Crash Frequency Models Research Articles

Exploring the modeling and site-ranking performance of Bayesian spatiotemporal crash frequency models with mixture components

The current study introduces the flexible approach of mixture components to model the spatiotemporal interaction for ranking of hazardous sites and compares the model performance with the conventional methods. In case of predictive accuracy based on in-sample errors (posterior deviance), the Mixture-5 demonstrated superior performance in majority of the cases, indicating the advantage of mixture approach to accurately predict crash counts. LPML (log pseudo marginal likelihood) was also calculated as a cross-validation measure based on out-of-sample errors and this criterion also established the dominance of Mixture-5, further reinforcing the superiority of the mixture approach from different perspectives.The site ranking evaluation results demonstrated the advantages of adopting the mixture approach. In terms of total rank difference (TRD) results, there were several discrepancies between the two approaches, suggesting that two approaches designate unsafe sites differently. Another site ranking criterion, site consistency test (SCT), was employed to explore the difference in identification of unsafe sites based on two datasets: estimated crash count (traditional) and the spatial variability across time. The advantage of mixture models to act as a complimentary approach for site ranking was revealed by the spatial variability SCT results. The method consistency test (MCT) results also indicate the advantages of mixture models over the Base one. These findings suggested that mixture approach may prove helpful in the network screening step of safety management process to identify sites which may turn unsafe in the future and escape the detection from traditional methods.

Mapping the knowledge domain of road safety studies: A scientometric analysis

As a way of obtaining a visual expression of knowledge, mapping knowledge domain (MKD) provides a vision-based analytic approach to scientometric analysis which can be used to reveal an academic community, the structure of its networks, and the dynamic development of a discipline. This study, based on the Science Citation Index Expanded (SCIE) and Social Sciences Citation Index (SSCI) articles on road safety, employs the bibliometric tools VOSviewer and CitNetExplorer to create maps of author co-citation, document co-citation, citation networks, analyze the core authors and classic documents supporting road safety studies and show the citation context and development of such studies. It shows that road safety studies clustered mainly into four groups, whose we will refer to as “effects of driving psychology and behavior on road safety”, “causation, frequency and injury severity analysis of road crashes”, “epidemiology, assessment and prevention of road traffic injury”, and “effects of driver risk factors on driver performance and road safety”, respectively. Through our analysis, the core publications and their citation relationships were quickly located and explored, and “crash frequency modeling analysis” has been identified to be the core research topic in road safety studies, with spatial statistical analysis technique emerging as a frontier of this topic.

The challenge of safe and active transportation: Macrolevel examination of pedestrian and bicycle crashes in the Austin District

Encouraging the use of nonmotorized modes of transportation is a goal at the intersection of public health, environment, and transportation, given active transportation’s numerous benefits to individuals and communities. However, increased use of nonmotorized modes can also bring increased pedestrian–vehicle and bicycle–vehicle crashes. About 4,000 fatal and serious injury crashes involving a motor vehicle and a pedestrian or bicyclist occurred between 2007 and 2014 in the Texas Department of Transportation Austin District. This study contributed to the field of research by developing four crash frequency and severity models for pedestrians and bicyclists to identify the factors associated with the frequency of crashes and the presence of more severe crashes across the census block groups in the Austin District. The models showed the important role of different variables in crash frequency and severity, including travel demand, commute behaviors, network characteristics, and sociodemographic features. Using the model results, areas of concern with the greatest potential for safety improvements were identified. The study results can help develop safety improvement interventions for vulnerable road users in the Austin District and exemplify how other transportation agencies can estimate pedestrian and bicycle crashes using their existing database and crowdsourced data.

Taxicab crashes modeling with informative spatial autocorrelation

Maintaining taxi safety is one of the important goals of operating urban transportation systems. Taxicabs are often prone to higher crash risk due to their long-time exposure to the complicated and dynamic traffic environments in urban areas. Despite existing efforts in understanding the safety issues associated with these vehicles, there were still few attempts that have specifically examined the relationship between taxi-involved crashes and other multifaceted contributing factors. To this end, this paper aims to develop crash frequency models for analyzing taxi-involved crashes. In particular, the spatial autocorrelations between variables were explored and the Poisson conditional autoregressive (Poisson-CAR) models for taxi-involved crashes were proposed. Unlike previous safety studies that mainly consider distance as the key indicator of spatial correlation, the present paper introduced the use of massive taxi trip data for constructing a more informative spatial weight matrix. The developed models with the taxi trip-based weight matrix were tested by using the 2016 taxi trip data collected in Washington D.C. The modeling results highlight the key explanatory factors such as road density, taxi activity, number of bus stops, and land use. More importantly, it demonstrates that the proposed Poisson-CAR models with the taxi trip-based weight matrix outperformed both the non-spatial Poisson model and the Poisson-CAR models using conventional distance-based weight matrix. Moran’s I tests further indicate that our proposed models have sufficiently accounted for the spatial autocorrelation of the residuals. Thus, it deserves to consider informative spatial weight matrices when applying spatial models in traffic safety studies.

Development of pedestrian crash prediction model for a developing country using artificial neural network

Urban intersections in India constitute a significant share of pedestrian fatalities. However, model-based prediction of pedestrian fatalities is still in a nascent stage in India. This study proposes an artificial neural network (ANN) technique to develop a pedestrian fatal crash frequency model at the intersection level. In this study, three activation functions are used along with four different learning algorithms to build different combinations of ANN models. In each of these combinations, the number of neurons in the hidden layer is varied by trial and error method, and the best results are considered. In this way, 12 sets of pedestrian fatal crash predictive models are developed. Out of these, Bayesian Regularization Neural Network consisting of 13 neurons in the hidden layer with ‘hyperbolic tangent-sigmoid’ activation function is found to be the best-fit model. Finally, based on sensitivity analysis, it is found that the ‘approaching speed’ of the motorized vehicle has the most significant influence on the fatal pedestrian crashes. ‘Logarithm of average daily traffic’ (ADT) volume is found to be the second most sensitive variable. Pedestrian-vehicular interaction concerning ‘pedestrian-vehicular volume ratio’ and lack of ‘accessibility of pedestrian cross-walk’ are found to be approximately as sensible as ‘logarithm of ADT’.

A multivariate random parameter crash frequency model for exploring the associations between shoulder rumble strips on different crash types

A systemic approach to safety management has potential to be more cost effective than a traditional hot-spot approach in reducing crash frequency as it aims to identify sites with promise (SWiPs) by targeting certain crash types and select countermeasures accordingly, and therefore, effectively connects target crashes to their corresponding countermeasures. Although it seems to be promising, there are many challenges to evaluate the effects of countermeasures under the systemic approach, i.e. evaluate the effects of countermeasures by crash types. These challenges mainly include (1) low sample mean, (2) correlation among crash types, and (3) correlation among the effects of countermeasures on different crash types. A random parameter multivariate Poison lognormal (random parameter MVPLN) model is proposed. It was shown that the random parameter MVPLN model not only mitigates the three challenges, but also provides useful information than traditional crash frequency models. Shoulder rumble strips were found to be effective in reducing fix-object crashes, the primary crash type targeted by this countermeasure. The effectiveness of shoulder rumble strips on fixed-object crashes was found to be positively correlated with opposite-direction sideswipe and head-on crashes, meaning that the effects of shoulder rumble strips on fixed-object crashes would spillover to opposite-direction sideswipe and head-on crashes.

Incorporating behavioral variables into crash count prediction by severity: A multivariate multiple risk source approach

The frequency and severity of traffic crashes have commonly been used as indicators of crash risk on transport networks. Comprehensive modeling of crash risk should account for both frequency and injury severity—capturing both the extent and intensity of transport risk for designing effective safety improvement programs. Previous research has revealed that crashes are correlated across severity categories because of the combined influence of risk factors, observed or unobserved. Moreover, crashes are the outcomes of a multitude of factors related to roadway design, traffic operations, pavement conditions, driver behavior, human factors, and environmental characteristics, or in more general terms: factors reflect both engineering and non-engineering risk sources. Perhaps not surprisingly, engineering risk sources have dominated the list of variables in the mainstream modeling of crashes whereas non-engineering sources, in particular, behavioral factors, are crucially omitted. It is plausible to assume that crash contributing factors from the same risk source affect crashes in a similar manner, but their influences vary across different risk sources. Conventional crash frequency modeling hypothesizes that the total crash count at any roadway site is well-approximated by a single risk source to which several explanatory variables contribute collaboratively. The conventional formulation is not capable of accounting for variations between risk sources; therefore, is unable to discriminate distinct impacts between engineering variables and non-engineering variables. To address this shortcoming, this study contributes to the development of multivariate multiple risk source regression, a robust modeling technique to model crash frequency and severity simultaneously.The multivariate multiple risk source regression method applied in this study can effectively capture the correlation between severity levels of crash counts while identifyinging the varying effects of crash contributing factors originated from distinct sources. Using crashes on Wisconsin rural two-lane highways, two risk sources – engineering and behavioral – were employed to develop proposed models. The modeling results were compared with a single equation negative binomial (NB) model, and a univariate multiple risk source model. The results show that the multivariate multiple risk source model significantly outperforms the other models in terms of statistical fit across several measures. The study demonstrates a unique approach to explicitly incorporating behavioral factors into crash prediction models while taking crash severity into consideration. More importantly, the parameter estimates provide more insight into the distinct sources of crash risk, which can be used to further inform safety practitioners and guide roadway improvement programs.

Evaluation of driving performance in relation to safety on an expressway using field driving data

ABSTRACTStudies on road safety evaluation aim at minimizing the dependence on real crash data by incorporating parameters that often lead to crashes. Many of these studies consider either geometric parameters or surrogate safety measures for safety assessment. Although these parameters represent the safety of a road to a certain extent, it overlooks the driving performance which is a crucial factor that causes crashes. This study proposes a methodology to evaluate the safety of roads using driving performance measures along with geometric parameters derived from field driving data. A crash frequency model is also developed using the parameters thus identified and historic crash data along an expressway. The results show a good correlation between driving performance, road geometry, and crashes.

Network screening for large urban road networks: Using GPS data and surrogate measures to model crash frequency and severity

Crash frequency and injury severity are independent dimensions defining crash risk in road safety management and network screening. Traditional screening techniques model crashes using regression and historical crash data, making them intrinsically reactive. In response, surrogate measures of safety have become a popular proactive alternative. The purpose of this paper is to develop models for crash frequency and severity incorporating GPS-derived surrogate safety measures (SSMs) as predictive variables. SSMs based on vehicle manoeuvres and traffic flow were extracted from data collected in Quebec City. The mixed multivariate outcome is estimated using two models; a Full Bayes Spatial Negative Binomial model for crash frequency estimated using the Integrated Nested Laplace Approximation approach and a fractional Multinomial Logit model for crash severity. Model outcomes are combined to generate posterior expected crash frequency at each severity level and rank sites based on crash cost. The crash frequency model was accurate at the network scale, with the majority of proposed SSMs statistically significant at 95% confidence and the direction of their effect generally consistent with previous research. In the crash severity model, fewer variables were significant, yet the direction of the effect of all significant variables was again consistent with previous research. Correlations between rankings predicted by the mixed multivariate model and by the crash data were adequate for intersections (0.46) but were poorer for links (0.25). The ability to prioritize sites based on GPS data and SSMs rather than historical crash data represents a substantial contribution to the field of road safety.

Development of countermeasures to effectively improve pedestrian safety in low-income areas

Abstract In recent years, many departments of transportation in the US have invested more resources to enhance pedestrian safety. However, there is still a need to effectively and systematically address pedestrian safety issues in low-income areas. Statistics show that pedestrians are fatally injured at disproportionately higher rates in the nation's poorer neighborhoods. Low-income areas often are sectioned by high-volume/high-speed arterials, which compound the problem. In this study, pedestrian-vehicle crash data in low-income areas were analyzed from two aspects: how demographic factors, road environment, and land use types influence pedestrian crash occurrence (based on frequency data) and how demographic and other factors influence severity in a pedestrian crash (based on severity data). The crash frequency modeling results show that major influential variables for higher pedestrian crash frequency include four demographic factors (proportions of older adults, commuters using public transit or biking, people with low education level, and zero-car ownership), three road environmental factors (densities of traffic signals and bus stops and proportion of higher-speed roads), and three land use factors (densities of discount stores, convenience stores, and fast-food restaurants). The injury severity modeling results show that a dark–not lighted condition is the most influential variable for severe injury pedestrian crashes, and the number of impaired pedestrians and aggressive drivers also greatly increases the probability of severe injury. Based on the analysis results, this paper makes specific recommendations for both engineering countermeasures and pedestrian safety education/outreach plans that resonate with a given area's demographics to effectively improve pedestrian safety in low-income areas.

Alternative multivariate multimodal crash frequency models

The central issue for successful implementation of a multimodal approach is the development of appropriate crash frequency models that can jointly estimate the crash risk of different mode users. This study proposed two multivariate spatial-temporal models to analyze 6 years of modal crash data from counties in California: one with fixed time trend applied to all modes, the other with mode-varying time trend coefficients. These models were compared with three other multivariate models from past studies. The major objective was to examine the benefits of the newly proposed models that have substantially increased computational cost, because both dimensions of time and space, and their interaction, are considered. The model fitness results from penalized criterion revealed that the proposed models significantly improved the model fitting by pooling strength from neighboring sites, consideration of time trend, as well as their interactions. The model with mode-varying time coefficients was observed to be superior in terms of prediction accuracy. The posterior deviance was observed to be the governing factor for overall fit and consistently showed a strong positive correlation between model fit and prediction accuracy. Overall, the study is anticipated to enhance the understanding of safety impacts from the interaction of various modes.

Utilizing Real-time Traffic and Weather Data to Explore Crash Frequency on Urban Motorways: A Cusp Catastrophe Approach

Abstract The investigation of crash frequency with freeway traffic and weather data has recently received significant attention by researchers. This paper extends previous research by proposing nonlinear models for modeling crash frequencies which incorporate real-time traffic and weather data collected from an urban motorway in Athens, Greece. Cusp catastrophe theory is applied and compared with traditional statistical models such as the negative binomial model. The results of crash frequency models provide evidence of the potential applicability of the cusp catastrophe theory to road safety, however it seems that linearity of the system is preserved. Hence, traditional models such as the negative binomial model are proved equally capable of describing the underlying phenomenon, even though the goodness-of-fit is not as good as that of the cusp model. Therefore, the explanation of crash frequency phenomenon only with nonlinear model can be supported. A number of interesting findings have also been disclosed. Firstly, is that rainfall intensity has a strong linear impact on crashes (high rainfall intensity causes more crashes). On the other hand, average flow is indicated to have a strong non-linear relationship with crash frequency. Finally, more research is needed to further understand the applicability of cusp catastrophe theory in road safety.

A Multivariate Copula-Based Macro-Level Crash Count Model

The current study contributes to safety literature both methodologically and empirically by developing a macro-level multivariate copula-based crash frequency model for crash counts. The multivariate model accommodates for the impact of observed and unobserved effects on zonal level crash counts of different road user groups including car, light truck, van, other motorized vehicle (including truck, bus and other vehicles), and non-motorists (including pedestrians and cyclists). The proposed model is estimated using Statewide Traffic Analysis Zone (STAZ) level road traffic crash data for the state of Florida. A host of variable groups including land-use characteristics, roadway attributes, traffic characteristics, socio-economic characteristics and demographic characteristics are considered. The model estimation results illustrate the applicability of the proposed framework for multivariate crash counts. Model estimation results are further augmented by evaluation of predictive performance and policy analysis.

Bayesian approach to model pedestrian crashes at signalized intersections with measurement errors in exposure

This study intended to identify the potential factors contributing to the occurrence of pedestrian crashes at signalized intersections in a densely populated city, based on a comprehensive dataset of 898 pedestrian crashes at 262 signalized intersections during 2010–2012 in Hong Kong. The detailed geometric design, traffic characteristics, signal control, built environment, along with the vehicle and pedestrian volumes were elaborately collected. A Bayesian measurement errors model was introduced as an alternative method to explicitly account for the uncertainties in volume data. To highlight the role played by exposure, models with and without pedestrian volume were estimated and compared. The results indicated that the omission of pedestrian volume in pedestrian crash frequency models would lead to reduced goodness-of-fit, biased parameter estimates, and incorrect inferences. Our empirical analysis demonstrated the existence of moderate uncertainties in pedestrian and vehicle volumes. Six variables were found to have a significant association with the number of pedestrian crashes at signalized intersections. The number of crossing pedestrians, the number of passing vehicles, the presence of curb parking, and the presence of ground-floor shops were positively related with pedestrian crash frequency, whereas the presence of playgrounds near intersections had a negative effect on pedestrian crash occurrences. Specifically, the presence of exclusive pedestrian signals for all crosswalks was found to significantly reduce the risk of pedestrian crashes by 43%. The present study is expected to shed more light on a deeper understanding of the environmental determinants of pedestrian crashes.

Surrogate safety and network screening: Modelling crash frequency using GPS travel data and latent Gaussian Spatial Models

Improving road safety requires accurate network screening methods to identify and prioritize sites in order to maximize the effectiveness of implemented countermeasures. In screening, hotspots are commonly identified using statistical models and ranking criteria derived from observed crash data. However, collision databases are subject to errors, omissions, and underreporting. More importantly, crash-based methods are reactive and require years of crash data. With the arrival of new technologies including Global Positioning System (GPS) trajectory data, proactive surrogate safety methods have gained popularity as an alternative approach for screening. GPS-enabled smartphones can collect reliable and spatio-temporally rich driving data from regular drivers using an inexpensive, simple, and user-friendly tool. However, few studies to date have analyzed large volumes of smartphone GPS data and considered surrogate-safety modelling techniques for network screening. The purpose of this paper is to propose a surrogate safety screening approach based on smartphone GPS data and a Full Bayesian modelling framework. After processing crash data and GPS data collected in Quebec City, Canada, several surrogate safety measures (SSMs), including vehicle manoeuvres (hard braking) and measures of traffic flow (congestion, average speed, and speed variation), were extracted. Then, spatial crash frequency models incorporating the extracted SSMs were proposed and validated. A Latent Gaussian Spatial Model was estimated using the Integrated Nested Laplace Approximation (INLA) technique. While the INLA Negative Binomial models outperformed alternative models, incorporating spatial correlations provided the greatest improvement in model fit. Relationships between SSMs and crash frequency established in previous studies were generally supported by the modelling results. For example, hard braking, congestion, and speed variation were all positively linked to crash counts at the intersection level. Network screening based on SSMs presents a substantial contribution to the field of road safety and works towards the elimination of crash data in evaluation and monitoring.

An empirical evaluation of multivariate spatial crash frequency models

Many studies have employed spatial, temporal, or a combination of both specifications for analysis of roadway crashes at different spatial levels. However, there is lack of a comprehensive study which compares the crash estimation performance of different spatial weight matrices and their combination with various temporal treatments. The current study fills the research gap by comparing different Full Bayesian (FB) multivariate spatiotemporal crash models. The pedestrian and bicyclist crash data across an eight-year period for 58 counties in California were used as a case study. Three groups of models were developed based on temporal treatment, where each group comprised of 17 models differing on the basis of different adjacency- and distance-based spatial weight matrices. The first group of multivariate models incorporated only unstructured random error term and spatially structured conditional autoregressive (CAR) term. The second group built upon the former and introduced a linear time trend to develop a spatiotemporal model, while the third group allowed the interaction of space and time. The predictive performance of the alternate models across and within groups was assessed by employing several evaluation criteria.The modeling results demonstrated the robustness of models based on the similar signs and closeness of coefficients for the posterior estimates of parameters. For overall model comparison, the pure-distance model D0.5 demonstrated the best performance for different evaluation criteria based on training and test errors across three groups. The variability in performance of other distance models suggested that caution must be exercised for the choice of exponents. The correlation analysis revealed the presence of positive correlations among the criteria based on training errors, as well as with cross-validation. However, a very strong positive correlation was observed between the criteria based on effective number of parameters and posterior deviance, indicating that an increased number of parameters may not lead to improved model fit. This finding reinforced the importance of selecting the optimum weight matrix for spatial correlation as a more complex structure may not lead to expected advantages at model performance. For comparison among three groups of different temporal treatments, the third group demonstrated the best performance and conveyed the benefits of incorporating the spatial and temporal interaction. The results from ANOVA (analysis of variance) and HSD (Honest Significant Differences) tests also established the existence of statistical differences for the superiority of space-time interactions models. However, the box and whisker plots demonstrated high variability among the models of the third group, suggesting that some models may not benefit from interaction term. For comparison among adjacency- and distance-based models, the distance-based models were mostly observed to be superior. However, the greater variability of model performance associated with distance-based models suggested for careful consideration during their selection. Additionally, it is important to note that the results observed in this study are specific to the county-level crash data of California. As such, the study does not recommend generalization of the results for extension to other spatial levels of roadway network, and readers and future research studies are advised to exercise caution before implementing the models.

Analysis of Nonsevere Crashes on Two- and Four-Lane Urban and Rural Highways: Effects of Wet Pavement Surface Condition

This study examines the effects of wet pavement surface conditions on the likelihood of occurrences of nonsevere crashes in two- and four-lane urban and rural highways in Alabama. Initially, sixteen major highways traversing across the geographic locations of the state were identified. Among these highways, the homogenous routes with equal mean values, variances, and similar distributions of the crash data were identified and combined to form crash datasets occurring on dry and wet pavements separately. The analysis began with thirteen explanatory variables covering engineering, environmental, and traffic conditions. The principal terms were statistically identified and used in a mathematical crash frequency models developed using Poisson and negative binomial regression models. The results show that the key factors influencing nonsevere crashes on wet pavement surfaces are mainly segment length, traffic volume, and posted speed limits.

A joint econometric approach for modeling crash counts by collision type

In recent years, there is growing recognition that common unobserved factors that influence crash frequency by one attribute level are also likely to influence crash frequency by other attribute levels. The most common approach employed to address the potential unobserved heterogeneity in safety literature is the development of multivariate crash frequency models. The current study proposes an alternative joint econometric framework to accommodate for the presence of unobserved heterogeneity – referred to as joint negative binomial-multinomial logit fractional split (NB-MNLFS) model. Furthermore, the study undertakes a first of its kind comparison exercise between the most commonly used multivariate model (multivariate random parameter negative binomial model) and the proposed joint approach by generating an equivalent log-likelihood measure. The empirical analysis is based on the zonal level crash count data for different collision types from the state of Florida for the year 2015. The model results highlight the presence of common unobserved effects affecting the two components of the joint model as well as the presence of parameter heterogeneity. The equivalent log-likelihood and goodness of fit measures clearly highlight the comparable performance offered by the proposed joint model relative to the commonly used multivariate approach. Overall, the model interpretations and fit measures clearly highlight the potential complementary role of the proposed approach for crash frequency analyses.

A Comparative Analysis of Factors Affecting the Frequency and Severity of Freight-Involved and Non-Freight Crashes on a Major Freight Corridor Freeway

Traffic crashes cost society billions of dollars each year as a result of property damage, injuries, and fatalities. Additionally, traffic crashes have a negative impact on mobility, as they are a primary cause of non-recurring delay. With the Interstate 10 corridor between the ports of Los Angeles and Houston being one of the most vital links for goods movement across the United States, safety and mobility along this freeway, particularly for freight traffic, are of significant concern. This study, which utilized six years of crash data from the state of Arizona, explores factors affecting the frequency and severity of crashes along the Arizona portion of the I-10 corridor, with a particular focus on freight-related crashes. The safety performance along the I-10 is analyzed through the development of crash frequency and severity prediction models using integrated crash, roadway, traffic, and environmental data. Negative binomial and ordered logit models, with the incorporation of random parameters, were estimated to provide a detailed understanding of factors associated with freight-involved crashes and how they compare to non-freight crashes in terms of frequency and severity. The results showed that several roadway- crash-, vehicle-, and person-related variables were associated with the frequency and/or severity of crashes along the study corridor. These findings provide important insights which can be used to develop or plan countermeasures aimed at improving the safety and efficiency of freight travel, which may include new ITS technologies, and targeted educational and enforcement campaigns.

Exploring the Effect of Different Neighboring Structures on Spatial Hierarchical Joint Crash Frequency Models

Corridor safety analysis is a primary interest of many road safety studies. Corridors typically contain intersections and roadway segments. Having both components while analyzing corridors in addition to corridor-level variables in a hierarchical joint model would provide a comprehensive understanding of the existing corridor safety problems. There will probably be spatial correlation among road entities along a corridor, especially if the distance between the road entities is not large. Therefore, it is crucial to consider spatial effects in the model. However, this data structure is relatively new, and the best spatial weight matrix for this hierarchical spatial joint model has yet to be investigated. Therefore, this study estimates a hierarchical Poisson-lognormal (HPLN) joint model with spatial effects and explores the effect of different neighboring structures. A total of thirteen HPLN joint models are estimated: one HPLN joint model with corridor random effect and twelve HPLN joint models with spatial effects. Four types of conceptualization of spatial relationships were considered: (a) adjacency-based, (b) adjacency-route, (c) distance-order, and (d) distance-based spatial weight features. The results show the importance of incorporating spatial effects in the model. It was found that having a joint model is important since one of the best models is the adjacency-based first-order model, where the feeding road entities in addition to the directly adjacent road entity of the same type as the road entity of interest are considered. The results confirm the importance of spatial autocorrelation between road entities along the same corridor.