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nikolaouspatialanalysistelematicsbased2025.md

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category: literaturenote citekey: nikolaouspatialanalysistelematicsbased2025 title: Spatial analysis of telematics-based surrogate safety measures authors: "Nikolaou, Dimitrios; Ziakopoulos, Apostolos; Kontaxi, Armira; Theofilatos, Athanasios; Yannis, George" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.jsr.2024.09.012 publication: Journal of Safety Research url: "https://doi.org/10.1016/j.jsr.2024.09.012" zotero_key: 4IJ8JMVS zotero_storage: XGC53WFW collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Nikolaou, Dimitrios"

status: converted

Contents lists available at ScienceDirect

Journal of Safety Research

journal homepage: www.elsevier.com/locate/jsr

Spatial analysis of telematics-based surrogate safety measures

Dimitrios Nikolaou a,* , Apostolos Ziakopoulos a , Armira Kontaxi a , Athanasios Theofilatos b , George Yannis a

  • a Department of Transportation Planning and Engineering, National Technical University of Athens, 5 Heroon Polytechniou Str., GR-15773 Athens, Greece
  • b Department of Civil Engineering, University of Thessaly, Pedion Areos, GR-38334 Volos, Greece

ARTICLE INFO

Keywords: Harsh braking Surrogate Safety Measures Spatial Autocorrelation Spatial Zero-Inflated Model Spatial Random Forest

ABSTRACT

Introduction: Surrogate Safety Measures (SSMs) such as time-to-collision, harsh braking, and post-encroachment time, are widely proposed in transportation science and are fruitful for road safety evaluations when detailed crash data are unavailable. Hence, this study aims to conduct spatial analysis of harsh braking events to explore their adaptability and informative power in a region with low crash counts, as this approach remains briefly addressed in the literature. Method: The analysis utilizes smartphone driving behavior data and OpenStreetMap road network characteristics of 6,103 road segments in the Region of Eastern Macedonia and Thrace, Greece. A series of advanced statistical and machine learning models were applied. In addition to developing non-spatial models, the identification of spatial autocorrelation led to the development of spatial modeling techniques to account for spatial dependencies. Results: The number of trips per segment, segment length, speeding and mobile phone use are positively correlated with harsh braking. Conversely, motorways exhibited fewer harsh braking events compared to other road types. Furthermore, the number of trips per examined road segment was the most influential predictor, highlighting its importance as a proxy measure of risk exposure. In terms of model performance, the Spatial Zero-Inflated Negative Binomial (SZINB) model outperformed the corresponding nonspatial model. Moreover, the Spatial Random Forest (SRF) model reduced the absolute values of spatial autocorrelation in the residuals and showed a better fit to the observed data compared to the conventional Random Forest model. Conclusions: Geometrical and behavioral parameters can be combined to meaningfully conduct road safety analysis spatially and proactively, as they are highly correlated with harsh braking SSMs, while the SZINB and the SRF model exhibited better model fit than their non-spatial counterparts. Practical Applications: The study results can assist policymakers in developing appropriate countermeasures to reduce harsh braking in targeted spatial units, thereby enhancing overall road safety.

1. Introduction and background

Road crashes and their consequences continue to be a serious global societal concern. This fact is also supported by estimates provided by the World Health Organization (WHO), which state that 1.19 million road users lost their lives in 2021 due to road crashes, ranking road crashes as the 12th leading cause of death globally (World Health Organization, 2023). Regarding the respective figures in the European Union, 20,640 road users lost their lives due to road crashes in 2022. In Greece, where the analyses of the present study were conducted, there were 60 road fatalities per million population recorded in 2023, ranking the country in the 22nd position among the 27 countries of the European Union (European Commission, 2023).

Road crashes are a complex phenomenon affected by several

parameters that can be categorized into three distinct aspects: (i) road users (drivers, riders, passengers and pedestrians); (ii) vehicles; and (iii) road infrastructure and environment. Among these main categories, it has been observed that the vast majority of road crashes can be attributed to human factors and human error, either exclusively or partially, accounting for rates as high as 94% (Singh, 2015). This particularly high percentage of responsibility for the human factor in the causal chain of road crashes points out the importance of studying and analyzing driver behavior.

A large number of existing studies in the broader literature have examined driver behavior by using a diverse array of methods. For instance, questionnaire surveys are a traditional way of collecting data of road users self-declared behavior in traffic and general road safety attitudes or perceptions (Rowe et al., 2015; Pires et al., 2020).

E-mail address: dnikolaou@mail.ntua.gr (D. Nikolaou).

* Corresponding author.

Furthermore, a common way of collecting data on driver compliance metrics (e.g., driver distraction, seatbelt use, traffic rule compliance etc.) is roadside observation (Yannis et al., 2011; Sullman, 2012; Prat et al., 2015). Another widely used family of methods is the utilization of driving simulators. A number of authors have recognized that driver simulators are useful tools to extract various metrics related to speed, reaction time, lane position, headway distance, distraction, fatigue and others in a safe and virtual road environment (Lenn´e et al., 1997; Calvi & D'amico, 2013; Papantoniou et al., 2019).

Apart from these methods, the recent swift technological development in naturalistic driver recording has led to a growing abundance of data from sensors in vehicles and smartphones, which can be used to assess driver behavior (Ziakopoulos et al., 2020). More specifically, smartphones are now equipped with sensors like accelerometers, gyroscopes, magnetometers and GPS, which enable the extraction of various driver performance metrics and Surrogate Safety Measures (SSMs) through a low-cost and rapid manner, without the need for user interaction (Mantouka et al., 2018; Liu et al., 2023). SSMs encompass a wide range of metrics and parameters, which are not directly derived from or rely on crash data. These measures possess various advantages when compared to historical crash data. Specifically, they serve as a proactive approach, enabling road safety analyses before the occurrence of road crashes (Tarko et al., 2009). In contrast, crash data collection relies heavily on manual methods, which can be related to limitations such as inaccurate data and under-reporting (Imprialou & Quddus, 2019; Yannis et al., 2014).

According to Tarko (2018), the adoption of SSMs in the field of road safety facilitates the understanding of crash-leading factors and allows for evaluating the effectiveness of different countermeasures. Wang et al. (2021) divided SSMs into two main groups: (i) SSMs and (ii) SSMbased models. The first group encompasses SSMs that are time-based, deceleration-based, or energy-based. It includes SSMs that use predefined thresholds for traffic conflicts' detection, such as Time-to-Collision (TTC), Post-Encroachment Time (PET), Time-to-Crash (TC) and Deceleration Rate to Avoid the Crash (DRAC) (Bonela & Kadali, 2022). On the other hand, the other group of SSMs focuses on establishing a direct link between each traffic conflict and either a crash or a non-crash outcome, by estimating its crash probability (Songchitruksa & Tarko, 2006; Wang & Stamatiadis, 2014). This kind of SSMs can be also derived from simulation processes (Gettman & Head, 2003).

In addition, the constant advancement in technology has made smartphones a key choice for collecting data on SSMs, particularly regarding harsh driving events such as harsh braking and harsh acceleration (Nikolaou et al., 2023). It is important to mention that the two aforementioned harsh driving events are distinct occurrences that take place in different traffic situations and should not be analyzed together as a single phenomenon. Firstly, drivers who experience higher levels of anger, frustration, and anxiety tend to exhibit increased acceleration values and apply higher physical pressure on the accelerator pedal (Stephens & Groeger, 2009). On the other hand, drivers more typically engage in harsh braking events as a reaction to various potentially hazardous situations, aiming to prevent near crashes or collisions (Ziakopoulos et al., 2022). Such events are of particular importance in evaluating driving risk (Gündüz et al., 2017) since they are inherently associated with the likelihood of a road crash (Tselentis et al., 2017).

Stipancic et al. (Stipancic et al., 2018) utilized GPS data of 21,000 trips in Quebec City, Canada and found that harsh braking and harsh acceleration events were positively correlated with crash frequency at the link and intersection levels. In another study focusing on 668 motorway segments in Greece, the results of a Negative Binomial (NB) regression model indicated that both the number of harsh braking events and harsh accelerations were positively correlated with the number of injury as well as property-damage only crashes (Nikolaou et al., 2023). Following this research, it was found that harsh braking events contribute significantly to predicting the crash risk level of the road sections under consideration, which is not the case for harsh accelerations. Therefore, it is concluded that harsh braking events are a plausible SSM that can be used either in various proactive road safety analyses before road crashes' occurrence or in cases of unavailable detailed road crash data (Nikolaou et al., 2023). Liu et al. (2023) also found a strong correlation between harsh braking events and road crashes from publicly available datasets, supporting their use as a safety surrogate.

When considering macroscopic infrastructure or network-based analyses, it is critical to note that road segments are not independent from other segments in their vicinity. Rather, it is more often the case that they share some features, and that events or flows that occur on one segment will typically affect the neighboring segments. Thus, spatial autocorrelation needs to be accounted for in such studies.

Spatial autocorrelation often occurs when treating frequencies of harsh braking events as point-type data (Ziakopoulos, 2021; Ziakopoulos et al., 2022). Consequently, it is important to consider spatial modeling techniques to capture spatial dependencies and enhance the reliability of the analyses, similar to studies that either analyze only historical road crashes or combine both SSMs and crash records (Ziakopoulos & Yannis, 2020; Aguero-Valverde & Jovanis, 2006; Stipancic et al., 2018; Satria et al., 2021; Yang et al., 2021; Li et al., 2021). However, spatial analysis of SSMs has not received significant attention in the road safety literature, making it a promising research direction in the field. This approach remains briefly addressed in the literature but has the potential to account for spatial dependencies and enhance the robustness of the analyses (Nikolaou et al., 2023).

Hence, this paper aims to investigate the application of spatial analysis of SSMs, and in particular harsh braking occurrences. More specifically, the objective of this paper is to carry out spatial analysis of harsh braking frequencies per road segment and correlating them with various road network characteristics and naturalistic driving metrics. The scientific contribution of this paper is further refined across several research aspects which are being explored, namely:

  • 1. The harsh braking data describe events performed during naturalistic driving across various road environments. Data are obtained from driving telematics utilizing smartphone sensors, which have become relatively recently available, and their applications in spatial analysis are under-researched in present literature.
  • 2. The analysis is conducted in an area of scarce transport and crash data in order to discover if harsh braking SSMs can provide fruitful insights therein.
  • 3. Newly available spatial machine learning models are utilized for the analysis alongside more traditional statistical methods, which are efficient methods for data processing that can be efficiently applied to a larger network of roadways.

Spatial modeling techniques, including the Spatial Zero-Inflated Negative Binomial (SZINB) model and the Spatial Random Forest (SRF) are employed to model harsh braking events frequencies. These objectives are achieved by utilizing smartphone driving data and OpenStreetMap (OSM) geometric data.

The rest of the paper is organized as follows. Section 2 describes the data sources and the corresponding data processing. Section 3 provides an overview of the theoretical background of the statistical methods employed in this research. Section 4 presents and discusses the key results obtained from the developed models. Finally, Section 5 concludes the paper and suggests potential avenues for future research.

2. Data collection and processing

To achieve the goals of the study, a framework for evaluating the safety of road segments utilizing high-resolution naturalistic driving data obtained from smartphone sensors was developed. The first step involves the definition of a study road network within specific boundaries. Within this road network, an analysis is conducted on all road

segments sourced from OpenStreetMap (OSM) to extract their geometric and network characteristics. Subsequently, naturalistic driving behavior data were extracted from a smartphone application, including the number and location of harsh braking events and other metrics, are aligned with the corresponding OSM segments. This process results in the development of a spatial dataset that encompasses aggregated behavior metrics, as well as geometric and network characteristics on a segment level.

The OSM initiative is a collaborative effort, which offers usergenerated street maps. About a decade ago, the accuracy of OSM data with regard to segment length was approximately 80% to 90%, with an error of ± 6 m. Since then, OSM has undergone continuous enhancements (Haklay, 2010; Zhang & Malczewski, 2019). It is also noted that the WGS84 coordinate system, which is widely utilized by GPS units and services, is also employed by OSM. All algorithms and analyses in this study have been conducted in R-studio (R Core Team, 2023) by using several packages. Specifically, the R library "osmdata" was used to extract the road segment data from OSM (Padgham et al., 2017). This library imports OSM data into R as simple features, which can be further processed with the R package "sf" (Pebesma, 2018).

The examined area of the Eastern Macedonia and Thrace Region is located in northeastern Greece, approximately 700 km driving distance from the capital of the country, Athens. As the authors mean to eventually expand the present analyses throughout Greece, issues of data availability were brought into consideration. Therefore, this particular area was selected as a challenging location for the initial analysis, due to limited data availability, with the rationale that if models converged in this area, they would probably do so be in other areas as well.

The examined road network is illustrated in Fig. 1 and consists of 6,103 road segments, with an average length of 288 m, resulting in a total road network length of 1,763 km. The distribution of road types is as follows: residential roads account for 67.8%, tertiary roads for 12.1%, secondary roads for 7.4%, motorways and motorway links for 3.8%, and the remaining 9% consists of other road types. It is noted that the maps presented in this paper were generated using the OSM/R-studio interface package and JavaScript library "leaflet" (Cheng et al., 2019).

The present study utilizes naturalistic driving data obtained from a smartphone application developed by OSeven Telematics (htt ps://www.oseven.io). This application operates in the smartphone's background collecting sensors data without requiring any user initiation while driving or any other engagement. Sensors like the accelerometer, magnetometer, GPS and gyroscope are utilized to record the data. To clean and normalize the data, sophisticated Machine Learning (ML) algorithms are implemented. Trip duration, trip distance, driver speed, instances of speeding, the frequency of harsh braking and harsh acceleration incidents and driver distraction from mobile phone use are computed, among other metrics.

The sensor-based detection of harsh events is made by algorithms under IP protection and are undisclosed to the authors. Importantly, these algorithms do not rely on predefined thresholds to classify harsh events. Instead, ML techniques and data fusion are implemented to identify abrupt spikes in the sensor data (Kontaxi et al., 2021a) regardless of absolute values. All naturalistic driving data used in this research were provided by OSeven Telematics in a fully anonymized format, complying with the relevant national and European personal data regulations, including the General Data Protection Regulation (GDPR). Importantly, OSeven smartphone application has been employed for research purposes pertaining mainly to driving behavior, as extensively documented in prior studies in the field (Papadimitriou et al., 2019; Kontaxi et al., 2021b; Ziakopoulos, 2021; Tarlochan et al., 2022).

The overlay and combination of behavioral data with infrastructure parameters typically entails some compromises as the measurement units are fundamentally different (i.e., mobile drivers vs. immobile segments), which inadvertently lead to some data loss. Thus, the term 'behavior' in this paper is used to more precisely refer to the main purpose and utility of telematics data that were analyzed, as opposed to a purely behavioral analysis, which would have to be based on the examination of individual drivers and their characteristics.

Thus, to achieve the aim of the present study, data from 5,129 trips that belong to the examined area in 2021 were utilized. Each trip is defined as the span between the first and last detection of vehicle movement by the smartphone sensors, including a buffer time period to avoid recording pauses in temporary vehicle stops. The trips were all conducted by private vehicle drivers. The respective smartphone recordings were obtained by drivers only, and neither passengers nor public transport users were included, as OSeven gives the option to flag trips recorded as passenger or public transport users. The trip duration had a mean value of 634 s and a standard deviation of 556 s. The histogram of trip durations is illustrated in Fig. 2. Among these trips, a total of 2,889 harsh braking events were recorded. It is noted that no raw acceleration data was provided for the present analysis. Rather, the focus of the paper lies on analyzing harsh braking events that were recorded as such during naturalistic driving in a point-type data approach similar to spatial analysis of crashes.

The objective of the data collection procedure was to generate a spatial dataset encompassing geometric and network characteristics, as well as aggregated driving behavior metrics on the road segment level.

Fig. 1. Examined road network of the Eastern Macedonia and Thrace Region (in grey).Base map from OpenStreetMap, edited by the authors.

Fig. 2. Histogram of trip duration frequencies in the examined road network.

The OSM segmentation was retained for the analysis, as there is a solid reasoning behind it that dictates that segments are separated when road/traffic conditions change (e.g., a lane is added or the speed limit changes). Smartphone data, which provide information for each second of a trip had to be associated with the corresponding road segment that each driver traveled through. To this end, a spatial map-matching procedure was followed. Initially, the centroid of each road segment linestring was identified using the "st_centroid" function from the "sf" R library (Pebesma, 2018). Centroids are point-type quantities and represent the geometric center of each road segment. Next, the aggregated driving behavior metrics were assigned to the nearest road segment centroid based on the latitude and longitude coordinates for each trip-second. This was accomplished using the "st_join" function and the "st_nearest_feature" geometry predicate function from the "sf" R library.

This procedure resulted in the creation of a spatial dataset comprising aggregated behavior metrics, geometric and network characteristics for 6,103 road segments in the Eastern Macedonia and Thrace Region. Table 1 presents the variables that were considered in this work, along with their abbreviations as well as key descriptive statistics. With regard to the curvature characteristics of the considered segments, an index termed "efficiency" has been calculated. Specifically, it is a metric of segment linearity expressed by the ratio of the Euclidean distance between the start and end points of a road segment to the total segment length. It is a dimensionless ratio between 0 and 1, with higher values indicating a more linear road segment, while lower values indicate higher curvature.

3. Methodology

After concluding the described data collection process, Zero-Inflated Negative Binomial regression was selected as a suitable method for the analysis of the correlation between harsh braking events and the other variables as mentioned in Table 1. This was also aided by exploratory modeling, which highlighted that traditional count-based models (such as Generalized Linear Model − Negative Binomial Regression) were unsuitable for the current spatial dataset, probably due to the significant excess of zeros, as shown in the histogram of harsh braking events in Fig. 3.

As observed from previous studies (Ziakopoulos, 2021; Ziakopoulos et al., 2022), statistical modeling of harsh braking events frequently exhibits spatial autocorrelation. The Moran's I coefficient is the most widely employed measure of spatial autocorrelation (Moran, 1950). If statistically significant spatial autocorrelation is detected, it becomes crucial to employ spatial modeling approaches to account for spatial dependencies and improve the robustness of the analyses. In the case of the 6,103 road segments within the Eastern Macedonia and Thrace Region, the observed Moran's I value is positive (0.0263) and statistically significant (p-value < 0.001), indicating that neighboring road segments tend to have similar harsh braking counts. Towards this direction, SZINB (Spatial Zero-Inflated Negative Binomial) and SRF (Spatial Random Forest) models have been developed in this study in order to consider such spatial dependencies.

3.1. Spatial Zero-Inflated Negative Binomial model

The non-spatial Zero-Inflated Negative Binomial (ZINB) regression is used for count data that exhibit overdispersion and excess zeros. The data distribution of the ZINB combines the negative binomial distribution and the logit distribution. The possible values of Y are non-negative integers such as 0, 1, 2, 3, and so on. Suppose that for each observation, there are two possible cases. If the first case occurs, the count is zero. However, if the second case occurs, counts (including zeros) are generated according to the negative binomial distribution. Suppose that

Fig. 3. Histogram of harsh braking events in the examined road segments.

Table 1 Key descriptive statistics of geometric characteristics and driving behavior metrics per road segment in the examined area.

| Variable Description | Abbreviation | Descriptive Statistics | | | | | | |----------------------------------------------------|---------------------|------------------------|----------------------------------------|--------|-----------|----------|--| | Numeric Variables | | Mean | Min | Median | Max | St. Dev. | | | Segment length [m] | length | 288.84 | 2.05 | 123.07 | 11,301.96 | 628.80 | | | Measure of segment linearity [dimensionless ratio] | efficiency | 0.94 | 0.01 | 1.00 | 1.00 | 0.13 | | | Number of trips [count] | trip_count | 32.12 | 0.00 | 1.00 | 1,272.00 | 102.58 | | | Duration of exceeding the speed limits [sec] | speeding_count | 16.05 | 0.00 | 0.00 | 19,126.00 | 312.64 | | | Duration of mobile phone use [sec] | mobile_usage_count | 13.51 | 0.00 | 0.00 | 2,461.00 | 88.78 | | | Number of harsh braking events [count] | harsh_braking_count | 0.47 | 0.00 | 0.00 | 117.00 | 3.85 | | | Categorical Variables | | Frequencies | | | | | | | Road type (motorway/motorway link) | motorway | | other road types: 5,872, motorway: 231 | | | | |

the first case occurs with probability π and the second case occurs with probability 1-π. Consequently, the probability distribution of the ZINB random variable yi can be written:

$$\Pr(\mathbf{y}_i = j) = \begin{cases} \pi_i + (1 - \pi_i)g(y_i = 0)ifj = 0\ (1 - \pi_i)g(y_i)ifj > 0 \end{cases}$$ (1)

The non-spatial Zero-Inflated Negative Binomial (ZINB) regression is used for count data that exhibit over where *πi*is the logistic link function and g ( yi ) is the negative binomial distribution. For more in-depth explanations on the underlying background of the ZINB, the reader can refer to Cameron and Trivedi (2013) and Garay et al. (2011).

Within the framework of this research, the non-spatial ZINB was transformed into a SZINB model by incorporating spatial lag of the dependent variable as an independent variable, where spatial lag is a parameter that indicates the degree to which a spatial feature is affected by its neighbors. It is also noted that the fit of the SZINB can be compared with the fit of its non-spatial counterpart by using the Akaike Information Criterion (AIC), with lower values of this criterion indicating better statistical model quality (Akaike, 1970; Sakamoto et al., 1986).

3.2. Spatial Random Forest

SRF is a powerful Machine Learning (ML) algorithm that combines the principles of conventional Random Forest (RF) with spatial analysis techniques. RF is a widely known and used ML technique, initially introduced by Ho (1995) and improved by Breiman (2001). This algorithm operates on the foundation of Decision Trees (DTs), an elemental component that is superimposed multiple times by its ensemble learning structure, which is a fundamental strength of the RF algorithm. Regression trees facilitate the prediction of continuous numerical values by segmenting the dataset using specific feature thresholds. RF features bagging, a process that involves generating numerous subsets of data by employing bootstrapping techniques from the original dataset. Subsequently, these diverse subsets contribute to the creation of multiple DTs. The essence of RF lies in the aggregation of predictions from these varied trees by averaging them, which collectively generate the final output. However, it should be noted that conventional RF models may fail to consider the spatial structure present in spatial datasets. Consequently, spatial relationships and autocorrelation in the residuals can lead to biased importance scores of non-spatial predictors and suboptimal model performance.

To overcome this limitation, one option is to generate spatial predictors. These predictors assist in taking into account the spatial structure of the training data, ultimately minimizing the spatial autocorrelation of the model residuals and providing accurate variable importance scores. One approach to accomplish this is by incorporating geographical proximity effects into the prediction process by adding the columns of the distance matrix of the examined road segments as explanatory variables, as suggested by Hengl et al. (2018). More specifically, Hengl et al. (2018) proposed the following generic SRF system:

$$Y(s) = f(X_G, X_R, X_P)$$ (2)

where XG represents covariates that consider the geographical proximity and spatial relations among observations:

$$XG = (d{p1}, d{p2}, \dots, d{pN})$$ (3)

In Equation (3), *dp*1 is the buffer distance to the observed location pi from s and N stands for the total number of training points. XR corresponds to surface reflectance covariates, while XP are process-based covariates. For a more comprehensive elucidation, interested readers are directed to consult the detailed explanations provided by Hengl et al. (2018). By including spatial predictors, the SRF manages to enhance its capability so as to minimize the spatial autocorrelation in the residuals and provide more precise variable importance scores.

4. Results and discussion

4.1. Spatial Zero-Inflated Negative Binomial model

Harsh braking events are SSMs that can be used in proactive road safety analyses before crash occurrence. To this end, the frequency of harsh braking events was selected as the dependent variable of the developed models. A series of various combinations of candidate independent variables were tested also including mathematical transformations such as logarithm usage. The best combination of variables was determined by having an adequate number of statistically significant variables and the lowest AIC values. The model was assessed for multicollinearity by means of the Variance Inflation Factor (VIF). Overall, present results showed no multicollinearity as VIF values were lower than the established empirical value of 5 (Sheather, 2009).

As also noted in the methodological section of this paper, traditional GLM count modeling techniques, such as NB regression, could not be fitted to the dataset under consideration. This limitation likely stemmed from the significant excess of zero occurrences in harsh braking events across the analyzed road segments. Additionally, the histogram of Fig. 3, depicting harsh braking frequencies on these road segments indicates a distribution following a ZINB pattern. Consequently, a ZINB model and a corresponding spatial model with spatial lag were created for this purpose. These models were developed using R-studio (R Core Team, 2023) and the "pscl" package (Zeileis et al., 2008; Jackman, 2020). ZINB models combine two components: one for modeling excessive zeros (using a logistic regression model) and another for modeling count data (using a NB regression model).

The count component, presented in the upper panel of Table 2, models the actual count of harsh braking events. The coefficients in this component explain the factors affecting the number of such events. Conversely, the zero-inflation component, shown in the lower panel of Table 2, models the probability of an observation being an excess zero (e.g., why there might be no harsh braking events). The coefficients in this component explain the factors influencing the likelihood of these extra zeros. Thus, the ZINB model provides two sets of coefficients: one for the zero-inflation process and one for the count process. Understanding both sets is crucial for a comprehensive analysis of safetyrelated data, as they offer insights into different aspects of event occurrence. The dependent variable of these two developed models is "harsh_braking_count" and the results are presented in Table 2.

As observed from the results presented in Table 2, the signs of the independent variable coefficients remain consistent among the two models. In particular, both the length of the examined road segment and the number of trips per segment can be considered as proxy indicators of risk exposure. As expected, they were found to be positively correlated with the number of harsh braking events, meaning that the number of instances where drivers perform harsh braking tends to increase with increased road segment length and/or number of trips taken through a segment. These exposure metrics provide disjointed exposure dimensions for assessing the frequency of harsh braking events. More specifically, the road segment length represents geographical, infrastructure-based exposure, which is more fixed, while the number of trips per segment reflects naturalistic driving exposure, which depends on travel elements, therefore, their inclusion is merited on approaches combining infrastructure and naturalistic driving data.

Moreover, variables related to speeding and mobile phone use while driving were found to be positively associated with the number of harsh braking events on road segments. In cases of exceeding speed limits, drivers are more likely to brake abruptly to avoid potential collisions or to reduce excessive speed. Similarly, mobile phone use while driving can lead to distraction, impacting reactions and increasing the likelihood of harsh braking. Lastly, the negative sign of the beta coefficient of the motorway variable indicates that the number of harsh braking events on motorways is lower than the respective number on other road types such as primary, secondary, and residential roads. This could be explained by

Table 2 Zero-inflated Negative Binomial and Spatial Zero-inflated Negative Binomial results for harsh braking events.

| Independent variables | Estimate | S.E. | z value | Pr(> z ) | VIF | Estimate | S.E. | z value | Pr(> z ) | | |-----------------------------|-------------------------------------------------------|-------|----------|------------------------------------------------------------------------------------|-------------------------------------------------------------------------|--------------------------|-------|----------|------------------------------------------------------------------|--| | | log link) | | | | Zero-Inflated Negative Binomial.Count model coefficients (neg.bin. with | (neg.bin. with log link) | | | Spatial Zero-Inflated Negative Binomial.Count model coefficients | | | (Intercept) | − 1.527 | 0.112 | − 13.605 | <0.001 | − | − 1.591 | 0.113 | − 14.111 | <0.001 | | | trip_count | 0.004 | 0.000 | 9.192 | <0.001 | 2.199 | 0.003 | 0.000 | 8.926 | <0.001 | | | log(1 + speeding_count) | 0.174 | 0.033 | 5.227 | <0.001 | 1.338 | 0.191 | 0.032 | 5.869 | <0.001 | | | motorway | − 1.429 | 0.380 | − 3.758 | <0.001 | 1.016 | − 1.359 | 0.367 | − 3.704 | <0.001 | | | length | 0.0002 | 0.000 | 4.423 | <0.001 | 1.104 | 0.0002 | 0.000 | 4.480 | <0.001 | | | log(1 + mobile_usage_count) | 0.273 | 0.038 | 7.242 | <0.001 | 2.440 | 0.264 | 0.037 | 7.066 | <0.001 | | | spatial lag | − | − | − | − | − | 0.109 | 0.032 | 3.436 | <0.001 | | | Log(theta) | − 0.818 | 0.074 | − 11.017 | <0.001 | − | − 0.794 | 0.074 | − 10.695 | <0.001 | | | | Zero-Inflated Negative Binomial. Zero-inflation model | | | | Spatial Zero-Inflated Negative Binomial. Zero-inflation model | | | | | | | | | | | coefficients (binomial with logit link)
coefficients (binomial with logit link) | | | | | | | | (Intercept) | 4.209 | 0.364 | 11.551 | <0.001 | − | 4.065 | 0.360 | 11.281 | <0.001 | | | trip_count | − 0.434 | 0.104 | − 4.188 | <0.001 | − | − 0.433 | 0.102 | − 4.258 | <0.001 | | | log(1 + speeding_count) | − 1.173 | 0.940 | − 1.248 | 0.212 | − | − 1.374 | 0.844 | − 1.628 | 0.103 | | | motorway | − 1.763 | 2.267 | − 0.777 | 0.437 | − | − 1.355 | 2.019 | − 0.671 | 0.502 | | | length | − 0.0003 | 0.000 | − 0.864 | 0.388 | − | − 0.0003 | 0.000 | − 0.784 | 0.433 | | | log(1 + mobile_usage_count) | − 0.402 | 0.172 | − 2.338 | 0.019 | − | − 0.421 | 0.177 | − 2.381 | 0.017 | | | spatial lag | − | − | − | − | − | 0.531 | 0.390 | 1.362 | 0.173 | | | AIC | 4,350.4 | | | | 4,336.4 | | | | | |

smoother traffic flow, more lane options and longer visibility distances on motorways.

The theta parameter refers to the dispersion parameter of the negative binomial distribution. Statistically significant estimates for log (theta) in the count component of both models indicate that there is substantial overdispersion in the examined data (i.e., the variance is much higher than what would be expected under a Poisson distribution), and the models appropriately account for this overdispersion by using the negative binomial distribution for the count data.

Within the zero-inflated component of Table 2 models, only "trip_count" and "mobile_usage_count" turned out to be statistically significant. In particular, their coefficients' signs imply that an increase in these variables corresponds to decreased probabilities of zero harsh braking occurrences on the examined road segments.

Additionally, among the two models of Table 2, the SZINB model demonstrates superior data fit, evident from the AIC criterion values. Noteworthy is the positive and statistically significant (p-value < 0.001) spatial lag term in the count component, indicating positive spatial autocorrelation.

Visual representation of the SZINB model's results for the Eastern Macedonia and Thrace Region's road network is displayed in Fig. 4, with

Fig. 5 offering a more detailed view focused on the city of Xanthi.

4.2. Spatial Random Forest

The results of the two models, as seen in Table 2, show a statistically significant relationship between the selected independent variables and the frequency of harsh braking events per segment. Thus, these variables and the efficiency variable of Table 1 were selected as input the SRF model. The R package "spatialRF" (Benito, 2021) was used for the development of the SRF model. The logarithm of the harsh braking count plus one "log (harsh_braking_count + 1)" was utilized as the response variable in the developed RF model, a strategy known to alleviate right-skewed distributions and zero inflation. Notably, this adjustment did not compromise the robustness of the models, as RFs demonstrate resilience to varying distributions of response variables, unlike traditional linear regression and GLMs. Following evaluation of the different combinations, the optimal set of variables emerged, distinguished by its ability to maximize the R2

Initially, a conventional non-spatial RF model is developed with defined distance thresholds for the examination of spatial autocorrelation in the residuals. If statistically significant and positive spatial

Fig. 4. Visualization of the SZINB results on the examined road network.

Fig. 5. Zoomed-in view of the SZINB results for the center of Xanthi.

autocorrelation exists, the SRF using spatial predictors is subsequently applied. These predictors are derived from the distance matrix of the considered road segments and are used as explanatory variables in the SRF model following Hengl et al. (2018).

Fig. 6 illustrates information on the non-spatial RF model residuals. Specifically, its upper panels demonstrate the results of the normality test, while the middle panel indicates the relationship between the residuals and the fitted values and the lower panel shows the Moran's I of the residuals across distance thresholds and their respective p-values. Moran's I is a measure of spatial autocorrelation, and in this case, it is positive and statistically significant for distances between 0 and 2000 m.

The presence of spatial autocorrelation in the residuals, based on the high Moran's I residuals as indicated by the large y-values in the lower distances of the bottom plot, indicates that the non-spatial RF model did not fully capture the spatial dependencies in the data. The non-spatial RF model was thus transformed into a SRF model by adding the columns of the distance matrix of the road segments as spatial predictors (Hengl et al., 2018). Fig. 7 presents the Moran's I of the residuals of the SRF model.

On the basis of the lower panels of Figs. 6 and 7, it can be observed that the SRF was able to reduce the absolute values of the Moran's I statistics. A likely explanation for the change from positive to negative spatial autocorrelation (in the residuals) is the inclusion of the additional spatial explanatory variables in the SRF model that incorporates spatial dependence structures as these additions help capture the spatial relationships among the observations. However, it should be noted that the values of Moran's I are not the sole criterion for model evaluation. Thus, Table 3 provides the key parameters of each RF model, along with some key model performance metrics.

When examining typical metrics (instead of out-of-bag metrics), for instance, R2 , and Root Mean Square Error (RMSE), it is observed that the SRF outperforms the non-spatial RF model. This is enabled by the inclusion of a large number of additional spatial predictors, capturing the unobserved traits for each road segment. However, out-of-bag

Fig. 6. Non-spatial RF model residuals.

Fig. 7. SRF model residuals.

Table 3 Key parameters and performance metrics of RF models.

Non-spatial RF SRF
Number of trees 500 500
Sample size 6103 6103
Number of predictors 6 6109
Mtry 2 78
Minimum node size 5 5
R2 0.900 0.928
R2 (out-of-bag) 0.526 0.440
RMSE 0.156 0.150
RMSE (out-of-bag) 0.309 0.336

performance metrics are examined as well. These are metrics on each fold, which are not utilized for model training and calibration, but can be used to obtain an unbiased assessment of the model's effectiveness without requiring a different validation set. Based on the out-of-bag performance metrics, it is found that the non-spatial RF model outperforms the SRF, hinting that the non-spatial model is likely performing better in terms of generalization on unseen data.

This deduction can be also enhanced by Fig. 8, which compares the predictive performance of the two RF models across 30 spatial folds.

Fig. 8. RMSE across 30 spatial folds.

Spatial folds are subsamples of the initial data that are separated in location clusters, a concept known as spatial cross-validation (Lovelace et al., 2019). In spatial cross-validation, each fold is defined by geographic location clusters rather than random sampling. In the present sample, 6,103 segments existed, which were divided into 30 folds of about 203 segments each. Each fold is used as a validation set, while the remaining folds serve as the training set. (Thus with 30 folds, the model is trained using 29 folds and the metric of interest is computed on the remaining fold). This process is repeated for each fold, and the results of the metrics are averaged to evaluate the algorithm's performance. The localized spatial aspects and unobserved traits are retained through the cross-validation process as opposed to traditional random crossvalidation. Overall, this is an expected result, as spatial information is not transferable or applicable to new areas as non-spatial patterns are (Ziakopoulos et al., 2022), which can be captured by ML algorithms more effectively.

Within the framework of the two RF models' development, the permutation variable importance technique was also employed to assess and rank individual predictors on the basis of their relative importance. Variable importance scores are visualized in Fig. 9, demonstrating the increase in mean error (computed on the out-of-bag data) observed across trees when a predictor is permuted. As a result, the SRF has an additional set of variable importance scores for the spatial predictors, with the maximum importance of a few of these spatial predictors matching the importance of the second and third most important predictors.

In both RF models, the number of trips per examined road segment (which serves as a naturalistic driving exposure metric) was found to be the most influential predictor, highlighting its significant relevance in predicting the frequency of harsh braking events. On the other hand, the motorway variable exhibited the lowest importance in both RF models, indicating that road type is relatively less influential in predicting the number of harsh braking events. This finding may suggest that factors other than road type such as driver distraction and speeding, might play a more crucial role in influencing harsh braking events frequencies.

5. Conclusions

The objective of this study was to conduct spatial analyses of harsh

Fig. 9. Permutation importance computed on the out-of-bag data.

braking events by utilizing naturalistic driving data from smartphones and OSM road network characteristics, aiming to enhance the current SSM knowledge. The examined road network consists of 6,103 road segments located in the Region of Eastern Macedonia and Thrace in Greece. A spatial dataset consisting aggregated naturalistic driving behavior metrics, as well as geometric and network characteristics on a segment level was analyzed. It is worth noting that the naturalistic driving behavior data reflect trips made throughout 2021, unaffected by the COVID-19 pandemic and the strict traffic restrictions implemented in Greece during 2020. Initially, non-spatial modeling techniques (such as ZINB and conventional RF regression models) were employed on harsh braking events frequencies. However, the existence of statistically significant spatial autocorrelation highlighted the need for the development of spatial models, such as SZINB and SRF, in order to address spatial dependencies.

The results of the ZINB and SZINB models showed consistent signs of the beta coefficients of the considered variables across all models. Specifically, road segment length and the number of trips per segment were identified as proxy indicators of risk exposure, positively correlated with harsh braking events. Variables related to speeding and mobile phone use were also positively associated with harsh braking events, while motorways exhibited fewer harsh braking events compared to other road types.

Regarding their performance, lower AIC values were observed for the SZINB model compared to the non-spatial ZINB model, suggesting a better fit of the SZINB model.

Moreover, the SRF reduced the absolute values of spatial autocorrelation in the residuals compared to the respective values of the conventional RF. In addition, the SRF outperformed the non-spatial RF model in terms of model fit to observed data, but the non-spatial model performed better in terms of generalization to unseen data. This is a typically expected finding, as spatial structures are typically unique and non-replicable, and would thus be very challenging to transfer to completely unexamined areas in a manner that is informative and that would provide an edge in forecasting. Regarding variable importance ranking, the number of trips per examined road segment emerged as the most influential predictor in both models, highlighting its significance in predicting harsh braking events. A key takeaway that this study confirms is that for causal or exploratory ML analysis in a given area, spatial crossvalidation would be reasonably more fruitful than its random

counterpart. This would apply especially in cases where few variables are present in the data, as the unobserved spatial effects would be more pronounced then.

Overall, SSMs have immense potential for road safety monitoring, countermeasure assessment and improvement, and rapid expansion of road safety data coverage. A limitation in the literature is the relatively recent appearance of studies on SSM modeling. To fill this literature gap, this paper identifies and demonstrated that with little effort, SSM-based spatial models can be used in scarcely-studied areas. Aided by technological developments such as telematics, which enable scalable and expedient data collection, high-quality data applications and monitoring in such areas is possible and can even be converted to the norm in the short term.

Despite the valuable insights gained from this study, a significant limitation that needs to be acknowledged is the lack of available traffic data (AADT or real-time) per examined segment, which could have provided additional insights into the influence of traffic volume on harsh braking events. However, the absence of AADT was attempted to be tackled by using the number of trips and the segment length as substitute risk exposure metrics. Several microscopic and mesoscopic spatial analysis studies have been shown to include more disjointed parameters such as land use (Ziakopoulos & Yannis, 2020), however the authors of the present study considered that SSM models warrant more directly related variables. A promising avenue for further research involves exploring temporal patterns. This exploration would encompass seasonal cyclical trends in both road crashes and harsh braking hotspots, as safety hotspots may vary across different times of day (Yang et al., 2019). Moreover, additional variables related to other driving compliance metrics, such as seatbelt use and alcohol consumption, could be taken into consideration.

Regarding the influence of examined variables, the present results are in line with previous studies for SSMs. From the reviewed literature, the variables have similar effects with the ones reported when crashes are spatially analyzed. Approaches such as the present one provide a wealth of data in order to deploy more data-demanding methods, such as the evolving ML algorithms, or complex analytical models in a more proactive manner without having to wait for sufficient crash numbers to occur and incurring their respective societal costs in the process. SSM models can also be extended in before-after analysis and used to model and monitor various types of interventions (such as enforcement or

infrastructure adjustments). Proactive SSM studies could serve as a diagnostic tool of a wider network, and justification for in-depth traffic studies for specific locations that are flagged as underperforming or problematic in terms of road safety levels.

In summary, this study provides valuable insights into the relationship between independent variables and harsh braking events, highlighting the relevance of exposure metrics and the impact of spatial autocorrelation in the models' development. Authorities can organize public awareness campaigns to educate drivers about the dangers of speeding and distracted driving, emphasizing on the positive correlation between such activities and harsh braking events, as revealed in the study. Furthermore, leveraging such spatial modeling techniques, authorities can identify high-risk areas for harsh braking events and deploy targeted enforcement efforts to address specific road safety issues.

CRediT authorship contribution statement

Dimitrios Nikolaou: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Apostolos Ziakopoulos: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Armira Kontaxi: Writing – review & editing, Writing – original draft. Athanasios Theofilatos: Writing – review & editing, Writing – original draft, Methodology. George Yannis: Writing – review & editing, Supervision.

Declaration of competing interest

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

Acknowledgments

This research is co-financed by the European Regional Development Fund of the European Union and Greek national funds through the Operational Program "Competitiveness, Entrepreneurship and Innovation", under the call "RESEARCH-CREATE-INNOVATE" (project code: Τ2ЕDΚ-04388).

References