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Modelling the effect of Traffic safety culture on road
fatalities: Linear and Nonlinear Stochastic Frontier Analysis
Mohammad Mahdi Mozaffaria
aDepartment of Industrial Management,
Imam Khomeini International University, Qazvin, Iran
E-mail: mozaffari@soc.ikiu.ac.ir
Mohammadreza Taghizadeh-Yazdib,
*
bDepartment of Industrial Management, Faculty of Management,
University of Tehran, Tehran, Iran.
E-mail: mrtaghizadeh@ut.ac.ir
Abdolkarim Mohammadi-Balanic
cDepartment of Industrial Management, Faculty of Management and Economics,
Tarbiat Modares University, Tehran, Iran
E-mail: a_mohammadi@modares.ac.ir
Salman Nazari-Shirkouhid
dDepartment of Industrial and Systems Engineering,
Fouman Faculty of Engineering,
College of Engineering, University of Tehran, Iran.
E-mail: snnazari@ut.ac.ir
Seyed Mohammad Asadzadehe
eDepartment of Electrical Engineering,
Technical University of Denmark, Denmark
E-mail: semoasa@elektro.dtu.dk
*
Corresponding author at: Department of Industrial Management; Faculty of Management; University
of Tehran, Tehran, Iran. P.O. Box: 14155-6311; Postal Code: 1411713114; Tel: +98(21)61117761
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Modelling the effect of Traffic safety culture on road
fatalities: Linear and Nonlinear Stochastic Frontier Analysis
Abstract
The literature on measuring road safety culture has been dominated by the use of
questionnaires. Some researchers criticize this approach for the untraceable relationship
between the questionnaire items and traffic safety culture, the disagreement between the
respondents’ thoughts and behavior, and the social desirability bias. This paper aims to use
time-variant stochastic frontier analysis (SFA) to quantitatively estimate the effect of road
safety culture on road fatalities. This study contributes to the safety culture assessment by
proposing a new methodology with two new features. Firstly, its parametric and flexible nature
allows using any type of linear or nonlinear frontiers to describe the relationship between
system characteristics and fatalities. Secondly, this analysis is purely data-driven; therefore,
there is no need to use qualitative methods like questionnaires. The real-world applicability
and significance of the proposed SFA framework are illustrated by evaluating the effect.
Results show the robustness of SFA for determining the effect of road safety culture on road
fatalities.
Keywords: Road Safety culture; Traffic safety culture, Road fatality; Transportation;
Stochastic frontier analysis; linear and logarithmic models
1. Introduction
Traffic safety culture (TSC) is a relatively new concept in the field of traffic safety, which
is increasingly gaining the attention of the transportation industry as well as the academic
society for being a fundamental and more sustainable approach toward zero fatality. It is almost
diminishing the traditional alternative frameworks (Coogan et al., 2014; Lewis et al., 2019;
Timmermans et al., 2019; Ward & Özkan, 2014).
Although the concept of traffic safety culture was introduced by Zaidel (1992), the term
safety culture itself may be traced back to the post-accident report of the 1986 Chernobyl
disaster by the International Nuclear Safety Advisory Group (1986). A variety of influencing
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factors has been identified in the literature since then. Managerial and organizational
involvement in safety culture, communications on incidents and changes in plans, commitment
to safety, behavioral culture, and personality traits are referred to as the most important
contributing factors to the safety culture (King et al., 2019; Mearns et al., 2013; Nordfjærn et
al., 2014; Xie & Zhang, 2019). Safety culture is finding its place among the critical national
and global issues. For example, the goal number 3.6 of the United Nation’s 2030 Agenda for
Sustainable Development (2015) has exclusively targeted to halve the current annual 1.35
million deaths and 50 million injuries caused by road traffic accidents (World Health
Organization, 2018) by 2030, marking the importance of TSC.
Similar to the term ‘culture,’ the academic literature has not reached an accord on the
definition of traffic safety culture, although many studies have attempted to present a general
definition to cover the diverse concepts in the field (Ward et al., 2019). Existing definitions
seem to be presented according to the context of the study rather than the TSC in general
(Guldenmund, 2000). Since traffic safety culture implies a collective behavior, many of the
studies in the literature have defined TSC using other fields that deal with the collective
behavior of humans, especially organizational and social sciences. Such approaches define
traffic safety culture under the wider umbrella of organizational safety culture (Nævestad et al.,
2019) or safety citizenship behavior (Wishart et al., 2019), arguing that TSC is weaved into a
broader culture and should be interpreted within the boundaries of the dominant culture.
Organizational safety culture is defined as any facets of the organizational culture that is related
to safety (Antonsen, 2009; Tear et al., 2020). Organizational safety climate is the temporary
appearance of the organizational safety culture and can be measured quantitatively (Huang et
al., 2016; Rao, 2007). Edwards et al. (2014), based on Edwards et al. (2013), defined TSC as
an amalgamation of some interacting social and behavioral building blocks, including
underlying assumptions, beliefs, values, and attitudes that the members of a community share.
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This unified system conducts a cloud of interactions with the underlying layers of the
community and influences behaviors related to TSC. Edwards et al. (2014) did not bound the
term community to a certain type of grouping of humans; hence, applying this definition, in
any case, needs further narrowing this term. However, they state that this boundary should not
go beyond national communities, which is also implied by Atchley et al. (2014) and
Timmermans et al. (2019). While applying the concept of organizational safety culture to the
firms active in hazardous industries, Nævestad & Bjørnskau (2012) mentioned that the TSC in
non-professional and professional drivers could be measured by two groups within a nation
(local communities and nations) and one group whose boundaries are beyond a nation (peer
groups).
Ward et al. (2019) proposed an integrated definition based on a six-layered model that
encompasses individuals to national norms and beliefs. The model is founded on ten principles
and can help develop strategies for TSC improvement in each of the six layers of the society.
Instead of defining what TSC is, Girasek (2012) identified four aspects that a positive TSC
should possess: (a) active involvement of the government in topics relating traffic safety, (b)
careful monitoring of drivers with frequent records of driving under the influence (DRUI), (c)
extensive discouragement for speeding, and (d) heavily abstaining aggressive driving. (Ward
et al. (2010) highlighted the role of the perception of the accepted behaviors and the expected
norm-violation punishments in the peer group as the pillars for defining TSC. This definition
covers a variety of behaviors, including risky and protective ones, in addition to the acceptance
or rejection of the traffic safety interventions made by the peer group itself or by government
agents. TSC’s definition by Ward & Özkan (2014) suggests that values, beliefs, attitudes,
perceived norms, and perceived control are the key aspects of TSC. This implies that
revolutionizing the traffic safety culture requires immense adjustments in hidden and explicit
layers of society, including the propagation of practices that make citizens prioritize safety to
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other issues, facilitation of the emergence and progression of transformational leaders, and
development of incentive programs that accelerate changes in TSC. Guldenmund (2000)
reviewed the literature on safety climate and distinguished three levels for studying the safety
culture: (a) basic assumptions (culture’s core functionalities), (b) espoused values (safety
attitudes and climate), and (c) artifacts (cognitive and behavioral responses as the results of
safety climate). Uncertainty is identified as a major player in TSC. In fact, taking risks and
avoiding ambiguity are recognized as the two underlying features of the traffic safety culture.
The concept of TSC is not confined to the drivers. Traffic safety culture has encompassed
the beliefs, attitudes, and behavior of pedestrians and upstream governmental policy-making
organizations in recent studies. It is worth noting that in this study, the term traffic safety culture
refers to the users of roads and the culture of the legislative and regulatory agencies who
develop policies and establish programs in this gamut. The effect of traffic safety culture is
twofold in such a conception of the system. In legislative bodies, TSC affects the legislative
process as well as the content of the laws passed. Drivers and pedestrians are influenced by
means of the acceptance or rejection of the risk (Ward & Özkan, 2014).
Nordfjærn et al. (2014) proposed a two-dimensional approach for the theoretical
conceptualization of TSC. The first approach suggests that TSC can be best described by the
data on various characteristics of the society’s culture. Hofstede’s five-dimensional model of
culture (Hofstede, 1984) is one of the popular models to be used in this approach (Allik &
Realo, 2004). The other approach considers road traffic culture as a symbol and is measured
individually (Geertz, 1973). This approach is built around how people understand the culture
and communicate it with each other as a symbol.
The existing literature contains evidence that safety culture contributes to safety
performance (Choudhry et al., 2007; Craig et al., 2005; Duarte et al., 2017; Morrow et al.,
2014; Park & Kim, 2018; Qayoom & H.W. Hadikusumo, 2019, 2019; Zhang & Lin, 2018;
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Mozaffari et al., 2021). There is also evidence from a similar relationship in the field of traffic
safety (Atchley et al., 2014; Nævestad et al., 2014). The risky behavior of the youth is one of
the concerning issues. Tilleczek (2004) found that cultural and contextual factors may affect
the fatality rate of young drivers. Özkan & Lajunen (2007) conducted a factor analysis on
various cultural and economic variables of 46 nations and showed that the unintentional
fatalities are composed of three components, one of which is traffic safety. Özkan et al. (2006)
hired negative binomial regression analyses and came to that drivers’ characteristics
significantly affect the frequency of accidents. However, the intensity of the relationship differs
among the six studied countries. Nordfjærn et al. (2014) gathered samples from four clusters
consisting of eight countries. They used Culture's Consequences framework, which states that
culture is defined by its consequences on attitudes, values, and beliefs, to test whether the
cultural differences between the clusters significantly affects the difference between their
traffic safety culture, which was confirmed. They also revealed that drivers’ behavior is more
influenced by ‘culture as symbol’ use rather than risk perception, especially for the countries
with low and middle income. Moreover, there is evidence in the existing literature that
traditional ways of safety improvement like education, engineering, and enforcement
corroborates that the driver behavior is the main contributing factor in traffic crashes (Hughes
et al., 2016; Tefft & Arnold, 2017; Ward & Özkan, 2014). Consequently, traffic safety culture
can influence traffic safety culture via the mediating variable of driver behavior. Mozaffari et
al. (2021) applied data envelopment analysis to investigate the impact on road fatalities of road
safety culture on Iran provincial road fatalities data in the time period 2012-2014.
Two approaches have emerged in the quantitative assessment of safety culture. The
dominant approach hires a direct methodology and gathers data about the main dimensions of
the safety culture (Casey et al., 2015; Coogan et al., 2014). In TSC, the community members
are usually measured by variables like attitudes toward traffic safety, self-reported driver
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behavior, and the risk perception status (Nordfjærn et al., 2014; Warner et al., 2011). Otto et
al. (2019) provided guidance on measurement and analysis of traffic safety culture. Lund and
Rundmo (Lund & Rundmo, 2009) proposed four indexes of the probability of perceiving the
risk of traffic accidents, consequences of risk perception in accidents, risk sensitivity, and the
willingness to risk. They conducted a cross-cultural comparison of the traffic safety culture in
Norway and Ghana. The other approach for quantitative measurement of TSC comprises of the
use of questionnaire interview (Farrington-Darby et al., 2005; Iversen & Rundmo, 2004;
Mearns et al., 2013; Petitta et al., 2017; Rundmo & Fuglem, 2000; Timmermans et al., 2019;
Warszawska & Kraslawski, 2016). Nevertheless, the use of questionnaires for quantitative
assessment of the effects of the safety culture has been criticized similarly to other fields.
Guldenmund (2007) states that questionnaires may not be suitable in that they may not be fully
able to reveal the inner layers of organizational safety culture and, consequently, the
relationship between the considered factors and safety indicators. Among the popular factors
are the prominence of safety training programs, management’s attitudes toward safety, personal
skepticism, the company’s policies toward safety, issues related to maintenance and
management, and personal motivations for safety. These factors mostly evaluate safety
management and are do not specifically address safety culture. Lajunen and Summala (2003)
argued that the responses to questionnaires are susceptible to bias toward socially desirable
responses. In addition, the respondents may normally show behaviors other than what they
have stated in the questionnaire (Kashima et al., 1992). Some questionnaires also are designed
to measure safety culture, but they tend to measure safety climate, which is only an ephemeral
manifestation of the underlying safety culture (Flin et al., 2000).
Proposed by Ward et al. (2010), the second approach uses an indirect measurement for
comparing traffic safety culture between multiple nations or regions. This approach assumes
that safety culture has a significant effect on safety performance. To implement this approach,
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one should first list some exogenous and measurable risk factors, including the demographic
composition of the users of the roads, quality of roads, population density, vehicle fleet size,
the share of youth and rural groups of the total population, and transit rate. Next, a fatality rate
is estimated based on exogenous variables and is compared to the actual fatality rates. The
difference between the estimated fatality rate and the actual fatality rate is attributed to the
endogenous variables, including TSC. In this sense, TSC is comprised of several aspects,
including values, beliefs, attitudes, perceived norms, perceived control applied by the
population themselves, and perceived control applied by regulatory organization in charge of
monitoring traffic safety policies and development of the road network.
The direct approach is based on how much the respondents have understood the
questionnaire’s items and how much the designers of the questionnaire were able to incorporate
various aspects of TSC in the questionnaire. The latter indeed is very hard to achieve and can
largely affect the inclusion of the variables. Meanwhile, the indirect approach uses the data
published by official sources, which are more comprehensive and reliable in both regional and
national levels. However, the appropriate application of the indirect approach raises two key
considerations: the comprehensiveness of the exogenous variables and the suitability of the
evaluation method. The exogenous variables included in the fatality rate estimation model
should be as comprehensive as possible. A well-prepared list of exogenous variables helps the
modeler to ascribe the residual of the model to the cultural aspects confidently. The basis to
select exogenous variables in this study is two-fold. First, an exogenous variable should
correlate, in an engineering view of road safety, with the number of road injuries and fatalities.
Second, an exogenous variable should not be a direct or indirect manifestation of traffic safety
culture. This means safety culture should not, in any form, appear in the list of exogenous
variables, rather it should remain as a hidden endogenous variable affecting road safety. For
example, the share of young drivers in the total driving population shall not be considered an
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exogenous variable as youth may correlate with risky behavior. With this view, Section 2.1
lists several possible exogenous variables. Indeed, the provided list is not exhaustive, and it
can be extended. However, one important requirement from a practical point of view is that the
data regarding any selected exogenous variable should be systematically collected. The chosen
technique used to estimate the fatality rate is also imperative since the accuracy of the model,
and the amount of required data are directly influenced by the modeling technique.
The SFA approach has been a commonly-used approach for efficiency assessment during
the last two decades, and its application still interests researchers in different areas including
road transport (Zhang & Lin, 2018), farming (Dudu et al., 2015), healthcare (Atilgan &
Çalişkan, 2015; Kinfu & Sawhney, 2015), power generation (Ghosh & Kathuria, 2016), public
utility (Mizutani & Nakamura, 2016), Electricity distribution markets (Anaya & Pollitt, 2017),
and manufacturing (Hailu & Tanaka, 2015). An interesting characteristic of this approach is its
ability to differentiate between technical inefficiency and heterogeneity of the entities under
study. To the best knowledge of the authors, no previous research has exploited the potential
of SFA for safety culture impact quantification. Studies showed how SFA could be used for
impact quantification of psychological and cultural factors in different disciplines (Holý &
Evan, 2021; Jarboui, 2016; Jarboui et al., 2014). Yet, the application of SFA for impact
assessment of traffic safety culture is not a well-considered or well-addressed area.
This study proposes an SFA approach for exploring the impact of safety culture on road
fatalities. This approach is parametric, and a special functional form should be presumed for
the relationship between exogenous variables and the fatality rate. In this approach, the
relationship between the exogenous variables and the fatality rate is modeled with two
production functions, namely, linear production function (Model 1) and logarithmic Cobb-
Douglas production function (Model 2). Moreover, the proposed methodology is a purely data-
driven method which is independent of qualitative tools like questionnaires for safety impact
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assessment of driving culture. SFA enables calculation of some cultural impact ratios, which
can be directly attributed to the impact of cultural aspects on the fatality rate.
The rest of this paper is organized as follows. In section 2, the methodology of the paper
is presented. Section 3 presents the results of the proposed methodology for the analysis of the
impact of road safety culture on road fatalities in different provinces of Iran. This paper ends
in section 4 by discussing the main findings and conclusions.
2. The Proposed Methodology
2.1. Exogenous Variables and Data
A variety of indexes may be used to surrogate other factors. In the context of aggregate
data related to the exposure to traffic crashes, such surrogate indexes are usually categorized
into six main classes. Indexes in the socioeconomic and demographic classes include GNP (or
income tax), literacy rate, total population, urban population, employment rate, age
distribution, vehicle density, age distribution, matrimonial status, suicide rate, drug offenses,
number of hospitals and medical personnel. Another class is the environmental and engineering
characteristics of the road network. Indexes like average precipitation, the average number of
days with rain, frost, hail, fog, and snow, curvatures, presence of ramps, number of lanes belong
to this class. Variables like road classification and road construction are categorized under the
policy-making class. Age chords and driver licensing rates are the common variables in driver
behavior class. Vehicle characteristics and vehicle mix is another class of variables that include
indexes like the relative number of trucks. Finally, variables like speed limit regulation and
seat-belt legislation are categorized under police enforcements class. The data for all of these
variables may be gathered in various levels like county, city, country, or other levels (Ahangari
et al., 2015; Anwaar et al., 2012; Castillo-Manzano et al., 2015; Coruh et al., 2015; Jamroz,
2015; Rakauskas et al., 2009; Tingvall et al., 2010; Mozaffari et al., 2021).
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The increased risk of a fatal crash in some Iran provinces can be traced back to various
features that distinguish provinces from one another. These differentiating provincial driving
risk variables include daily transit, road design improvement (including posted speed limits),
intelligent transportation systems (ITS), emergency service provision, user training, highway
share, road illumination, population density, the number of trips and the number of passengers.
Such factors may increase the chance of driving on non-illuminated unsafe two-way roads in
highly-populated areas, which are associated with high transit rates. This intensifies the
severity of crashes, including roadside hazards, non-informed users, and the absence of
intelligent technologies. These crashes are often not reported or detected quickly if being
detected at all, which in turn may incur delays. An important variable that may affect road
safety performance is the use of ITS in the roads (eSafetySupport, 2009; Kulmala, 2010). In
addition to all these exogenous variables, attitudes toward TSC can play a prominent role in
the development of dangerous driving behavior as well as denial of any traffic safety
involvements made by the governmental organizations.
The exogenous variables used for the analysis of the provincial systems’ safety, are
defined as follows:
Daily transit rate: number of vehicles passing a certain point in the road, which is
measured directly by traffic monitoring cameras. Daily transit data are recorded
by automatic systems installed in various strategic points across the provinces.
Number of projects especially launched to enhance the roads and eliminate their
dangerous points in each province.
Number of intelligent technologies (ITS) installed along all roads in the province
Number of emergency stations along all roads in the province
Number of road users trained for better road safety, rule compliance, situation
awareness, etc.
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The share of highways in the total length of provincial roads
Share of illuminated roads in the total length of provincial roads; the portion of
every 100 KM road illuminated for better vision
The total number of trips in every 100 KM
The total number of passengers transported in every 100 KM
Population density; the number of people in every 100 KM of roads
Fatalities; the number fatalities on the provincial roads
Fatality rate; the number of fatalities in every 100 KM of provincial roads
Data regarding the variables above are obtained from the statistical yearbook published
by Iran Road Maintenance And Transportation Organization (2015) website for all 31 Iran
provinces in the period between 2012 and 2014. The descriptive statistics are presented in Table
1.
Insert Table 1 Here
2.2. Research framework
From the perspective of road safety management, each province could be looked as an
individual entity, the road transportation system of which has a unique set of characteristics
including known characteristics described in terms of exogenous variables, cultural
characteristics (driving behavior and attitudes toward road safety), and some random
characteristics such as weather condition, unpredictable natural accidents along the roads, etc.
The important point about these random characteristics is that they are not, to a large extent,
predictable and controllable. Hence, they can be treated as a source of random variation in the
fatality rate.
If we accept the metaphor of the production unit to represent the safety transportation
system, then the SFA methodology allows executing performance assessment on this
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production system. A question that arises here is that what is the definition of system
performance? In order to answer this question, we compare two hypothetical provinces A and
B. The data about the same set of known characteristics (exogenous variables) are available.
Let us assume that the total fatalities happened in province B is more than province A. If the
total fatalities occurred in province A could be attributed to the known exogenous variables,
then the additional fatalities in province be may be ascribed to the characteristics of the
governing system in province B that are not included in those exogenous variables. In other
words, they should be attributed to either cultural factors or random factors. Now, the SFA
methodology, due to its mechanism, enables not only the determination of the effects of
exogenous variables but also the distinction between the effects of random variables and
cultural variables.
With that said, the research framework designed in this paper is presented in Figure 1. In
this framework, technical efficiency and heterogeneity in the provincial road transportation
system are evaluated using SFA. The evaluation takes place considering system characteristics
or exogenous variables as explanatory variables and fatalities as the dependent variable. SFA
calculates the cultural impact ratios for the transportation system in each province, which can
be translated into the impact of safety culture on road fatalities, according to what has
mentioned earlier. Provincial systems that are located on the stochastic frontier obtained by
SFA are considered as the provinces with the best cultural safety performance among the 31
provinces present in this study. For other provincial systems, their distance from the stochastic
frontier is an indicator of the portion of their fatalities that can be attributed to cultural aspects.
In the research framework proposed in this study, SFA divides the total fatalities into three
parts: (a) fatalities attributed to exogenous variables, (b) fatalities attributed to stochastic and
unknown variables, and (c) fatalities attributed to safety culture.
Insert Figure 1 Here
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Following Battese and Coelli’s (1995) specifications, the time-variant stochastic frontier
function for the fatality rate in provinces of Iran is presented in Model 1.
(1)
Furthermore, the time-variant stochastic frontier function with logged exogenous
variables for the logarithm of the fatality rate is presented in Model 2.
(2)
where is the vector containing unknown parameters. is the independent and
identically distributed (iid) random variable, which follows the normal distribution in the form
of
. is independent of the technical inefficiency in production (), which is a non-
negative random variable. SFA assumes that is independently distributed as truncation at
the point in the normal distribution
.
The logic behind this specification is that the observed traffic fatality rate in each of the
Iranian provinces is affected by two environmentally distinguishable random disturbances, that
retain different features. From a pragmatic point of view, this distinction can significantly
enhance the estimation of the stochastic frontier as well as its interpretation. The presence of
the non-negative disturbance variable suggests that the provinces’ fatality rate must be
located on or above its frontier ( ). Deviations from the frontier are caused by
factors relating to the province’s residents, including the will and effort of the people to prevent
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any incident, accident, or death. variables are estimations of those fatalities which have
been avoided because of controllable cultural aspects.
The constructed frontier for each province is stochastic, meaning that each province may
have its unique frontier. The frontier can also change as time passes. The random disturbance
term in the SFA model incorporates favorable and unfavorable external factors, including
chance, climate, topography, and vehicle performance. also encompasses observation and
measurement error of fatality rates.
One of the interesting outcomes of SFA is that it allows us to find evidence about the
relative size of and by estimating their variances. Specifically, the ratio
is the
proportion of the total random variations in fatality rate which is attributed to controllable
cultural factors, and similarly, the ratio
is the proportion of the total random
variations in fatality rate which is attributed to uncontrollable random variables. Another
implication of this approach is that the increasing impact of culture on the fatality rate should
be principally measured by the ratio
in Model 1 and by
in Model 2. Hereafter, we refer to as the cultural impact ratio.
In both Model 1 and Model 2, the cultural impact ratio (θ) is greater than zero and less
than or equal to one. The province-years with a cultural impact ratio of one are placed on
inefficiency frontier. It should be noted that the fatality rate is an undesirable output; therefore,
the frontier type is of inefficiency rather than efficiency, and this calculated inefficiency
frontier represents the worst provincial performances with respect to cultural safety. For those
provinces placed on this frontier, safety culture significantly contributed to fatalities incurred
in that province. On the other hand, the province-years with a cultural impact ratio less than
one are placed away from inefficiency frontier, which means road safety culture in such
provinces has significantly contributed to the avoidance of some fatalities. In summary, the
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less the cultural impact ratio (θ) calculated for a province-year, the more cultural aspects
positively contributed to safety performance.
It should be noted that Model 1 and Model 2 use two different functional forms of the
production frontier. However, they share the same set of exogenous variables and the same
underlying assumptions on probability distributions of the terms Uit and Vit. Therefore, the
probable difference between their results would be due to the functional form of their
production functions. We make use of this fact and provide a verification and validation
mechanism to ensure the robustness of SFA results. The main idea is that if the result of the
SFA model (2) is verified by the result of the model (3), then it shows the robustness of SFA
for quantification of the impact on the fatality rate of the road safety culture.
3. Results
As mentioned above, SFA cultural impact ratios are indications of the increasing impact
that cultural aspects have on road fatalities. To calculate the impact ratios, both SFA Models 2
and 3 are programmed and solved using the FRONTIER Version 4.1 (Coelli, 1998). The final
maximum likelihood estimates (MLEs) of the regression models are presented in Table 2. The
results show the significance of total random variations in both models. The estimates of total
variance
in both models are significant due to P-values below 0.05 (95%
confidence level). As mentioned before, the ratio is the proportion of the total random
variation in fatality rate attributed to controllable cultural factors, and by subtraction from one,
the ratio is the proportion of the total random variations in fatality rate attributed to
uncontrollable random variables. Results show that for SFA Model 1, 89% of the total random
variations can be attributed to cultural aspects, and 11% of the total variations are left for
uncontrollable random variables. These results are slightly different for SFA Model 2, where
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97% of the total random variations are attributed to controllable cultural aspects, and only 3%
remain for uncontrollable variation sources.
Insert Table 2 Here
Based upon the estimated stochastic frontiers, the cultural impact ratios for each of the
provinces in the period between 2012 and 2014 are calculated in Table 3. According to time-
variant SFA with original variables (Model 1), Kahkiluye in 2013, Kahkiluye in 2014, and
South Khorasan in 2014 are the best performing provinces, the safety culture of which has
effectively contributed to fatality prevention. On the contrary, Alborz, Gilan, and Lorestan are
the worst-performing provinces with respect to road safety culture. However, before going into
the details of these results and drawing interpretations and implications regarding the impact
of safety culture on fatalities, some statistical analyses should be performed to show the validity
and accountability of the SFA results.
Insert Table 3 Here
As is seen in Table 3, the cultural impact ratios of Model 1 are not the same as those in
Model 2. However, Pearson’s correlation coefficient was calculated, and its companion
significance test was conducted. It revealed that there is a significant correlation between the
cultural impact ratios of the two models (Table 4). Provinces can be ranked according to their
positive safety culture ratios of Table 3. Spearman’s rank correlation coefficient was calculated
between the two models’ provincial safety culture ranks and the significance test were
conducted, which showed a significant relationship (Table 4). Spearman’s rank correlation is
considered the most suitable to test the association between any two variables that contain
rankings (and not real values) and to show the probability of the association (Cohen, 1977).
According to Table 4, Spearman’s test revealed that there is a 64% correlation between the
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rankings obtained from Model 2 and Model 3, implying that the SFA Model 2 significantly
verifies the results of SFA Model 1.
Insert Table 4 Here
The ability of the obtained SFA model to differentiate between provinces using safety
culture impacts can be used to evaluate the robustness and reliability of the model. Two-way
analysis of variance (ANOVA) in a factorial design was used to test this capability
(Montgomery, 2017), where province and year are the two factors, and the cultural impact
rations obtained from SFA is the response variable. Table 5 and Table 6 show the results of the
ANOVA test, which was conducted using the SPSS software. The small p-values for SFA
Model 2 and SFA Model 3 suggest that the effect of cultural aspects significantly differs among
provinces. Therefore, the null hypothesis is rejected. It is worth mentioning that p-value is the
risk associated with rejecting the null hypothesis. The null hypothesis of the ANOVA model is
that there is no significant difference between the impact of cultural aspects on road safety
among provinces.
Insert Table 5 Here
Insert Table 6 Here
The main conclusion we have arrived at until here is that SFA Model 2 and SFA Model
3 have provided robust scores for fatalities of road safety culture, based on which the provinces
can be differentiated. The next section is dedicated to drawing comprehensive conclusions
about the impact of the safety culture based on these two models.
3.1. Impact of Safety Culture
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TSC is described by the quantifiable impact of drivers’ attitudes and behaviors on injuries
and fatalities. In this sense, TSC has a share in injuries and fatalities. SFA gives this quantified
share of TSC. Here TSC is described by its impact on safety performance rather than by its
formal definition, which is the basis for the direct approach.
In Figures 2 and 3, the averages of cultural impact ratios of provinces are compared
during 2012-2014. According to the results of Model 1 in Figure 2, provinces of Ardebil, South
Khorasan, Sistan, Kahkiluye, and Yazd are the best performing provinces according to the
contribution of their safety culture to reduction of the road fatalities. According to the results
of Model 2 in Figure 3, provinces of Ardebil, Tehran, Sistan, Kahkiluye, and Yazd are the best
performing provinces according to the contribution of their safety culture to the reduction of
road fatalities. In summary, both models confirm that Ardebil, Sistan, Kahkiluye, and Yazd are
the provinces that most benefitted from their good safety culture and could cut down their
fatalities.
At the top, there exist provinces that most suffered from cultural aspects. Results in both
Models 2 and Model 3 show that cultural aspects in Alborz, Kurdistan, Gilan, Lorestan,
Markazi, and Hamedan provinces had the biggest negative impact on road safety compared to
other provinces. The relative differences in safety culture between provinces are imperative,
especially for the managers at governmental organizations who oversee traffic safety.
Provinces with SFA scores above 0.7 need to have laws about traffic safety legislated more
carefully, with an exclusive accent put on cultural aspects. Further comprehensive studies may
be required to unravel the initiating factors that lead to unsafe behaviors and, consequently, to
more fatalities.
Insert Figure 2 Here
Insert Figure 3 Here
20
SFA model has also allowed tracking the chronological changes in safety culture impact.
Figure 4 displays how the average cultural impact scores had changed over the studied period
of 2012 to 2014. Unlike previous charts that showed results for provinces, Figure 4 depicts the
average performance for the whole country. It is evident that both models have identified
significant improvement for the country over the considered time interval.
Insert Figure 4 Here
4. Conclusion
This paper aims to propose a methodology for traffic safety culture assessment based on
the stochastic frontier analysis. The proposed approach is an indirect approach. This means
traffic safety culture is described by its impact on safety, i.e., by the quantifiable impact of
drivers’ attitudes and behaviors on injuries and fatalities. In this sense, TSC has a share in
injuries and fatalities. SFA gives this quantified share of TSC. This methodology is parametric
and flexible in the sense that any linear or non-linear frontier can be considered to describe the
relationship between exogenous system characteristics and the fatality rate. Moreover, the
proposed methodology is a purely data-driven method independent of qualitative tools like
questionnaires. This paper illustrates the use of time-variant SFA models for quantitative
assessment of the impact of road safety culture on road fatalities. Two functional forms of the
stochastic frontier, namely linear and logarithmic models, are used, and the comparison of their
results attests to the robustness of SFA for impact quantification of safety culture. The
applicability of the proposed SFA-based methodology is demonstrated by assessing the impact
of road safety culture on road fatalities based on real-world data. Results show that the SFA
models were able to provide scores for the impact of cultural aspects on the road fatality rate
that can significantly differentiate between provinces. Moreover, the results of the case study
signify the improvement in road safety culture throughout 2012 to 2014.
21
Funding None
Availability of data and materials All data and materials are available within the article and
codes are available from the corresponding author on request
Declarations
Ethical approval Not applicable.
Consent to participate Not applicable.
Consent to publish The authors agree with publish this paper in International Journal of
System Assurance Engineering and Management
Competing interests The authors declare no conflict of interest
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25
Figure 1: Research Framework
Exogenous Variables:
– Daily transit
– Road design improvement
– ITS
– Emergency service
– Users trained
– Highway share
– Road illumination,
– Population density
– No. of trips
– No. of passengers
Fatalities attributed to
exogenous variables
SFA
Fatalities
Fatalities attributed to safety
culture
Fatalities attributed to
stochastic and unknown
variables
26
Figure 2: Cultural safety impact across provinces (from Model 1)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
EastAzar
WestAzar
Ardebil
Isfahan
Alborz
Ilam
Boushehr
Tehran
Bakhtyari
SouthKhorasan
RazaviKhorasan
NorthKhorasan
Khuzestan
Zanjan
Semnan
Sistan
Fars
Gazvin
Qom
Kurdistan
Kerman
Kermanshah
Kahkiluye
Golestan
Gilan
Lorestan
Mazandaran
Markazi
Hormozgan
Hamedan
Yazd
Average cultural impact ratio
27
Figure 3: Cultural safety impact across provinces (from model 2)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
EastAzar
WestAzar
Ardebil
Isfahan
Alborz
Ilam
Boushehr
Tehran
Bakhtyari
SouthKhorasan
RazaviKhorasan
NorthKhorasan
Khuzestan
Zanjan
Semnan
Sistan
Fars
Gazvin
Qom
Kurdistan
Kerman
Kermanshah
Kahkiluye
Golestan
Gilan
Lorestan
Mazandaran
Markazi
Hormozgan
Hamedan
Yazd
Average cultural impact ratio
28
Figure 4: The trend of cultural safety impact over the years
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
2012 2013 2014
Average cultural impact ratio
Year
Model 2
Model 3
29
Table 1: Descriptive Statistics of the Model Variables
Model Variables
Abbreviation
Min
Max
Average
STDEV
Daily transit
trans
6552
218208
43786
46524
Road design improvement
design
3
76
19
15
ITS in 100 KM
ITS
1
18
6
4
Emergency service
emrg
16
107
41
25
User training
training
2874
27984
9183
5799
Highway share in 100 KM
highway
2
65
22
14
Road illumination in 100KM
illumn
1
30
7
7
Population
pop
459754
11860666
2447182
2198878
# of trips (in thousands)
trip
84
1478
570
364
# of passengers
pasng
1463
26533
6741
5830
Fatalities
fatalities
10
1023
356
210
Road network size (length)
length
375
7877
2722
1820
Source: RMTO, 2015
30
Table 2: The final maximum likelihood estimation of SFA parameters
Time-variant SFA with original variables
(Model 1)
Time-variant SFA with logged variables
(Model 2)
Coefficient
Value
St. error
t-ratio
P-Value
Value
St. error
t-ratio
P-Value
15.63
3.57
4.38
0.00*
0.15
0.77
0.20
0.85
0.00
0.00
1.92
0.06
-0.21
0.10
-1.99
0.05*
-0.03
0.03
-0.92
0.36
0.07
0.05
1.53
0.13
0.23
0.19
1.23
0.22
-0.02
0.09
-0.26
0.80
-0.04
0.06
-0.72
0.47
-0.14
0.13
-1.03
0.31
0.00
0.00
0.75
0.46
0.17
0.11
1.60
0.11
0.08
0.10
0.79
0.43
0.18
0.09
2.05
0.04*
0.89
0.30
2.96
0.00*
0.28
0.11
2.63
0.01*
0.00
0.00
-0.68
0.50
0.52
0.10
5.31
0.00*
0.00
0.01
0.89
0.37
0.24
0.18
1.31
0.19
0.00
0.00
-0.70
0.49
-0.26
0.17
-1.51
0.13
48.19
20.36
2.37
0.02*
1.70
0.52
3.25
0.00*
0.89
0.04
22.03
0.00*
0.97
0.01
89.21
0.00*
LLF
-251
-20
* Significant at α=5%; LLF: Log Likelihood Function
31
Table 3: The results of cultural impact ratios for the province-years
Time-variant with original variables
(Model 1)
Time-variant with logged variables
(Model 2)
#
Province-Year
2012
2013
2014
2012
2013
2014
1
EastAzar
0.70
0.66
0.61
0.93
0.90
0.85
2
WestAzar
0.66
0.61
0.55
0.90
0.85
0.79
3
Ardebil
0.50
0.43
0.34
0.64
0.52
0.39
4
Isfahan
0.51
0.44
0.35
0.83
0.76
0.68
5
Alborz
0.93
0.92
0.91
0.93
0.91
0.87
6
Ilam
0.51
0.44
0.35
0.94
0.91
0.87
7
Boushehr
0.52
0.44
0.36
0.82
0.74
0.65
8
Tehran
0.66
0.61
0.55
0.62
0.49
0.36
9
Bakhtyari
0.59
0.53
0.46
0.89
0.85
0.79
10
SouthKhorasan
0.34
0.24
0.12
0.91
0.88
0.83
11
RazaviKhorasan
0.54
0.47
0.39
0.89
0.84
0.77
12
NorthKhorasan
0.62
0.56
0.50
0.90
0.85
0.79
13
Khuzestan
0.53
0.45
0.37
0.75
0.65
0.54
14
Zanjan
0.65
0.60
0.54
0.89
0.85
0.78
15
Semnan
0.66
0.61
0.56
0.95
0.93
0.89
16
Sistan
0.40
0.30
0.20
0.68
0.56
0.43
17
Fars
0.66
0.61
0.55
0.96
0.94
0.91
18
Gazvin
0.50
0.43
0.34
0.92
0.88
0.83
19
Qom
0.68
0.64
0.58
0.90
0.86
0.80
20
Kurdistan
0.81
0.79
0.75
0.94
0.92
0.88
21
Kerman
0.58
0.52
0.45
0.86
0.80
0.72
22
Kermanshah
0.56
0.49
0.42
0.84
0.78
0.70
23
Kahkiluye
0.23
0.12
0.02
0.26
0.14
0.05
24
Golestan
0.66
0.61
0.55
0.83
0.76
0.67
25
Gilan
0.87
0.85
0.83
0.94
0.91
0.88
26
Lorestan
0.89
0.88
0.86
0.93
0.90
0.85
27
Mazandaran
0.69
0.64
0.58
0.83
0.76
0.67
28
Markazi
0.81
0.78
0.75
0.95
0.93
0.90
29
Hormozgan
0.53
0.46
0.38
0.90
0.86
0.81
30
Hamedan
0.80
0.77
0.73
0.93
0.90
0.86
31
Yazd
0.38
0.29
0.18
0.65
0.53
0.39
32
Table 4. Correlation test between the results of Model 1 and Model 2
Time-variant with logged variables
Time-variant with original variables
Efficiency
Rank
Efficiency
0.65*
-
Rank
-
0.64*
* Significant at 95% confidence level
33
Table 5: ANOVA test for SFA Model 1
Dependent Variable: cultural impact ratio from SFA Model 1
Source
Sum of Squares
df
Mean Square
F
P-value
Province
3.187
30
0.106
144.729
0.000
Year
0.243
2
0.122
165.792
0.000
Error
0.044
60
0.001
Total
3.474
92
R Squared = 0.987 (Adjusted R Squared =0.981)
34
Table 6: ANOVA test for SFA Model 2
Dependent Variable: cultural impact ratio from SFA Model 2
Source
Sum of Squares
df
Mean Square
F
P-value
Province
2.725
30
0.091
81.696
0.000
Year
0.247
2
0.124
111.290
0.000
Error
0.067
60
0.001
Total
3.039
92
R Squared =0.978 (Adjusted R Squared = 0.966)
