Factor analysis

Factor analysis has been used extensively in various fields, including psychology, education, and sociology, to analyze individual or group characteristics based on the data collected by various surveys [25–27]. In survey-based or various data-driven research, it is essential to verify whether each data item effectively explains the factors that the researcher intends to investigate. In other words, it is crucial to statistically examine the relationship between the survey items and the factors that researchers want to explain. For example, in this study, we aimed to confirm which factors in the daily lives of taxi drivers correspond to survey items and determine whether these factors have an impact on the likelihood of taxi crashes. Through this process, the insights gained from the survey results can be justified. Additionally, factor analysis can be particularly helpful in situations where there are high correlations among the observed variables. In parametric models, multicollinearity can lead to unstable parameter estimates and make it challenging to identify the unique contributions of each variables. Factor analysis helps address this issue by creating orthogonal (uncorrelated) factors, reducing the interdependency among variables and providing more reliable estimates.

Factor analysis has been used in the field of education to evaluate the satisfaction of classes or identify factors that influence the quality of lectures [26,28–30]. Similarly, in the field of public health, numerous studies have utilized factor analysis to examine the correlations between personal characteristics, such as age, gender, race, lifestyle habits, and brain or cardiovascular diseases [31–33]. The factor analysis, e.g., principal component analysis, allows them to condense multiple observed variables into a smaller set of factors that capture the essential information from the data. In these various fields, factor analysis is also used to reduce the dimensions of unquantified data and devise efficient alternatives.

In the field of traffic safety, as in other disciplines, some studies have utilized factor analysis. Syed and Khan [25] and Susilawati and Nilakusmawati [34] used factor analysis to examine socio-economic indicators and general conditions of commercial vehicles. Indeed, they identified the factors that impact mobility and safety of public bus transportation service in order to enhance the efficiency of public transportation operations. In addition, Ma et al. [35] and Zhang et al. [36] used factor analysis based on commonly available data, such as gender, age, driving experience, and the type of vehicle, to investigate risk factors in traffic safety. However, variables that capture the actual drivers’ characteristics or living environment were not included in these studies.

Taxi crashes, the focus of this study, have various intrinsic risk factors of occupational drivers. A detailed analysis incorporating data from multiple sources, including surveys (the primary method for collecting information on the inherent characteristics of drivers and their companies), is required to obtain practically meaningful results. Therefore, factor analysis is needed to analyze these datasets accurately and efficiently.

Hierarchical regression model

Extensive studies have been conducted to identify the risk factors that influence traffic crashes. However, traditional regression models have limitations in accurately identifying the various factors that impact traffic crashes. In order to derive unbiased estimation results through traditional regression models, the analysis data must satisfy the basic assumptions of the model. However, traffic crash data have characteristics that make it difficult to maintain the independence of residuals, which is one of these basic assumptions [37]. To ensure the independence of residuals, it is necessary to avoid any correlation among the individual traffic crashes under analysis. Nevertheless, real-world situations often exhibit correlations among individual traffic crashes occurring in the same vehicle, on the same road, or within the same area. Traffic crash data with such characteristics can be considered as data with a hierarchical structure, requiring the application of models that consider within-group correlations, with the same road or area treated as the upper-level group.

Crashes involving commercial vehicles exhibit a hierarchical structure and differ from general traffic crashes. In this regard, Park et al. [38] constructed a hierarchical model considering the correlation between individual crashes based on the transportation company for taxis, buses, and cargo vehicles. Using data from 86,622 commercial vehicle traffic crashes over five years (2010-2014), a Cross-Classified Multi-Level Model (CCMM) was developed, taking into account the influence of the company and regional heterogeneity. As a result, the model’s goodness-of-fit improved, enabling more precise identification of the causes of traffic crashes. Kim et al. [39] constructed a hierarchical model, focusing on the high fatality rate of pedestrian crashes in Korea using three years of data (2011-2013). The study identified that not only the micro-level characteristics of pedestrian crashes but also factors at the municipal level, such as population density, proportion of elderly population, and fiscal autonomy, influenced the occurrence of pedestrian crashes. It is a reasonable approach to apply a hierarchical regression model to traffic crash data with such a hierarchical structure.

An attempt has been made to elucidate the intrinsic factors of corporate taxi crashes through the construction of a hierarchical model using survey-based data [40]. However, due to the endeavour to explain multiple factors within a single model, challenges related to the correlation and causality among them were encountered. This can lead to undisclosed type I or type II errors, highlighting the need to control for the characteristics of these factors. Tanglai et al. [41] analyzed the influence of personality and attitude on risky driving behavior among the drivers of public vans. However, studies examining the intrinsic factors of public vehicle drivers, similar to the present study, are scarce.

Additionally, considering not only crash-related data but also a variety of variables including the personal attributes of transportation workers necessitates a re-evaluation of methodologies to overcome the uncertainty associated with these variables [42,43]. This comprehensive approach aims to enhance the accuracy and reliability of the analysis by addressing potential variability and ensuring robust outcomes in the study of transportation safety.

In this study, we deal with hierarchical data that includes various intrinsic risk factors. As mentioned earlier, taxi crashes involving taxi drivers are influenced not only by individual drivers but also by the company they belong to. Specifically, the occurrence of crashes varies depending on factors such as the company’s working conditions and the level of safety management systems. Additionally, important factors include the individual driver’s education level, income, driving distance, working days, and personality traits. To account for this hierarchical structure, we applied hierarchical modeling in this study. Hierarchical modeling allows us to consider the influence of both individual drivers and the companies they work for on the occurrence of crashes. By using hierarchical modeling, we can better understand the complex interactions and relationships between various factors and assess their impact on crash likelihood.

Research process

In this study, variable selection was conducted based on a dataset obtained through a survey administered by a public institution, i.e., the Korea Transportation Safety Authority. The selected variables exhibited high correlations or causalities among factors, necessitating dimension reduction. Principal Component Analysis (PCA), a technique in factor analysis, was used to reduce the dimensionality of the variables. By parameterization, the characteristics of each factor were identified. The data used in this analysis pertained to taxi drivers in the corporate taxi category, allowing for hierarchical differentiation due to the nature of the dataset being specific to individual companies. Using the derived hierarchical and differentiated new variables, modeling was conducted through Bayesian hierarchical probit regression with the occurrence of FI crashes as the dependent variable. The resulting model identified the risk factors associated with taxi drivers based on their respective companies, and the goodness-of-fit of the model was verified through the examination of Deviance Information Criterion (DIC) and Intra-Class Correlation (ICC) values.

Principal component analysis

In this study, factor analysis was used as a statistical technique to explore and explain the variability among correlated variables, which includes both quantitatively observed data and variables that are inherently difficult to quantify. Factors, by definition, represent latent variables with relatively fewer observable measures compared to the collected quantitative data. Factor analysis was used primarily for explanatory purposes, i.e., to identify and incorporate these latent factors into models. It can be categorized into exploratory factor analysis (EFA), confirmatory factor analysis (CFA), and correlation analysis (CA), each of which are suitable for different research objectives. EFA is used when survey data are available, allowing for the exploration of underlying factors when the certainty of the information is limited for variables with surface-level observations. Alternatively, it is also used when currently there is no statistical or theoretically established framework.

In this study, we used the EFA to identify latent factors using two distinct approaches, i.e., PCA and Common Factor Analysis. For the purpose of this research, the focus was placed on utilizing PCA. Through factor rotation, the exploration of the underlying factors was conducted, allowing for a clear understanding of how variables are relatively heavily loaded onto specific factors. In addition, the computation of inter-variable correlations facilitated the assessment of factor loadings, contributing to the determination of variables’ associations with the identified factors. The Kaiser-Meyer-Olkin (KMO) Measure, Bartlett’s test of sphericity, and communalities were computed, enabling the establishment of factor interpretability, while factor loadings provided valuable insights into the explanatory power of the identified factors.

The KMO Measure is an index that is used to assess the extent to which the correlations among variables can be explained adequately by other variables. Generally, a KMO value of 0.7 or higher is considered acceptable for factor analysis [44]. Bartlett’s test of sphericity is a metric that is used to evaluate the goodness-of-fit of the exploratory factor analysis model. The threshold for the significance level and the acceptance of the p-value vary depending on the desired level of confidence, but typically, a significance level of 0.05 within a 95% confidence interval is used as a criterion [45]. Communality refers to the proportion of variance in a variable that is accounted for by the extracted factors during the analysis. Variables with communality values below 0.4 generally are considered to have low common variance, and therefore they are excluded from the analysis [46]. After factor rotation, factor loadings can be computed from the rotated component matrix. These loadings serve as indicators for determining the classification of each factor. Usually, factor loadings of 0.4 or higher are considered significant, and when the rotated sum of squares loading is higher for a particular factor, the corresponding variables are classified under that factor [47].

The determination of the number of factors in Factor Analysis was based on the cumulative proportion of variance and eigenvalues derived from the analysis. Eigenvalues represent the sum of squared loadings for each factor and serve as an indicator of the explanatory power of a particular factor [48]. Eigenvalues were considered with respect to a threshold value of 1.0. Factors that yielded eigenvalues equal to or greater than 1.0 were retained for further analysis and grouping purposes. These factors were deemed to possess sufficient explanatory capacity to be considered meaningful in the study [49].

Bayesian hierarchical probit regression

Bayesian hierarchical probit regression is a methodology that commonly is used in analyzing traffic crashes, as shown in Fig 1. It is a suitable approach for analyzing data with a hierarchical structure [50]. In this study, the hierarchical model was structured with the upper level representing the taxi companies and the lower level representing individual drivers.

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Fig 1. Hierarchical structure of corporate taxi crashes.

https://doi.org/10.1371/journal.pone.0314743.g001

The limitation of traditional probit regression models is that they do not account for the correlation between lower-level crashes of drivers based on upper-level (i.e., corporate taxi company) factors in the hierarchical data analysis. If the regression model doesn’t account for the correlation between crashes across different companies, it could result in underestimating the standard errors of the coefficient values for the independent variables [51,52].

(1)

In this equation, is the probability that the binary outcome variable, , takes the value of 1 for the jth observation within the ith group, given the predictor variable . Φ denotes the cumulative distribution function of the standard normal distribution. The parameters of interest to estimate are and , which represent the fixed effects associated with the predictor variables. The term represents the random effects at the company level, capturing the unobserved heterogeneity between groups. Finally, represents the residual error term. Estimating the hierarchical probit model typically involves using advanced statistical techniques, such as maximum likelihood estimation or Bayesian methods, due to the complexity of the model. These estimation methods account for the correlation within groups and provide estimates of the fixed and random effects [53–55].

In order to conduct Bayesian hierarchical regression, an assessment of the model’s applicability was necessary, and it was performed using the ICC. The ICC indicates the proportion of variance accounted for by the upper level compared to the lower level, and this allows us to assess the extent to which lower-level crashes are influenced by upper-level factors. A high ICC value indicates a strong influence of the upper-level factors. Typically, a threshold of 5% or higher is used to determine the applicability of the model [51].

(2)

In the Bayesian paradigm, similar to the probit used in this study, various measures, such as Bayesian coefficients, the Bayesian Information Criterion (BIC), and the Watanabe-Akaike Information Criterion (WAIC) are used to evaluate and compare the performance of fitted models [56]. In this study, the DIC is employed as an indicator to evaluate model fit. A lower DIC value signifies a better model fit [57].

(3)

Where represents an estimation of fit, and a reduction in its value indicates an increase in log-likelihood, thereby suggesting an improved model fit. The serves as a penalty for the complexity of the model, and this ensures that there is a fair comparison between competing models with different degrees of complexity [58]. In this study, the Markov Chain Monte Carlo (MCMC) method was used for model estimation, which enables the calculation of the DIC.

Data preparation

This study focuses on the analysis of traffic crashes using data collected over the three years from 2017 to 2019. The study aims to explore the factors that contribute to traffic crashes and their implications for road safety. A survey was conducted to gather the relevant information needed to construct the variables for the analysis. Crash data has been integrated with various survey-derived variables of taxi drivers to establish a dataset that confirms whether intrinsic driver-related characteristics affect the risk of crashes. The data utilized in the analysis consisted of crash data and survey data from corporate taxi drivers, which were matched within the Korea Transportation Safety Authority system to form a unified dataset.

Fusion of crash data and survey data.

This study was focused on conducting an analysis of human factors, specifically the “Black Box,” that contribute to traffic crashes by surveying domestic transport workers in the transportation industry. Through the survey, data were collected and categorized into five distinct characteristics (Table 1), i.e., 1) the working environment, reflecting direct responses from transport workers during their work shifts; 2) the characteristics of the company, which encompasses system and education-related aspects based on the safety management criteria assigned to individual transport workers; 3) living conditions associated with the transport workers’ living environments; 4) physical condition, pertaining to individual’s health status; and 5) the driver’s characteristics, encompassing personal traits and passenger interactions.

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Table 1. Data description for company and driver levels.

https://doi.org/10.1371/journal.pone.0314743.t001

The data were collected based on a survey of 1,060 participants, and the analysis consisted of a total of 62 factors, which were categorized separately based on five selected characteristics and the level of the data. Then, these variables were restructured and reduced to 29 factors through dimension reduction, resulting in a reduction of 53.23%. The correlation among all variables was taken into consideration during the restructuring process. For the restructure, PCA was conducted to determine the commonality among the independent variables and to calculate the factor loadings. Exploratory factor analysis was performed using varimax rotation to extract the explanatory variables and to reduce the dimensionality of the data further. The values of the grouped variables were recalculated and used as independent variables in the Bayesian hierarchical probit model. The crash occurrence of taxi driver used as the dependent variables were collected and managed by the Korea Transportation Safety Authority, and the data were matched to all participants who responded to the survey.

Principal component analysis

A survey was conducted and the data from system collection items were utilized as variables among 1,060 taxi drivers. The variables were grouped as presented in Table 2, and the component matrix and interpretation according to each variable as shown in Table 3.

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Table 2. Output of principal component analysis for the company level.

https://doi.org/10.1371/journal.pone.0314743.t002

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Table 3. Output of principal component analysis for driver level.

https://doi.org/10.1371/journal.pone.0314743.t003

The PCA analysis was performed on input variables representing various types of basic states. The output variables were derived based on a loading threshold of 0.4, indicating the variables that showed significant influence on the data. All of the variables were grouped and interpreted effectively, undergoing the reparameterize process. Through this process, each variable was appropriately named according to its characteristics, resulting in the reconfiguration of the dataset for regression analysis. This restructured dataset serves as the input data for the Bayesian hierarchical probit model, with working environment and characteristics of company variables designated as the upper-level variables in the hierarchy, representing the company-related aspects.

When reparameterized from the original raw data, some variables may have loading values that are either negative or a mix of positive and negative values. In such cases, the interpretation of the reparameterized variables can differ from the original data’s meaning. For instance, the variable “each person owns a car” includes both a (−) value “working two shifts a day” and a (+) value “each person owns a car,” typically representing situations where respondents can only provide opposing responses to the original variable. Therefore, in such instances, one of the variables is selected for building the regression model. Another example is “social relationship,” where all included input variables have negative loadings, resulting in reparameterized variables with opposite meanings. Such cases offer various interpretations based on the characteristics of the loading values derived from PCA, and all possibilities were considered when utilized in the analysis.

Bayesian hierarchical probit regression

We developed a hierarchical traffic crash model for corporate taxis using a selected set of independent variables from the hypothesis testing stage, and the occurrence of crashes among taxi drivers in the past three years as the dependent variable. To assess the applicability of the Bayesian hierarchical probit model, we calculated the ICC, resulting in a value of 33.98% (Table 4). This result indicated that the construction of a hierarchical crash model is appropriate. The ICC value implies a substantial variability in individual taxi driver crash rates at the lower level, which is attributed to differences among upper-level taxi companies. In other words, the occurrence of crashes among taxi drivers varies significantly depending on the taxi company they belong to. A hierarchical model is necessary to identify the factors that influence this variability. Therefore, our findings demonstrate the necessity of a hierarchical approach in exploring the factors that contribute to the variation in crash occurrence among taxi drivers based on their affiliations with different taxi companies.

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Table 4. Performance of the Bayesian hierarchical probit Model.

https://doi.org/10.1371/journal.pone.0314743.t004

To construct the regression models, we examined the significance level of each variable, and those variables that did not reach a statistical significance level of 90% based on the 0.1 criterion were excluded from the model. To prevent multicollinearity issues among the variables, we assessed the Variance Inflation Factor (VIF) and ensured it did not exceed 10 [59].

After constructing the Bayesian hierarchical probit model, we set the dependent and independent variables identically and built comparative models (i.e., conventional logit and probit models and Bayesian hierarchical logit model). As a result, the DIC, which is used to assess the fit of the model, shows that 1291.248 for the Bayesian hierarchical probit model, 1293.724 for the Bayesian hierarchical logit model, and 1,463.893 for the general logit model (Table 4). This indicates that the Bayesian hierarchical probit model demonstrates a better fit compared to the conventional and Bayesian hierarchical logistic model.

As shown in Table 5, in the analysis at the company level (2-level), it was observed that the probability of traffic crashes decreases as the management of drivers’ fatigue levels are increased by the company. This factor includes management of lack of sleep, managing the driving hours, management of drivers’ breaks, and management of the psychological status. This finding supports the rationale that fatigue management at the company level is crucial, and it highlights the need for a more systematic approach to ensure the traffic safety of the drivers. Specifically, the factor “the need for fatigue measuring equipment” emerged as a significant factor at the driver level (1-level), indicating that establishing a fatigue management system within the company can effectively reduce traffic crashes [60–62].

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Table 5. Estimation results of the Bayesian hierarchical probit Model.

https://doi.org/10.1371/journal.pone.0314743.t005

The next noteworthy result pertains to disease-related factors. These factors are manifested as “driver crashes and disease management” at the upper-level, and at the lower- level, they include “importance of driver’s health care” and “digestive system/Kidney and urological diseases.” In fact, the presence of diseases among drivers is associated with other conditions, leading to negative synergistic effects [63]. Various studies have indicated that these diseases, as well as the medications taken for them, can have a direct or indirect correlation with traffic crashes [64,65]. Therefore, it can be observed that it is possible to mitigate the occurrence of traffic crashes by implementing health management at both the company and individual levels [66].

In addition, various intrinsic factors such as “social relationship” was found to be included in the analysis results, increasing the probability of traffic crashes, while “each person owns a car” and “the necessity of preventing passenger violence” were found to decrease it. The variable “each person owns a car” was reparameterized from the raw data as a variable related to the rotational shift pattern at the company level, and it is included as a 2-level variable. Research findings suggest that crashes involving taxi drivers who do not own the vehicle they operate have a higher likelihood of engaging in risky driving behavior compared to those who own their vehicles [67]. This indicates a close relationship between intrinsic factors, such as moral laxity and risky driving behavior. Some studies also have revealed a significant correlation between the social relationships of drivers and the occurrence of traffic crashes, highlighting the need for targeted management for specific drivers [65]. Furthermore, research has consistently shown that traffic crashes resulting from passenger types and behaviors are prevalent, emphasizing the importance of company-level education and regulations implemented by government or public institutions to mitigate the probability of taxi-related crashes caused by such issues.

Implications for preventing taxi crashes

Regarding the results of model construction, at the company level, taxi crashes (excluding personal taxi crashes) were found to be influenced by the management of drivers by the transportation company. In addition, at the driver level, it was found that the more importance the driver placed on health management and the need for fatigue measurement equipment, the more negative impact it had on traffic crashes. In Korea, commercial vehicle companies have the authority to manage affiliated drivers, but only a few companies manage fatigue or health. As long as it does not violate the Labor Standards Act or the contractual obligations between the commercial vehicle company and the driver, fatigue management for drivers is not strongly emphasized. In the Passenger Transport Service Act in Korea, safety inspections of transportation companies are conducted mainly on vehicles, and there are limitations in checking drivers’ compliance with recommended rest time. Although all commercial vehicles in Korea have a digital tachograph that records driving time, rest time, and risky driving behaviors, it is not utilized to punish drivers or commercial companies. However, it can be used by government agencies or transportation companies for driver education purposes.

Nevertheless, transportation companies do not actively educate or check fatigue management for drivers. Research on the objective determination of the correlation between driver fatigue and traffic crashes in Korea is limited, so it has not been firmly established institutionally. In contrast, in the United States, the National Transportation Safety Board (NTSB) revealed that fatigue was the leading cause of 31% of large truck fatal crashes based on the analysis of 182 crashes in 1990. In addition, the Federal Motor Carrier Safety Administration (FMCSA) stated that fatigue was the cause of 13% of severe commercial motor vehicle crashes. As a result, the National American Fatigue Management Program (NAFMP) for commercial motor vehicle drivers has been jointly researched and implemented by transportation companies, drivers, and research institutions in the United States for several years. The program’s manual covers transportation companies’ culture, education, and training, sleep disorder examination and treatment, fatigue monitoring technology, and scheduling. In Korea, legislation regarding fatigue and disease management for drivers by transportation companies should be prioritized, and after legislation, equipment to measure driver fatigue should be developed and disseminated.

Looking at another factor at the driver level from the results of model construction, it was found that drivers with digestive system diseases or kidney-related diseases positively impacted traffic crashes. Since individual medical data are susceptible, in this study, individual drivers’ traffic crash records were matched and analyzed based on surveys rather than individual medical data. Although the data in this study are based on survey results and not individual medical data, they have significant meaning if the reliability of these data is ensured. Taxi drivers work in shifts, work long hours sitting, and face high job-related stress, which can negatively affect health. These health implications can lead to drivers’ inattention, drowsiness, and cardiovascular diseases, and the result is likely to be adverse impacts, including traffic crashes. In particular, in Korea, the number of elderly drivers in commercial taxis is increasing, so it is urgent to check and manage the health status of drivers. There is a case in Queensland, Australia in which, according to the 2011 Queensland Work Health and Safety Act, taxi company operators should guarantee the health and safety their taxi drivers. Taxi company operators must register shift schedules for no more than 12 hours, register for no more than six days per week, and provide adequate rest time. They also must report to the company anything that affects the drivers’ fatigue. In addition, the law mandates that taxi companies install security devices, such as cameras and emergency buttons, to respond to passengers who threaten the safety of taxi drivers. In the analysis results of this study, taxi drivers who responded to the necessity of safety devices for dealing with violent passengers also had reduced traffic crashes.

The Korea Transportation Safety Authority in South Korea currently manages taxi and bus drivers, but the system lacks adequate periodicity and comprehensive management structures. To address the high proportion of traffic crashes involving commercial vehicles such as taxis and buses, it is crucial to integrate the intrinsic factors of transportation workers into the management system. This study highlights the need for collecting and managing accident data across various commercial vehicles, including corporate and individual taxis, buses, and Demand Responsive Transport (DRT) vehicles. By analyzing this data, the specific characteristics of each transportation company can be better understood, leading to more systematic and effective management strategies. Such an approach is expected to significantly reduce traffic crashes involving commercial vehicles and lower overall societal costs.