offer less protection when a crash occurs [27], potentially increasing the probability of minor injuries.

In addition, female drivers decrease minor and incapacitating injuries by −0.0018 and −0.0058 respectively for manual transmission crash model. One possible reason female drivers are less associated with minor and incapacitating injury when driving manual transmission vehicles is their tendency to be less risk-takers and more compliant with traffic rules. This cautious behaviour can be attributed to a higher level of risk aversion and a greater emphasis on safety [28]. In addition, driving a manual transmission car demands more attention, skill, coordination, and concentration [12]. This demanding task may assist female drivers in avoiding distractions and maintaining better control over their vehicle's speed and momentum, eventually resulting in reduction of crash-related injuries severity.

Similarly, male drivers may decrease the risk of incapacitating injury by −0.0044 and −0.0046 in crashes involving automatic and manual transmission vehicles respectively. The findings suggest that male drivers may benefit from driving automatic transmission cars as they are not required to shift gears. This allows them to concentrate more on the road, their surroundings, and react quickly to potential hazards [25,29,30]. With regard to manual transmission cars, male drivers may benefit from increased control and responsiveness, as well as the presence of robust braking systems [31], which is likely to contribute to a decreased risk of sustaining serious injuries in the event of a crash.

Nevertheless, male drivers increase the minor and fatal injuries by 0.0117 and 0.0092 respectively in crashes involving manual transmission vehicles. In accordance with previous studies, the finding suggests that male drivers tend to experience more severe injuries than female drivers [21,32]. Possibly, male drivers may be more susceptible to engaging in risky driving behaviours, including speeding and aggressive driving, which can increase the chances of crashes and injuries [33]. Again, male drivers tend to overestimate their skills when driving a manual transmission vehicle, which can lead to a higher risk of crashes and serious injuries. Furthermore, in the event of a collision, male drivers are more likely to sustain minor or fatal injuries due to larger body mass, and greater physical strength, which can increase the impact force and make injuries more severe.

Additionally, the female parameter is random and follows a normal distribution with a mean of 0.301 and a standard deviation of 1.046 in the minor injury for automatic transmissions model, suggesting that 61.3 % of the distribution specific to minor injuries are above zero, while 38.7 % are below zero. This indicates that female drivers are 61.3 % more likely to experience minor injuries and 38.7 % less likely to experience minor injuries when driving automatic transmission vehicles. Likewise, the parameter for male drivers is random and normally distributed, with a mean of 0.265 and a standard deviation of 2.934 in the context of fatal injuries for manual transmission vehicle model, signifying that 53.6 % of the distribution is above zero, while 46.3 % is below zero for male drivers specific to fatal injury. This suggests that male drivers increase the likelihood of fatal injury by 53.6 % and decrease it by 46.3 % while driving manual transmission vehicles. The results further confirmed that females tend to be safer drivers when using automatic transmission cars, while male drivers are more related to fatal injuries when driving manual transmission vehicles. This aligns with previous study [17], which found that male drivers were more likely to sustain fatal injuries compared to females.

3.2 Driving experience

The result indicates that young novice drivers have different probabilities of causing fatal injuries when driving automatic or manual transmission vehicles. In particular, young novice drivers are more likely to reduce fatal injuries when driving automatic transmission vehicles, but fatal injuries tend to increase when driving manual transmission vehicles. In accordance with previous study, the observed outcome can be attributed to the multitasking nature of manual transmission and novice drivers of this transmission experience considerably more stress compared to those driving automatics [11]. Novice drivers have less experience and driving manual transmission vehicles are likely to increase their driving errors, leading to more severe crashes and fatal injuries. This suggests that young, inexperienced drivers might benefits from using vehicles with automatic transmissions.

Nevertheless, experienced drivers are less likely to experience fatal and minor injury for both automatic and manual transmission respectively. The results could be that experienced drivers, as supported by various studies [34,35], possess a higher level of skill and tend to adhere to safe driving practices. Their ability to assess driving conditions and respond to potential hazards is enhanced, resulting in a reduced likelihood of crash injury severity [36,37]. A study has shown that most severe crashes stem from a loss of vehicle control and experienced drivers are usually able to perform a series of corrections to gain control [31]. Hence, these findings suggest that experienced drivers possess a better understanding of their vehicle's capabilities, enabling them to drive it safely and effectively.

3.3 Vehicle type

The result indicates that crashes involving saloon cars with automatic transmission increase probability of incapacitating injury by 0.0147 whereas, manual transmission saloon cars increase minor and fatal injuries by 0.0121 and 0.014 respectively. Consistent with previous study, perception that automatic transmission cars reduce effort required to drive the vehicle [38] can impair a driver's capability to respond appropriately to road traffic hazards, which is likely to lead to an increase in crashes and incapacitating injuries. This explains that in the event of a crash, incapacitating injuries (head trauma, spinal cord injuries, or severe fractures) may be more likely to occur in automatic cars. This can lead to long-term disability and reduced quality of life for the injured person, as well as financial and emotional costs for their family and loved ones.

For saloon cars with a manual transmission, the driver manually selects the gear range with higher level of driving skill and experience to drive effectively [39] hence, some drivers may be more prone to loss of control, leading to more frequent and fatal injuries. Additionally, driving manual transmission saloon cars may increase stress in heavy traffic [11], particularly for extended periods, which can increase the risk of crash and injuries.

Moreover, in line with a study [27] crashes involving pickup trucks and heavy goods vehicles (HGVs) with automatic transmission decrease the probability of minor injuries by −0.0248 and incapacitating injuries by −0.0096 respectively. Contrary, manual transmission heavy good vehicles increase fatal injuries by 0.0126 and buses with manual transmission also increase the odds of incapacitating injuries. Additionally, crashes involving buses equipped with manual transmission are more likely to increase minor injury, with random parameters having a mean of 0.956 and standard deviation of 4.149. This demonstrates that a manual transmission bus-involved crash increases the likelihood of minor injuries by 59.1 % and decreases the likelihood of minor injuries by 40.9 %. It could be that because automatic transmissions provide smoother and more predictable acceleration and braking, it helps drivers to maintain better control of vehicles and avoid crashes. This can be especially important for larger and heavier vehicles such as pickup trucks and HGVs, which may be more difficult to manoeuvre and require more space to come to a stop. However, manual transmission HGVs and buses which are often used to carry large amounts of cargo or passengers, tend to be linked with severe injury severity outcomes. The result supports the records that every year, about one hundred persons are killed in crashes involving heavy goods vehicles [40] and the degree of injury as well as disability associated with heavy goods vehicles may produce more serious consequences.

The result further shows that when pickup trucks manual transmission vehicles are involved in crashes, they are likely to increase minor and fatal injuries by 0.0087 and 0.0159 respectively. In accordance with previous studies, the result implies that crashes involving trucks with manual transmission were associated with a high probability of severe injuries [32,41].

Further, saloon car and heavy good vehicle parameters are random and follow a normal distribution, with a mean of 3.744 and −2.272 in incapacitating injury and a standard deviation of 3.350 and 4.597 respectively for automatic transmission model. The result explains that crashes involving cars with automatic transmissions are associated with an 86.8 % increase in the likelihood of incapacitating injuries and a 13.2 % reduction in such injuries. However, when a heavy goods vehicle equipped with automatic transmission is involved in a crash, the probability of incapacitating injury increases by 31.1 % and decreases by 68.9 %, suggesting that when automatic transmission heavy goods vehicles are involved in a crash, injury severity tends to be low.

3.4 Vehicle age

The result shows that vehicle age significantly and consistently influenced the severity of injuries. In particular, automatic transmission vehicles aged between 1 and 10 years were associated with decreased incapacitating and fatal injuries. Whereas vehicle age groups between 11 and 20 years are more likely to increase fatal injury by 0.0233.

It was also noticed that in crashes involving vehicles with manual transmission model, those aged between 1 and 10 years old were less likely to result in incapacitating and fatal injuries. Furthermore, manual transmission vehicles between the age of 11 and 20 years old increase the probability of minor injury by 0.0034, incapacitating and fatal injury by 0.0079 and 0.0105 respectively.

In Ghana, vehicles within the age of 1–10 years are considered as acceptable age whereas vehicles above 10 years are considered as over-aged. In support of the findings, a recent study found that the probability of serious injuries and deaths increased with increases in the age of the vehicles [42,43]. In addition, a report indicated that vehicles aged 18+ years are 71 % more likely to increase serious injury compared with vehicles aged below 3 years when fatal crashes occur [44]. This could be that over aged vehicles often lack modern structural design and materials that provide enhanced crashworthiness. Intuitively, over age vehicles have weaker body structures, less effective crumple zones, or inadequate occupant protection systems, which could increase the risk of sustaining incapacitating or fatal injuries in a crash. Another study found older vehicles and mechanical failure as factors contributing crashes [45]. Therefore, as vehicles aged their mechanical components can deteriorate, leading to compromised performance and reliability. Brake systems, tires, and suspension components may be worn or malfunctioning, diminishing the vehicle's ability to respond effectively in critical situations. This can increase the likelihood of crashes and contribute to more injury severities.

On the other hand, the likelihood of low age (1–10 years) vehicles associated with decreased injury severity outcomes could be attributed to the following reasons. New vehicles are often equipped with the latest safety technologies, including electronic stability control, automatic emergency braking, and lane departure warnings. These technologies have been shown to significantly reduce the risk of road traffic crashes and mitigate the injury severities [[46], [47], [48]]. Therefore, without these safety technologies, occupants are highly vulnerable to crashes and have a greater likelihood of sustaining incapacitating or fatal injuries.

3.5 Transport type

The factors related to transport type indicate that fatal injury increases by 0.0332 and 0.0138 respectively for public transport equipped with automatic and manual transmission. This suggests that public transport vehicles, regardless of whether they have automatic or manual transmissions, are likely to result in fatal injuries during a crash. A study by Xu et al. [49] stated that crashes involving passenger vehicles are more likely to lead to severe injuries. Another study found that commercial motor vehicle drivers who were at fault were more frequently involved in major injury crashes [50]. Therefore, the high incidence of fatal injury with both manual and automatic public transport could be attributed to commercial activities of the majority of public transport. Moreover, the pressure on public transport drivers to achieve daily sales targets can lead to some drivers violating traffic rules. Since most public transport operates in complex intercity and intracity traffic environments, the workload on drivers is high [11]. Consequently, higher traffic density makes the driving task more complex [51], particularly for manual transmission vehicles that require a higher level of driving skill and experience for safe operation.

The results further showed that private cars with manual or automatic transmissions have different probabilities of causing different types of injuries in the event of a crash. Specifically, private cars with manual transmissions have a higher probability of causing incapacitating injuries by 0.0072, while those with automatic transmissions have a lower probability of causing minor injuries. Reason for this difference could be that because manual transmission cars require gear shift and clutch pedals, it can be difficult to operate in stressful situations, increasing the driving errors and more severe crashes. Conversely, automatic transmission cars are generally easier to operate and require less driver effort [6]. Consistent with prior research, the findings suggest that automatic transmission technology contributes to improved well-being by reducing driver workload and enhancing safety through a reduction in errors associated with individual driving styles [52]. The increasing acceptance of modern automatic transmissions is based on their innovative technology, driving comfort, and seamless shifting capabilities [53]. According to Jamson et al. [52] automated vehicles could offer potential benefits by improving safety and reducing driver workload. Therefore, the incorporation of innovative technologies in automatic transmission vehicles can be key in reducing the severity of injuries.

3.6 Trip distance

The result shows that crashes involving automatic and manual transmission vehicles travelling a distance between 1 km and 200 km increases the likelihood of minor and incapacitating injuries respectively. Similarly, crashes involving manual transmission vehicles travelling a distance between 201 and 400 km increase the probability of minor and incapacitating injuries. Likewise, minor injury is likely to be increased for automatic transmission vehicles travelling a distance of 201 and 400 km. An automatic and manual transmission vehicle which is travelling a distance of 401 km–600 km has a probability of increasing minor injury. The same distance has the probability of increasing incapacitating injury for crashes involving manual transmission vehicles. The results suggest that crash incidents involving both automatic and manual transmission vehicles, within a specific distance range, are likely to increase minor or incapacitating injuries.

A study found that a driver's fatal injury from a traffic crash would increase when the distance gets longer [54]. The study further indicated that a relatively long distance would normally indicate that the driver would travel to an unfamiliar road environment and is likely to heighten severe crashes. Therefore, the length of the trip might influence the severity of injuries. When drivers are expected to cover longer distances, they often require more time behind the wheel. The extended periods of driving distances a driver plans to cover often result in higher speeds and deteriorates driving performance [55,56], which can substantially impair a driver's cognitive and physical abilities, leading to slower reaction times and reduced situational awareness [57].

3.7 Time of day

The result demonstrated that severity of injuries in relation to the time of day reveals that crashes which occurred between 6am and 9am and 4pm–6pm are associated with increased fatal injury for vehicles with either automatic or manual transmission. This finding emphasises the significance of considering peak traffic hours when examining crash-related injuries. In accordance with previous study, the results imply that injury severity that occurs at morning and evening peak is higher than other time periods [58] for both automatic and manual transmission vehicles. It could be that during peak hours, the traffic volumes influence crash severity because of anxiety and impatience [40]. Additionally, morning and evening peaks coincide with rush hours. During these times, drivers are more likely to be in a hurry to reach their destinations which result in aggressive driving behaviours, and subsequently contribute to fatal injury when crashes occur.

However, crash that occurred at the end of morning peak to noon (9am-12noon) and from noon to start of evening peak (12noon-4pm) is likely to decrease minor injury by −0.0120 and −0.0067 respectively for vehicles with automatic transmission and 12noon-4pm increase minor injury by 0.0039 for manual transmission vehicles. Further, vehicles with manual transmission involved in a crash between 9am and 12noon are likely to result in minor injuries, but decreased incapacitating and fatal injuries. The results, in line with the findings of study [59], indicate that drivers consistently drove slower in the late afternoon compared to other time periods, which is likely to decrease injury severity outcomes. The decrease in injury severity at off peak could also be related to low traffic volume [60]. However, minor injuries that occur during off-peak times might result from lack of patience and slower reaction times [40] among drivers of vehicles equipped with manual transmission. The results support the assertion that the time distribution might not align with the perception that daytime visibility is clearer and therefore safer [61].

3.8 Crash type

The results indicate that different types of crashes have varying levels of impact on severity of injuries for automatic and manual transmission vehicles. The head-to-head crash involving vehicles with automatic transmission increased the likelihood of both minor and fatal injuries by 0.0270 and 0.0321 respectively. However, head-to-rear crashes decrease minor and incapacitating injuries, whereas rollover crashes decrease the minor injuries by −0.0104, but increase fatal injuries by 0. 0818.

Regarding vehicles with manual transmission, head-to-rear crashes increase the likelihood of minor injuries by 0.0090, but decrease the chances of incapacitating and fatal injuries by −0.0052 and −0.0129. Rollover crashes, on the other hand, increase the likelihood of injury severity outcomes. Likewise, side hits increase minor and fatal injuries while head-to-head crashes increase minor injuries. This result contrasts with the prior study [65], which concluded that side collisions have insignificant effect on severity of injuries.

Studies on crash-related injuries have consistently shown that head-to-head crashes pose a greater risk of resulting in more severe injuries than other types of crashes [62,63]. The prevalence of one-way roads in Ghana might be a factor contributing to a high risk of severe injuries from head-on collisions, as it influences crashes between vehicles travelling in opposite directions. In head-to-head and side crashes, the occupants may be more vulnerable to injury due to the lack of structural reinforcements and specialised crash-avoidance systems found in certain other types of automatic vehicles.

Normally, head-to-rear crashes tend to decrease the likelihood of fatality [32,62]. One possible reason is that rear-end collisions often result in lower severity because the vehicles involved in a crash are usually travelling at low speeds and in the same line of travel [62]. Furthermore, rear-end collisions typically happen after both vehicles have started decelerating, leading to a less severe impact. However, consistent with a previous related study, the findings further suggest that rollover crashes significantly increase the likelihood of injuries or fatalities [64].

Moreover, the head-to-head crash parameter follows a random and normal distribution. It was observed that automatic and manual transmission, head-to-head crash parameter is random and normally distributed with a mean of 0.998 and 1.990 and standard deviation of 1.902 and 2.520 in the fatal and minor injuries respectively. This specifies that 70 % of the normal distribution is above zero and 30 %% is below zero for automatic transmission vehicles whereas for manual transmission vehicles 78.5 % of the normal distribution is above zero and 21.5 % of the distribution falls below zero. In other words, results suggest that head-to-head crashes involving vehicles with automatic transmission increase fatal injuries by 70 % and reduce the rate of fatal injuries by 30 %. Besides, vehicles with manual transmission involved in head-to-head crashes result in a 78.5 % increase in minor injuries and a 21.5 % decrease in minor injuries of the observation.

The result on crash involving vehicle with manual transmission further shows that for head-to-rear collisions, the crash parameter follows a random and normal distribution with a mean of 0.409 and a standard deviation of 1.817 in minor injuries, whereas rollover crashes, the parameter is also random and normally distributed with a mean of 0.670 and a standard deviation of 4.663 in fatal injury. Given these estimates, in head-to-rear crashes 58.9 % of the normal distribution for minor injuries is above zero, while 41.1 % is below zero, but for fatal injury in rollover crashes, 55.7 % of the normal distribution is above zero, and 44.3 % is below zero. This explains that manual transmission vehicles involved in head-to-rear crashes are likely to increase minor injuries by 58.9 % and reduce minor injuries by 41.1 %, while fatal injuries increase by 55.7 % and decrease by 44.3 % in rollover crashes. Consistent with a previous study, the findings show that head-on, rear-end, and rollover crashes are the primary crash type associated with injury severities [66], regardless of the vehicle type. Additionally, the study found that the nature of the crash influences the severity of injuries, regardless of the vehicle's transmission type [63].

3.9 Weather condition

It was observed that crashes occurring in rainy weather increases the likelihood of fatal injury by 0.0092 for automatic transmission vehicles and by 0.0079 for manual transmission vehicles. Moreover, crashes in rainy weather conditions increase the probability of incapacitating injury by 0.0136 for vehicles with automatic transmission, while for vehicles with manual transmission, the likelihood of such injuries decreases by −0.0152. The results align with previous studies that indicate an increased likelihood of fatal injuries in crashes during rainy conditions [21,67] for both manual and automatic transmission vehicles. This suggests that raining conditions are a contributing factor to higher injury severity among vehicle occupants, which is consistent with previous findings [68]. The increased risk of fatal and incapacitating injuries in rainy weather conditions is due to reduced visibility and slippery road surface, which reduce tyre traction and make it challenging for drivers to keep control of their vehicles. This supports the finding of a study that reported a higher likelihood of road crashes on wet and slippery roads compared to dry surfaces [69]. The reduced visibility caused by rain further compounds the hazards, as drivers may have difficulty noticing and responding to potential dangers in a timely manner. However, the lower incapacitating injury associated with manual transmission vehicles during rainy weather conditions may be due to patience. This corresponds with a previous study that found lower injury rates in foggy, snowy, rainy, and cloudy weather compared to clear conditions [67].

Similarly, crashes in a dusty environment increase the likelihood of minor injuries by 0.0078 for automatic transmission vehicles and 0.0059 for manual transmission vehicles. However, when a vehicle with manual transmission is involved in a crash in a dusty driving environment, the risk of incapacitating and fatal injuries decreases by −0.0033 and −0.0036 respectively. This explains that driving under dusty environmental conditions can obscure a driver's vision, which can lead to crash injury risks [67,70,71] for both drivers of automatic and manual transmission cars. This supports the finding that the causative factor in road traffic crashes is low-visibility weather conditions [72]. In sum, the results suggest that crashes in dusty environments are likely to lead to minor injuries, but have low risk of causing incapacitating and fatal injuries.

3.10 Roadway description

The result shows that crashes on straight roads significantly impact on injury severity with an increase in minor, incapacitating and fatal injuries for vehicles with automatic transmission. It was expected that vehicles travelling straight ahead are likely to be moving at a higher speed and could potentially cause fatal injuries [17,73,74]. A recent study also found that drivers tend to be less careful when driving on straight roads without any curves [75]. Therefore, the result suggests that vehicles with automatic transmission may have higher rates of incapacitating and fatal injuries during crashes on straight road alignments. At the same time, there may be a slight increase in the occurrences of minor injuries on straight roads for automatic transmission vehicles, potentially due to differences in vehicle dynamics or other factors like drivers being more alert [73].

It was further observed that crashes involving manual transmission vehicles on straight roads are 0.0208 more likely to result in minor injuries, while the likelihood of incapacitating injuries decreases by 0.0016. The reasons for this are complex and multifaceted, but some contributing factors to minor injury may include driver error, distraction, or lack of experience with manual transmission vehicles. The decrease of incapacitating results is contradictory to the commonly held belief that crashes in general increase the likelihood of injuries [73,74], regardless of the type of vehicle or the road. It is possible that certain characteristics of manual transmission vehicles or straight roads may decrease the risk of incapacitating injuries in a crash, but further research would be needed to confirm or refute such findings. Moreso, crashes on curve roads increase the likelihood of minor and fatal injuries by 0.0071 and 0.0093 respectively. This means that crashes on curved roads are more likely to result in both minor and fatal injuries [74]. This is probably caused by a mix of factors, such greater chances of losing control of vehicles, higher speeds when approaching curves [73] and reduced visibility when navigating curves [72].

3.11 Heterogeneity in means and variances of random parameters

To assess the heterogeneity in variables across the automatic and manual transmission vehicles model, the mean and variance of random parameters were examined. Analysis revealed that the automatic transmission vehicle model presented in Table 3 showed heterogeneity in the means of four random parameters, with two affecting the variances of two random parameters. Similarly, the manual transmission vehicle model in Table 4 demonstrated heterogeneity in the means of five random parameters, with four variables influencing the variances of three random parameters.

The results in Table 3 indicate that crashes occurring between 12noon and 4pm decrease the mean of minor injuries of the random parameter female drivers of automatic vehicles. These results demonstrate a notable decrease in minor injuries when females are behind the wheel during an hour of 12noon to 4pm. It is important to understand that the decrease in minor injuries does not necessarily mean that females are better drivers than male drivers. Rather, it may reflect broader societal influences that impact the safety of all drivers, including traffic patterns, road conditions, and other external factors. Besides, crashes occurring between 4pm and 6pm increase the mean of fatal injuries of the random parameter head-to-head collision involving automatic vehicles. Further, head-to-rear crashes increase the incapacitating injury of the random parameter heavy goods vehicle with automatic transmission, but decrease the incapacitating injury of the random parameter saloon cars. This means that more crash victims are expected to be incapable of performing activities after rear-end collisions involving heavy goods vehicles equipped with automatic transmission. The results emphasise that the significant weight of heavy-duty vehicles results in a greater impact force on occupants during rear-end collisions, which consequently increase the likelihood of incapacitating injuries [76]. Moreover, automatic transmission vehicles aged 11–20 years old, involved in a crash were found to increase the mean of incapacitating injuries of the random parameter saloon car. This result implies that higher incapacitating injury is expected when overaged automatic cars are involved in crashes. Regarding the heterogeneity in the variances of the random parameters, it was observed that head-to-rear crashes reduce the variances of random parameter female drivers and automatic saloon car variables. However, crashes during raining decrease the variances of random parameter automatic transmission cars indicator.

The result from the manual transmission vehicle model, as shown in Table 4 indicated that side hits were observed to be associated with an increase in the mean of minor injury of the random parameter buses. This implies that the likelihood of minor injuries is higher when buses with manual transmission are involved in a side crash. Additionally, the study noted that rainy weather conditions and dusty environments increase the minor injury of the random parameter head-to-rear crash of a manual vehicle. This result could be attributed to the vehicle's braking system being less responsive on wet road surfaces or driver vision being compromised in a dusty environment. Similarly, curved roads increase risk of minor injury of the random parameter head-to-head crash of a manual vehicle, suggesting that curves obstruct the driver's view of incoming traffic, which could lead to a crash injury. According to Atombo et al. [72], one factor contributing to the increasing rate of road traffic crashes is unseen oncoming traffic and vehicles' failure to stay within their lanes in a curve, leading to head-to-head crash in a curved road. Again, saloon cars with manual transmission are likely to increase the mean of fatal injuries of the random parameters' male driver and rollover indicators. Regarding the heterogeneity in the random parameters' variances, the findings further suggest that side hits lead to an increase in the variances of random parameter male drivers' indicators. In addition, a dusty environment increases the variances of the random parameter head-to-head crash variable. Dusty environments on the other hand decrease the variances of random parameter rollover crash, but curve roads increase variances rollover crash involving manual transmission vehicles.

4 Practical implications

The practical implications of this research emphasise the need to consider various factors, including transmission type, when addressing road safety. Risk of injury on the road is significantly influenced by various factors, including the driver's gender, level of experience, travel distance, time of day, weather conditions, type of road, type of crash, vehicle type and mode of transport.

One important finding is the gender-specific risks associated with transmission type. It was found that female drivers benefit from using vehicles with automatic transmission vehicles, as it increases the minor injuries while lowering the risk of fatal injuries. Female drivers also have a lower risk of both minor and incapacitating injuries in crashes involving both automatic and manual transmission vehicles. Conversely, male drivers have lower risk of incapacitating injuries in crashes involving both automatic and manual transmission vehicles. However, male drivers are related to an increase in minor and fatal injuries in crashes specifically involving manual transmission vehicles. These results highlight the importance of considering gender-specific risks and the type of transmission when promoting road safety and developing preventive measures. To address the risks of fatal injuries, it is important to promote automatic transmission vehicles as a safer option for female drivers. Public awareness campaigns should also be developed, focusing on defensive driving techniques for male drivers to address the increased risk of minor and fatal injuries in crashes involving manual transmission vehicles.

Driver experience is another crucial factor to consider. Young novice drivers are more likely to lower the risk of fatal injuries by driving automatic transmission vehicles, while they face a higher risk of fatal injuries when driving manual transmission vehicles. However, experienced drivers decrease the likelihood of both fatal and minor injuries regardless of the transmission type. This highlights the importance of implementing graduated licensing systems to gradually introduce novice drivers to manual transmission vehicles. Continued skill development among experienced drivers is also crucial for injury prevention on the roads.

The specific vehicle type and transmission are important factors when assessing injury risks in crashes. For saloon cars, automatic transmission increases the probability of incapacitating injuries, while manual transmission increases both minor and fatal injuries. However, in the case of pickup trucks and heavy goods vehicles (HGVs), automatic transmission decreases the likelihood of minor and incapacitating injuries, respectively. Conversely, manual transmission heavy goods vehicles and buses increase fatal, minor, and incapacitating injuries. Notably, crashes involving pickup trucks equipped with manual transmission are more likely to result in both minor and fatal injuries. These findings highlight the need for tailored safety measures and training specific to vehicle types and transmission systems to effectively mitigate injury risks.

The age of the vehicle in conjunction with its transmission type is also an important consideration. Automatic transmission vehicles with a low age are associated with a decreased probability of incapacitating and fatal injuries. However, as vehicles age, the likelihood of fatal injuries increases. Similarly, manual transmission vehicles within the low age bracket decrease the probability of incapacitating and fatal injuries, while over-aged manual transmission vehicles increase the likelihood of minor, incapacitating, and fatal injuries. To address the increased risk associated with ageing vehicles, it is important to consider implementing vehicle age restrictions or mandatory safety inspections for all vehicles. Additionally, regulations for vehicle retirement or replacement programs should be developed and enforced to reduce the presence of over-aged vehicles on the roads.

The study also indicates that public transport has a higher probability of increasing fatal injuries compared to private cars, regardless of transmission type. Private cars with manual transmissions are more likely to cause incapacitating injuries, while those with automatic transmissions have a lower probability of causing minor injuries. Targeted enhanced safety measures should be implemented in public transport systems to reduce the risk of fatal injuries. Providing proper training and skill development for private car drivers, especially those using manual transmissions, can also help mitigate the risk of fatal and incapacitating injuries.

It was also observed that specific distance ranges in crashes involving both automatic and manual transmission vehicles can increase the probability of minor or incapacitating injuries. To mitigate these risks, it is crucial to implement interventions such as improved road infrastructure, stricter enforcement of speed limits, and promotion of defensive driving practices. Additionally, encouraging the use of advanced safety technologies can further enhance safety in crashes within specific distance ranges.

The time of day and transmission type also play a significant role in injury severity outcomes. Crashes occurring during morning and evening peak hours pose an increased risk of fatal injuries for both automatic and manual transmission vehicles. However, crashes that take place at the end of the morning peak to noon and from noon to the start of the evening peak have different effects on injury probabilities. For automatic transmission vehicles, these times decrease the likelihood of minor injuries, while for manual transmission vehicles, they increase the probability of minor injuries. Furthermore, crashes involving manual transmission vehicles during the end of the morning peak to noon show a decreased likelihood of incapacitating and fatal injuries. To reduce injuries during peak hours, improvements in road design and infrastructure are necessary to enhance safety. Additionally, providing drivers with training programs focused on defensive driving and navigating high-traffic situations can significantly contribute to safer road conditions.

The study findings also shed light on the impact of crash types on injury severity. Head-to-head crashes in vehicles with automatic transmission increase both minor and fatal injuries. Conversely, head-to-rear crashes decrease minor and incapacitating injuries. Rollover crashes typically result in more severe injuries, increasing the likelihood of fatal injuries and decreasing the occurrence of minor injuries. For vehicles with manual transmissions, head-to-rear crashes are more likely to cause minor injuries, but decreases the risk of incapacitating and fatal injuries. Additionally, both side-hit and head-to-head crashes increase minor injuries, but side-hit crashes further increase the risk of fatal injuries. To minimise road traffic crashes and associated injuries, it is essential to implement safety measures such as enforcing safe driving behaviours, improving visibility, utilising collision avoidance technologies, and advocating for vehicle safety features and crash prevention measures.

Weather conditions also have an impact on injury risks. Crashes during rainy conditions increase the probability of fatal injuries for both automatic and manual transmission vehicles. Additionally, crashes during rainy conditions further increase the risk of incapacitating injuries for vehicles with automatic transmission, while the risk of incapacitating injuries decreases for vehicles with manual transmissions. Similarly, crashes in dusty environments increase the risk of minor injuries for both transmission types. However, crashes involving vehicles equipped with manual transmission in dusty driving environments show a decrease in both incapacitating and fatal injuries. To enhance safety during adverse weather conditions, it is important to promote cautious driving practices, address issues related to drainage and road surface conditions, maintain clear visibility through proper windshield wiper maintenance, and utilise tires with good traction.

Road type also plays a role in injury severity outcomes. Crashes on straight roads involving vehicles with automatic transmission are associated with a higher likelihood of minor, incapacitating, and fatal injuries. On the other hand, crashes involving manual transmission vehicles on straight roads have a slightly increased probability of resulting in minor injuries, but a decreased likelihood of incapacitating injuries. To mitigate these risks on straight roads, efforts should be made to enhance or implement driver assistance technologies for automatic transmission vehicles. Additionally, crashes on curved roads are also linked to a higher likelihood of both minor and fatal injuries. Policymakers can address this by improving road design and signage, and visibility by relying on highway system technologies to alert drivers about the potential risks in blind spots in curves.

4.1 Conclusion

Road traffic crashes are a leading cause of death and disability around the globe. Vehicle crashes involving manual and automatic transmission vehicles can result in serious injuries to drivers and passengers. Severity of injuries is key in road safety research as it helps to identify the factors contributing to the severity of injuries and develop appropriate safety measures.

There is a growing interest in the development of models to predict injury severity in vehicle crashes in recent years. One of the challenges in developing such models is to account for the heterogeneity in the injury severity of different crashes. Previous related studies have used traditional regression models to predict crashes involving manual and automatic transmission vehicles. However, these models do not account for the variation in the injury severity across various crashes and may not capture the intricate interactions between the different factors influencing injury severity. Therefore, a Random Parameter Mixed Logit Model (RPMLM) was employed to analyse severity of drivers’ injuries in crashes with manual and automatic transmissions. Heterogeneity in means and variances were also considered to capture the variations in severity of injuries across different crashes. The RPMLM allows the estimation of the effects of various factors, such as driver sex, driver experience, range of distance, time of day, weather conditions, road type, crash type, vehicle type, and transport type, on injury severity while accounting for the heterogeneity in the data.

Overall, results suggest that type of transmission in a vehicle impacts injury severity outcome in a crash. It was observed that use of manual transmission is associated with a higher risk of incapacitating and fatal injuries compared to automatic transmission. Specifically, female drivers benefit from automatic transmission vehicles, reducing the risk of fatal injuries and increasing minor injuries. Male drivers decrease incapacitating injuries in crashes involving both transmissions but have higher risks of minor and fatal injuries in manual transmission crashes. Novice drivers are safer in automatic transmissions, while experienced drivers show reduced risks regardless of transmission. Transmission types affect injury probabilities differently for vehicle types, with manual transmissions increasing risks in saloon cars and pickup trucks, and automatic transmissions reducing risks in heavy goods vehicles. Vehicle age affects injury risks, with low age vehicles lowering risks in both transmissions. Public transport has higher fatal injury risks, and private cars show transmission-specific risks. Factors such as distance to be covered, time of day, and road conditions also impact injury probabilities differently for each transmission type. These findings inform policymakers, manufacturers, and drivers in implementing targeted interventions and safety measures to promote road safety. This can help identify emerging trends, assess the effectiveness of existing policies, and inform the development of evidence-based interventions to further enhance road safety.

The relationship between transmission type and injury severity may be complex and might differ depending on the driver's attributes and the type of vehicle involved in the crash. Therefore, future studies could examine the relationship between transmission type and injury severity across various vehicle types and consider additional factors that may impact injury severity. The use of sophisticated statistical models such as the random parameter can help to account for heterogeneity in the data and to control for confounding factors, which can improve the understanding of the various factors that impact injury severity in motor vehicle crashes.

Ethics statement

The study does not require ethics approval. It used anonymised records and datasets on road traffic crashes and casualties, for which permissions have been granted, and individuals cannot be identified.

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Charles Atombo: Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

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

Acknowledgements

I appreciate the support of the National Road Safety Authority, Insurance companies, and the Driver and Vehicle Licensing Authority for providing the data for the analysis.
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