Effect Of Unobserved Heterogeneity Research Articles

Investigating built environment and traffic flow impact on crash frequency in urban road networks

While numerous studies have examined the factors that influence crash occurrence, there remains a gap in understanding the intricate relationship between built environment, traffic flow, and crash occurrences across different spatial units. This study explores how built environment attributes, and dynamic traffic flow characteristics affect crash frequency by focusing on proposed traffic density-based zones (TDZs). Utilizing a comprehensive dataset from Greater Melbourne, Australia, this research emphasizes on the dynamic traffic flow variables and insights from the Macroscopic Fundamental Diagram model, considering parameters such as shockwave velocity and congestion index. The association between the potential influencing factors and crash frequency is examined using a random parameter negative binomial regression model. Results indicate that the data segmentation based on TDZs is instrumental in establishing a more refined crash model compared to traditional planning-based zones, as demonstrated by improved goodness-of-fit measures. Factors including density (e.g., employment density), network design (e.g., road density and highway density), land use diversity (e.g., job-housing balance and land use mixture), and public transit accessibility (e.g., bus route density) are significantly associated with crash occurrence. Furthermore, the unobserved heterogeneity effects of the shockwave velocity and congestion index on crashes are revealed. The study highlights the significance of incorporating dynamic traffic flow variables in understanding crash frequency variations across different spatial units. These findings can inform optimal real-time traffic monitoring, environmental design, and road safety management strategies to mitigate crash risks.

Waiting for signalized crossing or walking to footbridge/underpass? Examining the effect of weather using stated choice experiment with panel mixed random regret minimization approach

It is a challenging task for pedestrians to cross a road with multiple traffic lanes and busy traffic. Many footbridges and underpasses have been built in the urban area of metropolitan cities such as Hong Kong to resolve the problem of vehicle-pedestrian conflict. To maximize the utilization and benefit of the installation of such crossing facilities, it is crucial to understand the choice behaviour of pedestrians. Although many studies have examined pedestrian walking behaviour and preference towards crossing facilities, the influence of ratio of perceived values between waiting and walking time on the choice of crossing is not explored. In addition, individual perception and choice may vary with the environmental conditions, which has not been fully accounted for in existing studies. Exposure to extremely hot weather, crowded walkways, and roadside traffic emissions are not favoured. In this study, a stated choice experiment is developed to examine the relationship between possible influencing factors and the crossing choices of pedestrians in Hong Kong. In addition, a regret-based panel mixed multinomial logit approach is adopted to model the choice, accounting for the effects of unobserved heterogeneity and panel data. The results indicate that the choice decision of pedestrians is more sensitive to an increase in waiting time at signalized crossings than to an increase in walking time to access footbridges and underpasses. These findings shed light on future urban and transport planning strategies to improve the walking environment and promote walkability.

Do footbridge and underpass improve pedestrian safety? A Hong Kong case study using three-dimensional digital map of pedestrian network

Hong Kong is a compact city with high activity and travel intensity. In the past decades, many footbridges and underpasses were installed to reduce the pedestrian-vehicle conflicts on urban roads. However, it is rare that the effects of configuration of pedestrian network on pedestrian crashes are investigated. In Hong Kong, many footbridges and underpasses are connected to major transport hubs and commercial building development and become parts of giant elevated and underground walkway systems. It is challenging to characterize such a complicated pedestrian network. In this study, a three-dimensional digital map is applied to estimate the connectivity and accessibility of pedestrian network, and measure the relationship between pedestrian network characteristics and pedestrian safety at the macroscopic level. Hence, the effects of footbridge and underpass on pedestrian safety are examined. For example, comprehensive built environment, pedestrian network, traffic, and crash data are aggregated to 379 grids (0.5 km × 0.5 km). Then, multivariate Poisson lognormal regression approach is applied to model fatal and severe injury (FSI) and slight injury pedestrian crashes, with which the effects of unobserved heterogeneity, spatial correlation, and correlation between crash counts are accounted. Results indicate that population density, traffic volume, walking trip, footpath density, node density, number of vertices per footpath segment, bus stop, metro exit, residential area, commercial area, and government and utility area are positively associated with pedestrian crashes. In contrast, average gradient, accessibility of footbridge, accessibility of underpass, and number of crossings per road segment are negatively associated with pedestrian crashes. In other word, pedestrian safety would be improved when footbridge and underpass are more accessible. Findings have implications for the design and planning of pedestrian network to promote walkability and improve pedestrian safety.

Effects of design consistency on run-off-road crashes: An application of a Random Parameters Negative Binomial Lindley model

Run-off-road crashes are one of the most common crash types, especially in rural roadway environments contributing significantly to fatalities and severe injuries. These crashes are complex and multi-dimensional events, and factors like road geometry, driver behaviour, traffic characteristics and roadside features contribute to their occurrence, separately or interactively. Sudden changes in road geometry, in particular, can influence driver behaviour, and therefore, in developing a micro-level crash risk model for run-off-road crashes, one of the challenges is incorporating the effects of driver behaviour (disaggregated information) that may arise from the variations in road geometry (aggregated information). This study aims to examine the interaction between road geometry and driver behaviour through a set of measures for design consistency on two-lane rural roads. Multiple data sources, including crash data for 2014–18, traffic data, probe speed data and roadway geometric data, for twenty-three highways in Queensland, Australia, have been fused for this study. Seventeen types of design consistency measures with regard to alignment consistency, operating speed consistency and driving dynamics are tested. A run-off-road crash risk model is estimated by employing the Random Parameters Negative Binomial Lindley regression framework, which accounts for excess zeros in the crash counts and captures the effects of unobserved heterogeneity in the parameter estimates. Results indicate that the geometric design consistency capturing the interaction between driver behaviour and operational factors better predicts run-off-road crashes along rural highways. In addition, roadside attributes like clear zone width, infrastructures, terrain, and roadway remoteness also contribute to run-off-road crashes. The findings of the study provide a comprehensive understanding of the influence of variations in roadway geometry on driver behaviour and run-off-road crashes along rural highways.

Factors Associated With the Severity of Motor Vehicle Crashes Involving Electric Motorcycles and Electric Bicycles: A Random Parameters Logit Approach With Heterogeneity in Means

Exploring the heterogeneity of factors influencing the severity of electric bicycle crashes and electric motorcycle crashes can help target accident prevention policies to improve traffic safety. Therefore, this paper establishes a mean heterogeneity random parameter logit model using crash data from 2016 to 2020 in Guangxi to explore the different factors influencing the severity of crashes involving electric motorcycles and electric bicycles. The results show that the key influences on crash severity differ in electric motorcycle crashes and electric bicycle crashes. At the same time, some common factors affect the two types of crashes to different degrees. In addition, the complex interaction effects of unobserved heterogeneity were considered to explore the random parameters of the two types of crashes. The effect of unobserved heterogeneity on the distribution characteristics of the random parameters was then determined. For example, in electric motorcycle crashes, street lighting at night has a random parameter characteristic. The likelihood of serious crashes decreased when both street lighting at night and vehicle left turn were involved, and decreased when both street lighting at night and no signal control were involved. In electric bicycle crashes, large trucks have a random parameter characteristic. The likelihood of serious crashes increased when both large trucks and motor vehicle lights not turned on were involved, and increased when both large trucks and visibility less than or equal to 200 meters were involved. The results provide a basis for improving the road safety of electric motorcycles and electric bicycles.

Demographic and behavioural factors affecting public support for pedestrianisation in city centres: The case of Edinburgh, UK

This paper provides an integrated analytical framework to investigate the demographic and behavioural factors that significantly influence public support for pedestrianisation. Pedestrianisation is often introduced by local authorities with the intention of improving air quality, the walkability of streets, road safety and opportunities for the local economy, however, issues remain regarding how accessible pedestrianised areas are for individuals who have conditions that limit their mobility. Using data from a survey, conducted during 2020 in Edinburgh (UK), public perceptions towards pedestrianisation were investigated through statistical testing and the development of random forest and ordered probit models. The random forest approach can help identify the relative importance of explanatory variables, whereas the ordered probit models can unveil the demographic and behavioural determinants of public support. To account for the potential effect of unobserved heterogeneity within respondents’ perceptions, random parameters were also considered in the ordered probit modelling framework. Initial results showed that residents are generally supportive of most issues surrounding pedestrianisation. Random parameters ordered probit modelling identified mode of travel and trip frequency as significant factors affecting key aspects of public support, such that active travellers were significantly more likely to support pedestrianisation, while those who rarely visit Edinburgh city centre were more likely to oppose pedestrianisation. Overall, a variety of independent analyses and modelling approaches suggest common influences on opinion, including behavioural patterns relating to transport modal choice and trip frequency, while disability was also found to have considerable effect on support as a fixed and random parameter. The statistical models are evaluated in terms of goodness-of-fit measures, before policy implications are discussed.

Identifying the economic determinants of individual voting behaviour in UK general elections

Abstract We explore the economic determinants of individual voting behaviour in five UK electoral cycles during 1992–2014. Using the Understanding Society and the British Household Panel Surveys, we investigate the importance of political sentiments and subjective economic evaluations disentangling persistence of party support and unobserved heterogeneity effects. We estimate joint dynamic tripartite models of party support and egocentric perceptions of current and prospective finances, permitting longitudinal simultaneous determination of perceptions of personal finances and political preferences. The results validate the economic voting hypothesis in cycles adjacent to economic downturns: support for the governing political party is positively related to individual perceptions of own financial well-being. Failing to account for simultaneity and not accounting for dynamics and initial political party support inflate the impact of personal financial evaluations.

A random parameters copula-based binary logit-generalized ordered logit model with parameterized dependency: Application to active traveler injury severity analysis

A copula-based dependence approach accommodates various facets of dependence structures in building multivariate stochastic models. In existing studies, applications of copula for ordinal random variables are predominantly modeled by employing traditional ordered models (ordered logit/probit) while assuming the effects of parameters to remain the same across all observations. The methodological contributions of this study are grounded in addressing the abovementioned significant methodological gaps in the application of copula formulation by proposing a copula-based random parameters nominal-ordinal joint model construct of correlated random variables. Specifically, we propose and develop a random parameters binary logit-generalized ordered logit copula formulation while also complementing the proposed approach by accommodating the effects of unobserved heterogeneity in parameter estimates. To the best of the authors’ knowledge, this study is the first instance to incorporate generalized ordered formulation within copula in extant econometrics literature. Further, to obtain a direct effect of exogenous variables on dependence, we parameterize the copula dependence structure as a function of different covariates in six different copula structures including a wide range of dependency structures which represent radial symmetry and asymmetry, and asymptotic tail dependence. The empirical contributions of this study are grounded in the application of the proposed copula-based formulation by examining ‘active traveler (pedestrian and bicyclist) crash type’ and ‘active traveler injury severity outcomes’ as two dimensions of active travel injury severity mechanism. The model is estimated by using crash data for the years 2012 through 2018 from the state of Queensland, Australia, by employing a comprehensive set of exogenous variables. In addition, the analyses are further augmented by complementing the elasticity effects of exogenous variables.

The effects of occupational hazards and health-related behavior on workers’ health: A multivariate probit approach

The effects of occupational hazards and health-related behavior on workers’ health: A multivariate probit approach

Evaluating the correlation between risky riding behaviour and self-reported crashes in India: Minimizing unobserved heterogeneity

Riding Behaviour is found to be the main cause of Powered Two-Wheeler (PTW) crashes in more than90% of the crash events. The high percentage of PTW crashes resulting in fatalities has sought a serious need for research to examine risky riding Behaviour. A widely used instrument for measuring the self-reported riding Behaviour of PTW riders is the Motorcycle Rider Behaviour Questionnaire (MRBQ). In this study, exploratory factor analysis of the MRBQ revealed a four-factor solution viz., traffic errors, control errors, speed violations, and stunts. Despite the popularity of MRBQ, it is capable of covering only a small fraction of the large number of elements that affect the riding Behaviour. Many other elements remain overlooked in the analysis, resulting in unobserved heterogeneity. Therefore, the present study uses a random parameter negative binomial (RPNB) model to minimize the effect of unobserved heterogeneity. It was inferred from the RPNB model that variables like gender, control error, and speed violation have a randomly distributed regression coefficient. Further, it is found that traffic errors are the most significant predictor of crash risk. Additionally, results depict that male riders are positively associated with crashes, and they are more likely to involve in crashes as compared to female riders. The finding of this paper will be valuable for policymakers and decision-makers to improve the rider training program, licensing system, and design road safety campaigns.

Modeling the unobserved heterogeneity effects of the factors influencing the fuel consumption of heavy-duty diesel trucks under real road conditions: A preliminary investigation in China

Heavy-duty diesel truck (HDDT) is one of the major sources of air pollution and energy consumption. To reduce the estimation bias and improve the interpretability, the random parameters logit (RPL) model was employed to examine the effects of influencing factors on fuel consumption of HDDTs in the real world. The unobserved heterogeneity effects varying across the samples on fuel efficiency were extracted from the long-term daily trip-based data. In order to further illustrate the advantages of the RPL model in explaining the impacts of factors, a fixed parameters logit model with twenty parameters was constructed and compared. The Akaike information criterion and the Bayesian information criterion were used to select a more reasonable model structure. The findings show that the RPL model performs better and the unobserved heterogeneity would affect the effects of factors of rolling without engine load proportion and temperature and, consequently, map the level of fuel consumption. This reveals the variability of the fuel consumption among the samples. Driving compensation effects were also identified in this study (i.e., the drivers tend to perform the fuel-saving operations in adverse driving circumstances and vice versa). The methodology proposed in this paper can provide a new insight for researchers to identify the instability of energy-related factors under real road conditions. Future research could be implemented to assess the similar effects of alternative fuel vehicles.

The impact of COVID-19 on future public transport use in Scotland.

This paper examines the determinants of changes in future public transport use in Scotland after the COVID-19 pandemic. An online questionnaire was distributed to 994 Scottish residents in order to identify travel habits, attitudes and preferences during the different phases of the COVID-19 outbreak and travel intentions after the pandemic. Quota constraints were enforced for age, gender and household income to ensure the sample was representative of the Scottish population. The respondents indicated that they anticipated they would make less use of buses and trains at the end of the pandemic. Over a third expect to use buses (36%) and trains (34%) less, whilst a quarter expect to drive their cars more. As part of the analysis, a random parameter bivariate probit model with heterogeneity in the means of random parameters was estimated to provide insights into the socio-demographic, behavioural and perceptual factors which might affect future public transport usage. The inclusion of random parameters allows for the potential effects of unobserved heterogeneity within the independent variables to be captured, whilst making allowances for heterogeneity in the means of the random parameters. The model estimation showed that several factors, including pre-lockdown travel choices, perceived risk of COVID-19 infection, household size and region significantly affected intended future use of public transport. In addition, several variables related to age, region, pre-lockdown travel choices and employment status resulted in random parameters. The current paper contributes to our understanding of the potential loss of demand for public transport and the consequences for future equitable and sustainable mobility. Our findings are highly relevant for transport policy when developing measures to strengthen the resilience of the public transport system during and after the pandemic.

Determinants of energy demand for residential space heating in Turkey

A significant portion of household energy requirements is used for space heating. Although the fundamental factors determining household energy consumption have been the focus of many studies, they have neglected to consider the effect of unobserved heterogeneity, which has the potential to play a significant role as a determining factor in energy consumption. The study analyzes household decisions in choosing an energy source for residential space heating applying a random effect ordered logit model on Income and Living Conditions Longitudinal Micro Data Set for the years 2016–2019 to fulfill this gap in the literature. The results indicate that selection of residential space heating type (dried animal dung, charcoal, wood, natural gas, electricity) is influenced by socioeconomic and dwelling factors. We also found that the energy ladder hypothesis is valid for households in Turkey.

Analysis of pedestrian accident injury-severities at road junctions and crossings using an advanced random parameter modelling framework: The case of Scotland

This paper investigates the determinants of injury severities in pedestrian-motor vehicle accidents at signalised and unsignalised junctions, and at physically-controlled and human-controlled crossings in Scotland. The accident data were drawn from the official police crash report database of the UK spanning a period between 2010 and 2018. Correlated random parameter ordered probit models with heterogeneity in the means were developed in order to account for the multi-layered impact of unobserved heterogeneity on statistical estimation. The model estimation results showed that the severities of accident injuries are affected by roadway, location, weather, vehicle, and driver characteristics as well as temporal attributes (including time and day of the accident). Factors such as the urban context, lighting and weather conditions and road surface conditions were found to result in correlated random parameters, thus capturing the intricate, yet interactive effects of unobserved heterogeneity, and particularly the unobserved behavioural response of road users to different traffic control types at junctions and crossings. Vehicle type, driver’s gender and day-of-the-week were observed to influence the random parameters' distributions. Empirically, the results showcase variations in the determinants of injury severities at signalised and unsignalised junctions, and at physically-controlled and human-controlled crossings. Even though most of these variations were related to the magnitude of impact of the determinants, differences in the directional effects on injury severities were also identified, mainly for factors related to weather conditions, hazard presence on the road, and temporal characteristics of the accidents.

Exploring Unobserved Heterogeneity in Cyclists’ Occupying Motorized Vehicle Lane Behaviors at Different Bike Facility Configurations

Cyclists occupying motorized vehicle lanes disrupt road traffic order and increase collisions. Exploring the contributing factors could help develop countermeasures to regulate such behaviors. The purpose of this study is to explore the intrinsic features influencing the behavior of cyclists in occupying motorized vehicle lanes at different bicycle facilities. We investigated a total of 34,631 cycling behavior samples in the urban area of Pingdingshan, China. A Bayesian random parameter logit model was used to account for the unobserved heterogeneous effects. The experimental results of all bike facilities demonstrate that the bike type, dividing strip type, bike lane width, temporary on-street parking, and whether it is a working day significantly affect cyclists’ occupying motorized vehicle lane behaviors. Factors associated with unobserved heterogeneity are age, barriers dividing strip, vehicle lane numbers, bike volume, vehicle volume, and daily recording time intervals. Comparing the estimated model of five type bike lane facilities across different dividing strips, we find that cyclists have a significantly different occupying probability and the heterogeneity factors of the various bike facilities also have their focus. When the non-motorized road conditions become more open, the cyclist behavior becomes more random and the heterogeneity factors become broader.

Sociodemographic Factors Affecting Outdoor Exercise Trips During the COVID-19 Lockdown

We employ a state-of-the-art modelling framework to determine the significant factors affecting rates of outdoor exercise trips during Scotland’s COVID-19 lockdown, using data from public surveys conducted by Transport Scotland. The random parameters ordered probit modelling approach is used for its ability to account for the potential effect of unobserved heterogeneity stemming from explanatory variables. The framework is extended further to also allow for detection of heterogeneity among the means of random parameters. We show that various sociodemographic factors (relating mainly to household social grade, employment status and disability) significantly influenced the frequency at which outdoor exercise trips were made during lockdown. Specifically, those who are self-employed, those from a social DE household (the household’s main income earner is employed in a manual occupation or is unemployed) and those with a health problem or disability, were shown to be significantly more likely to complete no outdoor exercise during lockdown, and therefore, these groups are at greater risk of the associated mental and physical illnesses. Model results are linked to issues surrounding transport equity, as personal vehicle ownership was found to significantly affect the rate of outdoor exercise trips made by disabled individuals. Policy implications are discussed with regards to mitigating the effects of the pandemic on the future health state of groups exhibiting low exercise levels.

Investigating factors influencing rollover crash risk on mountainous interstates

Introduction: The risk of rollover crashes on mountainous roads is a major concern for transportation authorities due to adverse weather conditions and complex topography. Such crashes incur hazardous consequences on road users’ lives. Therefore, it is crucial to identify the contributing factors that give rise to these severe crashes in order to identify preventive measures. Furthermore, exploring the potential sources of heterogeneity of rollover crash contributing factors is equally important. Method: By having a dataset of single-vehicle crashes that occurred on mountainous curved sections in Wyoming, we applied a random parameters, otherwise known as mixed, logit model to identify the factors contributing to the increased risk of rollovers. Vehicle, driver, roadway, environmental, and crash attributes variables were considered as potential predictors in the model. Then, random parameters were identified to uncover the unobserved effects. Results: Weather, road surface conditions, and speeding were found to have a significant impact on rollover crash risk. These factors were also found to exhibit unobserved heterogeneity effects, which could be attributed to the drivers’ responses and conditions. Furthermore, it was found that the propensity of rollovers was higher for sports utility vehicles (SUVs) and pick-up trucks among other vehicle types. Conclusions: The results indicated that investigating the impact of these factors on the risk of rollovers while taking into account unobserved heterogeneity effects is an essential step for implementing countermeasures to reduce the frequency and severity of rollover crashes. Practical applications: This study uncovered insights into the factors that lead vehicles to overturn. This aids in suggesting appropriate safety countermeasures that mitigate the occurrences of rollover crashes to transportation agencies.

Adoption of complementary climate-smart agricultural technologies: lessons from Lushoto in Tanzania

BackgroundAgriculture is important for economic growth and development in many countries in Sub-Saharan Africa, including Tanzania. However, agricultural production and productivity remain relatively low, with significant yield gaps attributed to factors such as limited access to and low adoption of appropriate agricultural technologies, and climate-related risks resulting from climate variability and change. This paper explores the drivers of adoption of climate-smart agricultural (CSA) technologies and practices, taking into account the complementarity among agricultural technologies and heterogeneity of the farm households, using data from Lushoto in Tanzania.MethodsWe use a Multivariate Probit analysis of cross-sectional data collected from 264 smallholder farmers in Lushoto—a climate hotspot in Tanzania—to understand the drivers of household decisions to adopt CSA technologies and practices. The technologies included diversification of multiple stress (drought, floods, pests, diseases)-tolerant crop varieties, use of fertilizers, and application of herbicides and pesticides. The Multivariate Probit model was preferred as it takes into account the inter-relationships of the technologies as well as heterogeneity of the smallholder farmers for more robust estimates. The independent variables used in the analysis included household socio-economic factors such as the relative importance of crop and livestock enterprises, household land size, social capital, access to agricultural credit and weather information, previous experience with fertilizer use and household characteristics (age, education and gender of household head, and household size).ResultsAbout 63% of the households diversified their crop enterprises, shifting to improved resilient crops and crop varieties. Another 37% adopted fertilizers, while 38% applied pesticides and herbicides. Conditional on the unobservable heterogeneity effects, the results show that household adoption decisions on diversification of multiple stress-tolerant crops and crop varieties, fertilizer, and pesticides and herbicides are complementary. In addition, the results confirm existence of unobserved heterogeneity effects leading to varying impact of the explanatory variables on adoption decisions among farmers with similar observable characteristics.ConclusionsThe findings indicate that any effective CSA technology adoption and diffusion strategies and policies should take into account the complementarity of the technologies and heterogeneity of the smallholder farmers. Therefore, inter-related technologies should be promoted as a package or bundled while taking into consideration household and farm-level constraints to adoption.

Diagnostic analysis of environmental factors affecting the severity of traffic crashes: From the perspective of pedestrian–vehicle and vehicle–vehicle collisions

Objectives Traffic crashes under low-visibility conditions are frequent and serious. The aim of this study was to investigate how the road environment affects the severity of pedestrian–vehicle and vehicle–vehicle collisions under low-visibility conditions. Methods The injury severity of pedestrian–vehicle collisions and vehicle–vehicle collisions under low-visibility conditions was set as the dependent variable and divided into 2 categories: “killed or severe injury collision” and “slight injury collision.” Ten variables, including environment conditions, road traffic facility status, collision characteristics, and road attributes, were selected as independent factors according to the existing research and the traffic collision data set. Based on 656 valid pedestrian–vehicle collisions and 1,430 valid vehicle–vehicle collisions under low-visibility conditions, 2 random parameter logit models were established to evaluate the impacts of influencing factors on the severity of pedestrian–vehicle collisions and vehicle–vehicle collisions, in which the effect of unobserved heterogeneity was accounted for. Results The results show that visibility, presence of a roadside protection, road type, road pavement condition, and road alignment were significant factors affecting the severity of pedestrian–vehicle collisions. In addition, the presence of a median divider, location of the collision, road type, road surface condition, road pavement condition, and road alignment were significant factors affecting the severity of vehicle–vehicle collisions. Furthermore, the injury severity of both pedestrian–vehicle collisions and vehicle–vehicle collisions under low-visibility conditions on highways, poor road pavement, and non-straight-line sections was more likely to be fatal or serious. Conclusion These results have implications for the design of more effective strategies to reduce casualties from traffic crashes under low-visibility conditions.

Do auditors price litigious tone?

AbstractWe investigate whether audit fees are shaped by litigious tone. Using a sample of listed firms in the US, we find litigious tone in 10‐K reports is associated with higher audit fees. This finding remains robust when we account for sample selection bias, firm‐level unobserved heterogeneity effects, endogeneity concerns, or when subsections in 10‐K reports are analysed. In addition, we document the relationship is of a lower magnitude among high‐risk client firms, suggesting that auditors are already cautious when auditing high‐risk clients. This suggests that auditors rely less on litigious tone in determining audit fees when faced with high‐risk clients.