Analysis of Spatial and Environmental Factors Beyond Speed Limits Affecting Drivers’ Speed Choice

Abstract

Managing vehicle speed is crucial for reducing crash risks and crash severity. South Korea’s ‘Safety Speed 5030’ policy introduced lower urban speed limits to enhance road safety, but speed limit reductions alone may not be sufficient to change driver behavior. This paper investigates how spatial and environmental factors beyond speed limits affect drivers’ speed choice. Using point-level speed data from Jeju Island’s C-ITS dataset combined with GIS information, spatial econometric techniques were employed to capture spatial dependencies in speeding degree. Results show that a spatial lag model (SLM) outperforms ordinary least squares (OLS) and spatial error models (SEMs), providing higher explanatory power and more consistent parameter estimates. Key factors influencing drivers’ speed choice include road geometry (e.g., curvature, number of lanes), node-level features (e.g., intersections, property change points), and the presence of enforcement measures. The findings suggest that the reduction in speed limits alone may not guarantee a corresponding decrease in vehicle speed. This underlines that sustainable traffic safety requires not only regulation but also careful consideration of spatial and environmental contexts.

1. Introduction

Vehicle speed is a critical factor influencing traffic safety, directly linked to crash probability and crash severity [1,2,3,4,5]. Globally, speed management policies have been introduced as key strategies to reduce road crashes and fatalities, driven by evidence suggesting a strong link between vehicle speed and pedestrian fatalities [2,3]. Previous studies consistently show that higher vehicle speeds correlate with increased collision risk and severity [6,7,8], emphasizing the need for effective speed control measures. Recent evidence shows that speeding—both excessive and inappropriate—contributes to about 54% of global road traffic fatalities, with a much higher burden in low- and middle-income countries (LMICs, 57%) than in high-income countries (28%). This means that one person dies every 49 s worldwide due to speeding, with nearly 95% of these fatalities occurring in LMICs [9], and revealing a significant correlation between vehicle speed and crash severity [10]. Additionally, variations in vehicle speed, rather than just absolute speed, have been shown to impact crash rates, highlighting the complex dynamics of speed-related traffic incidents [11,12,13,14].

Despite the implementation of speed management policies worldwide, there remains a persistent challenge in ensuring driver compliance with posted speed limits. Many studies have focused on macro-level analyses, utilizing aggregated data that may mask localized speeding behaviors and the influence of specific road characteristics. Simple regression models commonly used in past research often fail to account for spatial dependencies and spillover effects, potentially leading to incomplete or biased conclusions about the factors influencing vehicle speed. This gap in literature underscores the need for more granular analyses that can capture the nuanced interactions between drivers and their environments [15,16].

Recognizing the strong relationship between vehicle speed and traffic safety, the South Korean government implemented the ‘Safety Speed 5030’ policy in April 2021. The policy aimed to enhance pedestrian safety by setting a default speed limit of 50 km/h in urban areas and 30 km/h on residential streets. The primary goal was to reduce braking distances and minimize sudden stops, thereby lowering the risk of accidents. However, empirical observations indicate that merely reducing speed limits does not guarantee compliance. In many cases, drivers continue to exceed the posted limits, suggesting that other factors influence their speed choices. This discrepancy suggests that focusing solely on speed limits may overlook other important determinants of vehicle speed, such as road design, traffic conditions, and spatial context [17,18].

Moreover, existing research indicates that drivers’ speed choices are influenced by a complex interplay of factors beyond just the posted speed limits. Road geometry, including features like lane width, curvature, and the presence of medians, can significantly affect a driver’s perception of safe and appropriate speeds [16,17,18]. Traffic conditions such as congestion levels, traffic signal timing, and the behavior of surrounding vehicles also play critical roles in influencing driving speed [19,20]. Additionally, spatial context factors—such as land use patterns, roadside environments, and the presence of enforcement measures like speed cameras—can impact how drivers interpret and respond to speed limits [21,22].

To address these complexities, spatial autocorrelation models have emerged as valuable tools in traffic safety research. These models account for the spatial dependencies and spillover effects by considering how observations in one area are related to those in adjacent areas [23,24]. By incorporating spatial relationships, more accurate and nuanced understanding of the factors influencing vehicle speed can be delivered. This methodological advancement is particularly relevant in urban settings, where the spatial arrangement of roads, intersections, and traffic controls can vary significantly over short distances [19].

In this context, Jeju Island presents an ideal case study for exploring the spatial factors affecting vehicle speed. As a popular tourist destination with a diverse road network that includes urban, suburban, and rural areas, Jeju Island offers a unique opportunity to examine how unfamiliar drivers interact with varying road conditions and speed limits. This study environment offers an opportunity to examine whether speed limit reductions alone can effectively influence driver behavior, or if spatial factors exert a more substantial influence.

To address this research gap, this paper utilizes data from the Co-operative Intelligent Transport Systems (C-ITS) pilot project conducted on Jeju Island from 2018 to 2020. Figure 1 illustrates the extensive road network of Jeju Island, showcasing a diverse range of speed limits from 20 km/h to 80 km/h. This variety, combined with the implementation of C-ITS technology, provides an ideal setting to investigate how different road environments and speed regulations interact with real-world driving behavior. It also facilitates a detailed spatial analysis, allowing us to examine the impact of both speed limits and surrounding road characteristics on vehicle speeds across various segments of the island.

The project involved equipping 100 rental cars with advanced driver assistance systems (ADAS), which collected detailed data on vehicle speed and location across the island. Notably, the dataset predominantly captures driving behavior from unfamiliar drivers, such as tourists and business travelers, offering a broader perspective on speed choice behaviors that are less influenced by habitual local knowledge. By integrating this speed data with detailed GIS information on road features, this paper aims to comprehensively examine the influence of spatial factors on vehicle speed beyond the effects of speed limits alone.

Upon analyzing the speed of ADAS vehicles relative to Jeju Island’s speed limit, Figure 2 shows that average speed generally aligns with posted speed limits, but speed violations spike when limits are set below 50 km/h, reaching 100% at the 20 km/h limit. This suggests that lower speed limits are less effective in curbing speeding behavior, likely due to road design or perceived low risk by drivers. These observations indicate that factors beyond speed limits, such as road geometry and spatial context, play a significant role in influencing driving speed. This aligns with the core aim of this paper to examine the impact of spatial factors on vehicle speed using GIS data and spatial models. Previous study [20] have also shown that actual driving speeds often exceed the posted speed limits, indicating the impact of additional factors beyond just the speed limit itself.

Therefore, the primary objectives of this paper are twofold:

• To identify the spatial factors that significantly influence vehicle speeding degree beyond posted speed limits on Jeju Island.
• To assess the effectiveness of spatial autocorrelation models in capturing the spatial dependencies and spillover effects inherent in vehicle speed data, compared to traditional regression models.

By utilizing point-level speed data and GIS-based road characteristics from the C-ITS dataset, this paper provides a more granular analysis of the factors influencing speeding behavior across different road segments on Jeju Island. In this study, “speeding degree” is defined as the difference between a driver’s actual speed and the posted speed limit. While previous studies have used varying definitions of speeding—such as binary indicators of limit violations or speed-related crash metrics—our approach explicitly quantifies the magnitude of deviation from the speed limit. This provides a continuous measure that can be directly incorporated into spatial econometric modeling. Understanding these interactions is crucial for policymakers seeking to enhance the effectiveness of speed management strategies and improve road safety.

This paper unfolds as follows: Section 2 provides a literature review concerning vehicle speed and spatial autocorrelation and explains the utilization of the model and spatial factors. Section 3 elucidates the dataset used for the analyses by comparing statistics, while in Section 4, the methodologies for spatial autocorrelation modelling process is delivered. Section 5 proceeds with the modeling and discusses its findings, preceding the conclusions in Section 6.

2. Literature Review

Vehicle speed is influenced by numerous factors, studied across several traffic engineering fields [1]. Depending on the specific focus, various models and variables have been employed. Speed-focused research can be broadly divided into macro-level studies, which utilize aggregated data such as average speeds across road segments, and micro-level studies that analyze individual vehicle speeds.

Macro-level studies typically examine road-specific variables such as traffic attributes and road geometry, which remain unaffected by individual drivers [10,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. Many have investigated the relationship between road design aspects (e.g., curvature radius, slope) and vehicle speed [38,39,40]. For example, refs. [35,36,37] developed prediction models based on curve geometry under unconstrained suburban or highway conditions, while [20] examined how design speed relates to actual speed. Other studies considered factors such as traffic characteristics [24,28,29], spatial characteristics (urban vs. suburban in [23], or lane position [27].

Micro-level studies, in contrast, focus on detailed roadway and driver-specific factors [41,42,43]. These include analyses of road geometry and site-specific conditions [41], speed changes before and after speed limit revisions [42], and operating speed in relation to urban road design [43]. Other work has incorporated driver- or vehicle-specific variables [44,45,46,47,48,49], such as compliance with reduced speed limits [44], the influence of surrounding traffic [45], and environmental visibility [48]. Related work also indicates that portable and automated enforcement can improve speed-limit compliance; for example, Owais et al. [50] found that strategically positioned portable excess-speed detectors in Riyadh reduced localized speeding and increased adherence to posted limits. Some studies employed advanced modeling techniques, including Gaussian mixture models to capture speed distributions by vehicle type [49].

Importantly, vehicle speed itself has often been modeled as the dependent variable in micro-level analyses, with several studies even adopting spatial econometric approaches to account for spatial dependence [51,52]. In addition, a smaller subset of research has considered speeding degree (actual speed minus the limit) as the outcome [25,41,44], although these studies were typically limited to specific road sections and relied on survey data or fixed cameras rather than continuous, large-scale observations.

Beyond the choice of dependent variables, prior research has also identified a broad range of explanatory factors affecting speed, including geometric (shoulder, curve, sight distance, lane width, medians), traffic (speed limits, traffic lights, heavy vehicle ratio, on-street parking), land use and socioeconomic conditions (population density, poverty rate, land-use mix), and driver/environmental characteristics (vehicle size, familiarity, rainfall/snowfall).

From a methodological perspective, macro-level studies have predominantly relied on classical statistical models such as OLS, t-tests, and ANOVA [20,21,23,24,26,27,29,30,31,32], with some exploring machine learning (e.g., neural networks [22,33]). Micro-level studies have also used OLS [13,45,46], but many employed panel models to reflect driver or vehicle heterogeneity [41,42,43,44]. In addition, some studies applied spatial econometric techniques to explicitly capture spatial dependencies in speed data [51,52]. Yet, for the most part, spatial dependence has not been systematically addressed, even though observations in traffic contexts are rarely independent—nearby vehicles and road segments can strongly influence one another [53]. Ignoring this dependence can bias estimates and reduce reliability. In other disciplines, spatial autocorrelation models are widely used (e.g., urban heat islands, energy use, air pollution, housing markets), underscoring the importance of modeling spatial effects [54,55,56,57].

In transportation research, spatial econometric models have been applied to a range of topics, but their use has been predominantly concentrated on crash analysis at macroscopic levels. Many studies have relied on traffic analysis zones (TAZ) or other aggregated spatial units as the basis for spatial modeling [58,59,60,61]. This approach has clear advantages: socioeconomic and traffic statistics are readily available at these levels, enabling large-scale modeling and facilitating policy interpretation across urban or regional systems. However, aggregation also entails important limitations. By collapsing observations to zone-level averages, micro-level variations in driver behavior are often obscured, making it difficult to capture phenomena such as speeding degree or localized compliance with speed limits. As a result, while TAZ-based studies have provided valuable insights into broad spatial patterns of crash risk and safety factors, they may not fully reflect the fine-grained dynamics of vehicle speed and driver responses on individual road links. These studies examined variables such as crash counts, population density, or vehicle ownership, and found associations with factors like speed limits, bus lane length, and age composition. Pedestrian crashes have also been investigated [62], and more recent work has shifted from zones to road-link data for predicting accident frequency [63]. While these studies offer valuable insights into spatial factors affecting safety, they largely focus on aggregated crash outcomes. Micro-level applications to speed and speeding behavior remain comparatively fewer.

Against this backdrop, our study makes several contributions:

• We use speeding degree (vehicle speed minus the posted limit) as the dependent variable, providing a direct measure of speeding behavior at the individual vehicle level.
• We employ large-scale point-level ADAS data covering the entire Jeju Island road network, instead of survey responses or fixed surveillance cameras, which allows for a fine-grained and continuous analysis of driver behavior across diverse spatial contexts.
• We analyze the behavior of predominantly non-local rental car drivers, thereby reducing potential bias from habitual local driving patterns and improving the generalizability of the findings.
• We incorporate network centrality measures (closeness and betweenness) to capture structural traffic dynamics within a closed island network—an aspect rarely integrated into prior micro-level spatial models.

By also considering roadway and traffic variables such as median strips, lane numbers, speed limits, traffic lights, on-street parking, bus stops, and enforcement cameras, this study captures a comprehensive set of factors influencing vehicle speed. In summary, our approach complements and extends prior research by moving beyond aggregated crash analyses and focusing on micro-level speeding behavior. This allows for deeper insights into how spatial context affects driver compliance with speed limits and can inform more effective speed management strategies.

3. Data Description and Variable Processing

In this section, the detailed process of data preparation and variable definition is presented, which forms the foundation for the spatial autocorrelation analysis conducted later in the paper. This section introduces the data sources utilized, describes the methodology for defining the dependent and independent variables, and provides an exploratory overview through descriptive statistics.

To effectively model vehicle speed behavior, the selection and processing of variables account for the spatial and structural characteristics of the road network. Factors such as road geometry, surrounding land use, and network connectivity are considered to reflect the spatial dynamics influencing speed choices. By integrating these elements, the data preparation stage lays comprehensive groundwork for capturing the complex spatial dependencies present in driving behavior, thereby enhancing the robustness of subsequent model analysis.

3.1. Data Sources

This paper utilizes three primary data sources to examine the spatial factors influencing vehicle speed across Jeju Island: Jeju C-ITS ADAS data, Korea Transport DataBase (KTDB) road GIS data, and Jeju Point of Interest (POI) data. Together, these datasets provide a comprehensive basis for analyzing speed behavior while considering spatial interactions, road network characteristics, and contextual environmental factors.

The Jeju C-ITS ADAS dataset forms the core of the analysis, comprising approximately 99,851 event notifications recorded between 21 June 2020, and 31 December 2020. These data points, collected from 100 rental vehicles equipped with advanced driver assistance systems (ADAS), include precise information on vehicle speed, latitude, and longitude. The use of rental vehicles, predominantly driven by tourists and business travelers, offers a distinct advantage by minimizing biases associated with habitual local driving patterns. Consequently, the dataset provides a more representative picture of how various road and environmental characteristics influence speed choices, aligning well with the focus on understanding mobility behaviors within different spatial contexts. Unlike static datasets collected at fixed points, this dynamic dataset is gathered as vehicles move, allowing an examination of how speed behavior evolves through varying spatial environments. This dynamic quality enriches the contextual interpretation of speed patterns, enabling more nuanced insights into spatial dependencies and driver decision-making. The high-resolution, point-level nature of this data allows for an in-depth analysis of speed variations across diverse segments of the road network, making it an ideal source for examining the potential spatial dependencies in speed behavior. Vehicle speed data collected from the ADAS-equipped rental cars inevitably reflect a mixture of free-flow and congested traffic conditions. Due to data limitations, it was not feasible to explicitly distinguish between these two states for each of the 99,851 point-level observations. As a result, the constructed models incorporate both free-flow and congested speeds. This scope is explicitly acknowledged as a limitation of the study, but it also reflects the reality of mixed traffic conditions on Jeju Island’s road network.

In addition to the ADAS data, the Korea Transport DataBase (KTDB) road GIS data was employed to capture detailed spatial attributes of the road network. This dataset includes information on road link characteristics such as speed limits, the number of lanes, road hierarchy, and the presence of medians. By spatially joining this GIS data with the ADAS vehicle location data, the analysis is enriched with contextual information on road design and infrastructure. This integration enables a deeper exploration of how physical road attributes influence driving speed, addressing core concepts in transport geography related to network connectivity and the built environment. The road geometry and infrastructure details captured in the GIS data are essential for understanding the relationship between road design elements and driver behavior, forming a key component of the independent variables used in the subsequent spatial models.

To further enhance the contextual analysis, this paper incorporates Jeju Point of Interest (POI) data, which includes information on key roadside features such as bus stops, on-street parking areas, school zones, and enforcement cameras. These POI features were spatially merged with the road GIS data to develop a comprehensive set of independent variables that reflect the influence of the surrounding environment on speed behavior. The inclusion of POI data allows for a nuanced assessment of how land use patterns and roadside environments shape driver responses to speed limits. For instance, the proximity of bus stops or the presence of school zones can significantly alter speed choices, reflecting the importance of spatial interactions. By integrating these environmental variables, the analysis captures the broader context in which speed decisions are made, beyond the physical attributes of the road alone.

The integration of these three data sources involved careful spatial joining and data cleaning processes to ensure consistency and accuracy across datasets. The ADAS event notifications were aligned with the corresponding road link and POI data using latitude and longitude coordinates. Rigorous data preprocessing was conducted to address issues such as missing values, duplicate entries, and any discrepancies in the location data. This thorough preparation ensures a robust and reliable dataset, forming the foundation for defining both the dependent variable (speeding degree) and the independent variables related to road and environmental characteristics.

Overall, the combined use of ADAS, GIS, and POI data provides a detailed, multidimensional view of vehicle speed behavior across Jeju Island. This integrated dataset enables the analysis to reflect key transport geography concepts, such as spatial interaction, network connectivity, and urban structure. By leveraging these diverse data sources, this paper attempts to set a solid groundwork for the spatial autocorrelation analysis conducted in subsequent sections, aiming to uncover the complex interplay between road characteristics, environmental context, and speed choice behavior.

The analytic sample consists of point-level observations from 100 rental vehicles predominantly driven by non-local visitors, and therefore is not representative of all drivers on Jeju Island. Accordingly, the findings should be interpreted as associations characterizing speeding degree among rental/non-local drivers, not the resident driving population, while this focus simultaneously helps reduce route-familiarity and habitual-speed biases common among local commuters.

3.2. Dependent Variable (Speeding Degree)

The final dataset used for the analysis consisted of 99,851 point-level speed observations collected from 100 ADAS-equipped rental vehicles. The primary outcome of interest in this paper is the speeding degree, defined as the difference between a vehicle’s observed speed and the posted road speed limit. This variable was derived by spatially joining the ADAS vehicle location data with the KTDB road link data, ensuring accurate matching of speed observations to specific road segments. Positive values indicate instances of speeding, while negative or zero values reflect compliance or driving below the speed limit. We retain both positive and negative values in the baseline analysis to examine speed deviation around the posted limit, as sub-limit observations capture meaningful slowdowns due to traffic and control features (e.g., congestion, intersections, protected zones).

The speeding degree captures the interplay between road environments and driver behavior, highlighting how varying spatial contexts influence speed choices. In urban areas, where road geometries are complex and pedestrian activity is high, the likelihood of speeding degree is generally lower. In contrast, suburban and rural areas, with fewer restrictions and more open road segments, often experience higher probabilities of speeding [64]. These spatial variations reveal the influence of different road network characteristics and built environments on driver speed decisions, offering insights into localized patterns of speed dynamics.

The distribution of the speeding degree, as shown in Figure 3a, reveals a near-normal pattern with a mean of −8.9 km/h, indicating that vehicles generally travel below the speed limit across the dataset. Also, the slight left-skewed distribution indicates a significant number of vehicles driving considerably below the speed limit, which is consistent with congested or regulated urban environments where traffic conditions necessitate slower speeds. In Figure 3b, the spatial distribution of speeding degree across Jeju Island reveals distinct geographical patterns. The red and orange road segments, representing higher speeding degrees, are primarily located in suburban and rural areas where road conditions are less restrictive, and the traffic flow is freer. Conversely, the green areas, which indicate lower speeding degrees, are concentrated in the urban centers, particularly in Jeju City. This spatial pattern aligns with the expectation that dense urban environments, characterized by complex road geometries, existence of public transit, and pedestrian facilities, tend to limit vehicle speeds more effectively [65].

Additionally, the spatial variation in Figure 3b suggests the influence of localized road characteristics on speeding degree. Roads exhibiting high-speed violations (in red) may correspond to arterial routes with fewer intersections and higher speed limits, while areas with low speeding degrees (in green) likely coincide with residential streets or zones with stricter traffic regulations, such as school zones and commercial districts. This highlights the need for a more nuanced understanding of how road type, traffic density, and surrounding land use affect driver speed choices, which will be explored further in the subsequent modeling analysis.

These visual patterns underline the importance of considering both spatial and contextual factors in analyzing speeding degree, supporting the use of spatial autocorrelation models to capture these dependencies.

3.3. Independent Variables

In this section, the independent variables are defined by integrating detailed road GIS data and spatial attributes to comprehensively capture the diverse factors influencing vehicle speed. These variables are grouped into road link and road node characteristics, reflecting key aspects of road environment and network structure that align with spatial and transport geography concepts, including network connectivity and urban morphology.

3.3.1. Road Link Variables

The development of road link variables was achieved by spatially merging vehicle location data from the ADAS speeding records with the KTDB road GIS link data. This method allowed for precise alignment of speed observations with corresponding road characteristics, providing a detailed understanding of the interactions between vehicle speed and road environment. Several key variables were considered in this analysis, reflecting distinct elements of the road infrastructure that influence driving behavior.

The presence of on-street parking and number of bus stops was identified as road link variables using Jeju POI data integrated with the road GIS data. These features are fundamental aspects of urban road environments, as they introduce areas of potential conflict that can alter the flow of traffic. On-street parking, particularly in high-density urban areas, creates risks along road segments as vehicles slow down or stop to park or exit spaces [66]. This can lead to lower average speeds, as drivers anticipate possible interruptions and adjust their behavior accordingly. Similarly, bus stops act as temporary disruptions in the traffic flow, especially when buses decelerate to board or alight passengers [67]. This results in reduced speeds, not only due to the physical presence of the bus but also due to increased pedestrian activity, which necessitates greater caution from drivers. These variables highlight the influence of local road features on speed behavior, underscoring how specific infrastructure elements designed for accessibility and convenience can inadvertently affect vehicle speeds.

Additionally, school zones and silver zones were included in the road link variables list, derived from the Jeju C-ITS Pilot Project Center data. These zones are strategically designated to enhance safety for vulnerable road users, such as children and the elderly, by enforcing lower speed limits and implementing additional safety measures. The impact of these zones is typically significant, as drivers are expected to comply with stricter speed regulations due to heightened enforcement and visible safety interventions like road markings and warning signs [68]. The reduced speeds observed in these areas are a direct consequence of regulatory policies aimed at protecting pedestrians, particularly in environments with higher pedestrian traffic. Beyond mere compliance with posted speed limits, the behavioral adaptation of drivers in these zones reflects an increased awareness of potential risks, aligning with broader goals of urban road safety and regulatory design.

The analysis of these road link variables highlights the complex relationship between road design, land use, and speed choice behavior. In segments characterized by frequent on-street parking or dense bus stop locations, a significant reduction in speed is typically observed due to the need for increased vigilance and the likelihood of encountering unexpected vehicle or pedestrian movements. This behavior is consistent with theories in transport geography that emphasize the impact of the built environment and spatial interactions on travel behavior [69,70]. By integrating these features, this paper can capture the localized effects of road design on speed dynamics, offering a more nuanced understanding of how specific micro-scale attributes can shape broader traffic patterns in both urban and suburban contexts.

Furthermore, the inclusion of school zones and silver zones in the analysis underscores the importance of policy-driven interventions in influencing driving behavior. These designated areas represent deliberate efforts to modify speed patterns through targeted regulations, aiming to reduce risks for specific populations. Unlike other road segments where speed choices may be influenced predominantly by road geometry and traffic conditions, the behavioral changes in school zones and silver zones are driven by enforced compliance and heightened safety awareness. This interplay between regulatory measures and driver behavior illustrates the critical role of transport policies in shaping speed outcomes, aligning with the broader objectives of urban traffic management and public safety enhancement.

The selected road link variables offer a robust framework for examining speed behavior by integrating diverse aspects of the road environment, such as physical attributes, land use, and regulatory influences. By capturing elements like on-street parking, bus stops, and designated safety zones, this analysis provides valuable insights into how micro-scale road features and policy interventions shape speed dynamics. The integration of these variables reflects an understanding of the complex interplay between road design and driver behavior, facilitating a detailed exploration of the localized effects of urban infrastructure on speed choices across varying road segments.

3.3.2. Road Node Variables

A road node, in this study, refers to a topological point within the road network that represents intersections, junctions, or other critical points where traffic conditions or road attributes may change. The road node variables were constructed by identifying the downstream nodes of each vehicle’s location and attaching these node-level attributes to the vehicle data. This approach enabled a dynamic analysis of how specific node characteristics influence vehicle speed behavior along the road network. The downstream node was selected based on proximity, determined by the decreasing distance to the vehicle over time, ensuring the accurate assignment of node-level features to the observed vehicle speeds.

The road node attributes included key elements such as traffic light presence, speed enforcement cameras, and road property change points derived from the KTDB road node data and Jeju Provincial Police Agency records. The presence of traffic lights and enforcement cameras introduces regulatory controls that directly affect driver decision-making processes. Specifically, speed enforcement cameras act as deterrents, prompting drivers to adjust their speed well before reaching the node due to the legal requirement of prior notification of camera presence. This behavioral adaptation is particularly notable in Korea, where average road link lengths are relatively short (average 174 m, median 59 m). Hence, incorporating these variables effectively captures the immediate influence of traffic regulations on driver speed adjustments at the node level.

Additionally, road property change points, such as variations in the number of lanes, shifts in speed limits, and changes in road hierarchy, were integrated into the analysis. These changes often signal transitions in the road environment, prompting drivers to modify their speed accordingly. For instance, a reduction in the number of lanes or a drop in the speed limit typically results in deceleration as drivers adapt to the new conditions. The inclusion of such variables allows the model to account for the dynamic responses of drivers to shifts in road characteristics, reflecting the fluid nature of driving behavior across different segments of the road network.

To further capture the spatial dynamics and network effects, two centrality measures—closeness centrality and betweenness centrality—were included as node-level independent variables. The centrality measures were derived from social network theory, adapted to the road network context to explain the structural importance of different nodes within the transportation system [71,72,73,74]. Closeness centrality measures how close a node is to all other nodes in the network, indicating its accessibility [75]. Nodes with high closeness centrality are typically found in densely connected urban areas, where the reduced average distance to other nodes facilitates faster travel times and higher traffic volumes. This measure reflects the significance of urban form and spatial configuration in influencing vehicle speed, as higher closeness centrality often correlates with increased traffic activity and potential congestion.

Closeness centrality is calculated using Equation (1), which measures the inverse of the sum of distances from the node to all other nodes, indicating accessibility.

$${\displaystyle \frac{g-1}{\sum _{j=1}^{g}d(n_i,n_j)}}$$

(1)

where $g$ is the total number of nodes, $d(n_i,n_j)$ is the distance between nodes $i$ ando $j$.

Betweenness centrality, on the other hand, quantifies the frequency with which a node lies on the shortest path between other nodes. This metric highlights nodes that serve as critical connectors or “hubs” in the network, often located on major arterial roads or key intersections. High betweenness centrality suggests that these nodes play a pivotal role in facilitating movement across the network, acting as bottlenecks where traffic flow may slow due to increased merging, turning, and crossing activities. The inclusion of betweenness centrality provides insight into how network structure and connectivity shape speed variations, as drivers may decelerate at nodes with high betweenness centrality due to the increased likelihood of encountering traffic congestion or conflicting movements.

Betweenness centrality is calculated using Equation (2), reflecting the proportion of shortest paths passing through the node.

$${\displaystyle \frac{\sum _{j<k}{g}_{jk}(n_i)/g_{jk}}{\left[\right(g-1\left)\right(g-2)/2]}}$$

(2)

where $g_{jk}$ is the number of shortest paths from node $\mathrm{j}$ to $\mathrm{k}$, $g_{jk}\left(n_i\right)$ is the count of those paths that pass through node $\mathrm{i}$.

The spatial distribution of these centrality measures is shown in Figure 4. High closeness centrality is predominantly observed in the northern urban area of Jeju Island, where a dense road network minimizes travel distances between nodes. This pattern aligns with the expected influence of urban form on accessibility and vehicle speed dynamics. Conversely, high betweenness centrality is concentrated along major arterial roads, such as those connecting key tourist destinations and commercial hubs. These roads often serve as the primary routes for through-traffic, reinforcing their role as critical connectors within the network.

In this context, closeness centrality can be interpreted as partly reflecting the characteristics of congested conditions, where vehicle interactions are more frequent at closely connected nodes. Conversely, betweenness centrality tends to be higher on arterial roads, and thus can be seen as capturing aspects of free-flow conditions, where uninterrupted travel is more likely. Although our dataset did not allow us to explicitly separate free-flow from congested speeds, incorporating these centrality measures enables the models to account for such contrasting traffic dynamics indirectly.

Overall, the integration of road node variables, including centrality measures and regulatory attributes, into the analysis provides a comprehensive framework for understanding the effects of local infrastructure and network connectivity on speed behavior. By capturing both regulatory elements and structural characteristics of the road network, the analysis can reflect the nuanced ways in which drivers respond to their immediate surroundings and the broader spatial context of the road system.

3.4. Exploratory Data Analysis and Descriptive Statistics

To gain a comprehensive understanding of the dataset and ensure the effective modeling of vehicle speed dynamics, exploratory data analysis is presented. The descriptive statistics outlined in

Table 1. Data description.

	Category	Variable	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.	SD
Dependent Variable	-	Speeding degree (vehicle speed-speed limit)	−74.667	−19.000	−10.000	−8.893	0.667	85.000	16.323
Independent Variables	Road Link Variables	Number of lanes	1.000	2.000	4.000	3.327	4.000	8.000	1.409
		Speed limit	20.000	50.000	60.000	59.02	70.000	80.000	12.675
		Presence of one-way lanes	0.000	0.000	0.000	0.026	0.000	1.000	0.159
		Presence of bus dedicated lane	0.000	0.000	0.000	0.038	0.000	1.000	0.190
		Presence of median	0.000	0.000	0.000	0.356	1.000	1.000	0.479
		Presence of on-street parking lot	0.000	0.000	0.000	0.033	0.000	1.000	0.178
		Number of bus station	0.000	0.000	0.000	0.575	1.000	8.000	1.035
		Presence of school zone	0.000	0.000	0.000	0.179	0.000	1.000	0.384
		Presence of silver zone	0.000	0.000	0.000	0.067	0.000	1.000	0.249
	Road Node Variables	Presence of traffic lights	0.000	0.000	0.000	0.037	0.000	1.000	0.189
		Presence of speed enforcement camera	0.000	0.000	0.000	0.067	0.000	1.000	0.250
		Road property change points	0.000	0.000	0.000	0.224	0.000	1.000	0.417
		Closeness centrality	0.020	0.027	0.030	0.030	0.033	0.036	0.004
		Betweenness centrality	0.000	0.004	0.021	0.032	0.053	0.17.0	0.034

summarize the key characteristics of the dataset, offering an initial glimpse into the variability and distribution of the chosen variables.

The dependent variable, speeding degree, reveals a wide range of values, from −74.67 km/h to 85 km/h, with a mean of −8.89 km/h, suggesting that, on average, vehicles tend to travel below the speed limit across the dataset. However, the substantial standard deviation (16.32 km/h) indicates significant variability in speed behavior, which warrants a deeper investigation into the factors influencing these deviations, such as road design, traffic conditions, and regulatory elements.

Among the road link variables, the data highlights the diversity of road characteristics present in the Jeju Island road network. For instance, the number of lanes varies from single-lane roads to eight-lane roads, reflecting the mix of urban and suburban environments. The speed limits range from 20 km/h in residential and school zones to 80 km/h on arterial roads, aligning with the island’s varied road hierarchy and land use patterns. Other attributes, such as the presence of one-way lanes, bus dedicated lanes, and medians, capture specific road features that can impact driving behavior by altering flow dynamics and creating points of friction or regulation. The mean values indicate that while features like bus lanes and on-street parking are less common, their presence in certain segments may play a significant role in localized speed reductions due to increased pedestrian and vehicle interactions.

For the road node variables, attributes like traffic lights, speed enforcement cameras, and road property change points were included to reflect critical regulatory and environmental transitions within the network. The low average values for these variables indicate that while they are not widespread across the entire dataset, their localized effects are expected to be pronounced, particularly in high-traffic or regulated zones. The descriptive statistics show a notable presence of speed enforcement cameras, which, despite being limited in number, are strategically placed to influence driver behavior significantly. Additionally, changes in the road environment, such as variations in the number of lanes or speed limits, are captured through road property change points, offering a way to model dynamic adjustments in speed as drivers encounter different road conditions.

Lastly, the measures of closeness centrality and betweenness centrality provide insight into the structural positioning of nodes within the road network. High values of closeness centrality are likely to be associated with nodes in densely connected urban areas, where the short average distances between nodes enhance accessibility. In contrast, betweenness centrality identifies nodes that act as critical connectors or bottlenecks, often located on key arterial routes facilitating the through-traffic. The relatively high mean and maximum values for betweenness centrality underscore the importance of these nodes in managing network flow and highlight their potential impact on speed variability due to congestion and merging activities.

The exploratory analysis and descriptive statistics presented here form a crucial foundation for the subsequent modeling phase. By summarizing the characteristics of both the dependent and independent variables, this section establishes a clear context for understanding the complex interplay between vehicle speed behavior and the underlying road infrastructure, regulatory measures, and network connectivity.

4. Methodology and Model Development

This section outlines the methodology and modeling framework used to analyze spatial autocorrelation in vehicle speeding degree. The approach leverages spatial statistical techniques to account for dependencies inherent in transportation networks. Specifically, the analysis involves constructing a spatial weight matrix, calculating Moran’s I statistic to determine spatial autocorrelation, and selecting the appropriate spatial model—spatial lag model (SLM) or spatial error model (SEM)—based on diagnostic tests. This process ensures that the spatial relationships influencing vehicle speeds are rigorously captured and modeled.

4.1. Overview of Spatial Autocorrelation Models

Understanding spatial dependencies is critical because road networks and traffic systems naturally exhibit spatial autocorrelation due to their interconnected structure and the continuous flow of vehicles. Spatial autocorrelation describes the tendency for observations near each other in space to exhibit similar characteristics. In the context of vehicle speed, this represents that the speed at one location can be influenced by speeds at neighboring locations via spatial effects, capturing patterns such as congestion spillover, spatial dependencies in traffic flow, and the impact of road design and network topology [76].

Traditional regression models assume independence among observations, an assumption that often does not hold true in spatial analyses. This oversight can lead to biased estimates and misleading conclusions, as these models fail to account for the influence of spatial relationships. To address this limitation, spatial autocorrelation models, such as the spatial lag model (SLM) and spatial error model (SEM), have been developed. These models explicitly incorporate spatial dependencies, allowing for a more accurate and nuanced analysis of vehicle speeding degree.

By integrating spatial relationships into the modeling process, these models align closely with transport geography concepts such as spatial interaction and network connectivity. They enable researchers to capture how spatial factors, such as proximity to traffic signals or road property changes, influence driver speed choices across different segments of the road network. This is particularly relevant in a case study like Jeju Island, where diverse road environments and varying traffic conditions create distinct spatial dynamics.

The spatial autocorrelation modeling process involves four key steps. The first step is to construct a spatial weight matrix that quantifies the spatial relationships among observations based on their geographical proximity. Then, the presence of spatial autocorrelation will be determined via Moran’s I statistic. This statistic identifies whether the dependent variable exhibits significant spatial clustering. Thirdly, the Lagrange multiplier test determines whether spatial dependencies are better modeled using a spatial lag or spatial error approach. Finally, the analysis proceeds with the most suitable model (SLM or SEM) to capture spatial dependencies in the data [77,78].

4.2. Spatial Weight Matrix

A critical component of spatial autocorrelation models is the construction of the spatial weight matrix ($W$), which quantifies the spatial relationships between observations by assigning weights based on their proximity [61]. This matrix reflects the intensity of spatial interactions and is essential for capturing the inherent spatial dependencies in transportation networks due to the interconnectedness of road segments and traffic flow. The spatial weight matrix can be constructed using various methods, depending on the nature of the spatial units and the research context.

For polygon data, such as administrative districts or traffic analysis zones (TAZ), proximity-based methods are commonly employed. The Queen proximity method recognizes neighbors that share either a common edge or vertex, effectively capturing all immediate neighbors. Alternatively, the Rook proximity method considers only those polygons that share a common edge, excluding vertex-only contacts. These methods are particularly suitable for lattice data structures and have been widely used in transportation research where socioeconomic indicators and accident data are aggregated at the TAZ level [58,59,60,61,62].

For point-level or non-proximity spatial data, such as individual vehicle locations or road segments, distance-based methods are more appropriate. The Euclidean distance method defines spatial relationships based on the straight-line distance between observations. This method involves setting a distance threshold within which observations are considered neighbors. Observations located within this predefined distance are assigned a weight, typically binary (1 for neighbors within the threshold, 0 otherwise), reflecting immediate spatial dependence. This approach is suitable for capturing spatial autocorrelation in datasets where observations are not confined to predefined administrative boundaries but are dispersed across continuous space.

In this paper, the spatial weight matrix is constructed using a Euclidean distance rule with a threshold of 991.07 m. This threshold was selected because it is the minimum distance required to ensure that each observation in the dataset has at least one neighbor, thereby avoiding isolated units and ensuring network connectivity. This approach follows common practice in spatial econometrics, where distance-based thresholds are often determined to guarantee connectivity among all observations [79,80]. While Euclidean distance is a proxy for actual network distance, it is widely used in large-scale point-level transportation studies due to its tractability and consistency.

This binary weighting scheme assumes that only observations within the threshold distance exert influence on each other, which is appropriate for modeling the localized spatial dependence relevant to vehicle speeds. While vehicles travel along road networks, Euclidean distances are used for computational efficiency and due to data constraints. Network distances, representing actual travel paths along the road network, would provide a more accurate representation of spatial interactions but require extensive computational resources and detailed network data, which may not be readily available or practical for large datasets. The use of Euclidean distances serves as a reasonable approximation in this context, especially given the relatively compact and uniform geography of Jeju Island.

By capturing the influence of nearby observations on vehicle speed, the spatial weight matrix reflects the interconnectedness of the road network and the spatial diffusion of driving behaviors. This approach allows for a more accurate and nuanced analysis of vehicle speeding degree, accounting for spatial spillover effects and the impact of the surrounding environment on driver decisions.

4.3. Moran’s I Statistics

To assess the presence and degree of spatial autocorrelation in vehicle speeding degree, Moran’s I statistic was calculated using the spatial weight matrix constructed in the previous section. Moran’s I is a global measure of spatial autocorrelation widely used in spatial analysis to quantify the extent to which similar values of a variable cluster together in space [56]. Moran’s I, as shown in Equation (3), helps determine whether speeding degree at one location is similar to that at nearby locations, reflecting spatial patterns influenced by road network characteristics and driver interactions. This formula measures the covariance between observations weighted by their spatial proximity, normalized by the overall variance of the variable. A positive Moran’s I value indicates positive spatial autocorrelation, meaning that similar values (either high or low) are clustered together in space. A negative value suggests negative spatial autocorrelation, where high and low values are interspersed. A value near zero implies a random spatial pattern with no autocorrelation.

$${\mathrm{M}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{n}}^{\prime }\mathrm{s} \mathrm{I}={\displaystyle \frac{n{\sum }_i{\sum }_{i\ne j}{w}_{ij}(y_i-\overline{y})(y_j-\overline{y})}{({\sum }_i{\sum }_{i\ne j}{w}_{ij}){\sum }_i(y_i-\overline{y}{)}^2}}$$

(3)

where $n$ is the number of spatial units, $w_{ij}$ is the element of the spatial weights matrix ($W$) corresponding to the spatial relationship between locations i and j, $\overline{y}$ is the mean of the variable $y$ and $y_i$ and $y_j$ are the values of the variable of interest (speeding degree) at locations i and j, respectively.

In the context of vehicle speeding behavior on Jeju Island, a positive Moran’s I would indicate that areas with high speeding degrees are surrounded by other areas with high speeding degrees, and similarly for low speeding degrees. This clustering could result from factors such as consistent road characteristics, traffic conditions, or driver behaviors in neighboring areas, aligning with concepts of spatial interaction and diffusion.

Using the spatial weight matrix with a distance threshold of 991.07 m, the Moran’s I statistic for the speeding degree was calculated to be 0.302, as shown in Figure 5a. This value is greater than zero, indicating a moderate positive spatial autocorrelation in the speeding degree across the study area. The positive spatial autocorrelation suggests that drivers’ speeding behaviors are influenced by spatial factors, and that nearby locations exhibit similar speeding patterns. This could be attributed to shared road characteristics, such as speed limits, number of lanes, or presence of enforcement measures, as well as to the influence of neighboring drivers’ behaviors, consistent with the idea of spatial spillover effects.

To further investigate the localized patterns of speeding degree, a hot spot analysis (using the Getis-Ord Gi* statistic) was performed. As illustrated in Figure 5b, this analysis identifies statistically significant clusters of high and low speeding degrees, effectively differentiating “hot spots” and “cold spots” [81,82,83]. Hot spots, indicated in red, represent areas where speeding degrees are consistently higher and statistically significant—often observed along arterial roads or suburban corridors with fewer traffic controls, where drivers may feel more at ease exceeding speed limits due to road design or limited perceived enforcement. In contrast, cold spots, shown in blue, signify clusters of lower-than-expected speeding degrees, commonly appearing in urban centers or residential neighborhoods characterized by lower speed limits, heavier traffic, and more frequent enforcement measures, thus encouraging more cautious driving.

The hot spot analysis provides valuable insights into the spatial distribution of speeding degree, highlighting specific areas where speeding is more prevalent and where interventions may be needed. These spatial patterns reflect the influence of urban form, network connectivity, and road environment on driver behavior. The identification of significant spatial clusters underscores the necessity of incorporating spatial dependencies into the modeling process. Ignoring these spatial patterns could lead to biased estimates and incorrect inferences about the factors influencing vehicle speeding degree. Therefore, the subsequent modeling employs spatial regression techniques, specifically the spatial lag model (SLM) and spatial error model (SEM), to account for the detected spatial autocorrelation.

In summary, the Moran’s I statistics and hot spot analysis confirm the presence of significant positive spatial autocorrelation in vehicle speeding degree on Jeju Island. This finding aligns with transport geography theories that emphasize the role of spatial relationships and network structures in shaping transportation phenomena. It validates the use of spatial econometric models to capture the complex interplay between spatial factors and driver behavior.

4.4. Spatial Lag Model and Spatial Error Model

To appropriately model the spatial dependencies identified in vehicle speeding degree, spatial econometric models are employed. Two primary models used to account for spatial autocorrelation in regression analysis are the spatial lag model (SLM) and the spatial error model (SEM). The selection between these models depends on the nature of the spatial processes influencing the dependent variable.

The spatial lag model, as shown in Equation (4), is suitable when spatial dependence arises from endogenous interactions among the dependent variable. In this context, the speeding degree at one location is directly influenced by the speeding degrees at neighboring locations, reflecting spatial spillover effects. This aligns with transport geography concepts where drivers adjust their speeds in response to the speeds of nearby vehicles due to interactions and traffic flow dynamics. In this model, the term $\rho WY$ incorporates the influence of neighboring observations’ dependent variables on each observation, and the magnitude of $\rho$ encapsulates phenomena like spatial diffusion or spillover [55].

$$Y=\rho WY+X\beta +ϵ,ϵ~N(0,{\sigma }^{2}I)$$

(4)

where Y is a vector of dependent variables (speeding degree, n × 1), $\rho$ is the spatial autoregressive coefficient representing the intensity of spatial lag dependence, X is a matrix of k explanatory variables (n × k), $W$ is the spatial weight matrix (n × n), $\beta$ is a vector of parameters (k × 1), $ϵ$ is the error term, assumed to be independently and identically distributed (n × 1).

The spatial error model, as shown in Equation (5), is appropriate when spatial dependence is due to omitted variables that are spatially correlated, leading to spatial autocorrelation in the error terms. For vehicle speeding degree, this could occur if unobserved factors affecting speed choices, such as localized enforcement practices or environmental conditions, are spatially clustered. In the SEM, the spatial autocorrelation is captured in the error structure, acknowledging that the error term at one location is influenced by errors at neighboring locations. A statistically significant $\lambda$ suggests that model factors induce spatial autocorrelation amongst error terms, with $\lambda$, the spatial autoregressive coefficient, representing the impact of adjacent area residuals on local area residuals [56].

$$Y=X\beta +ϵ \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} ϵ=\lambda W+\mu ,\mu ~N(0,{\sigma }^{2}I)$$

(5)

where Y, X, and $\beta$ have the same structure as SLM, but there is difference in $ϵ$ (n × 1), $\lambda$ is the spatial autocorrelation coefficient in the error term, and $\mu$ is a vector of uncorrelated error terms.

To determine the appropriate model, the Lagrange multiplier (LM) tests will be utilized. For the spatial lag model, the null hypothesis of having no spatial lag dependence ($\rho =0$) is assessed. For the spatial error model, the null hypothesis of having no spatial error dependence ($\lambda =0$) is assessed. If both tests are significant, indicating potential spatial dependence in both lag and error terms, robust versions of the tests are applied to identify the predominant form of spatial autocorrelation.

By incorporating spatial lag or spatial error components into the regression model, the analysis accounts for the spatial dependencies inherent in vehicle speeding degree. This methodological approach aligns with transport geography principles by recognizing the spatial interconnectedness of transportation networks and the influence of spatial factors on driver behavior. It ensures that the spatial relationships influencing vehicle speeds are rigorously captured, leading to more accurate and reliable modeling outcomes.

The spatial regression models are implemented using specialized software capable of handling spatial econometric analyses, such as GeoData 1.2 and GeoDa Space 1.2. This software facilitates the estimation of spatial models and provides diagnostic tools for assessing model fit and the significance of spatial parameters.

5. Spatial Autocorrelation Model Results

This section outlines the analytical progression from traditional regression models to spatially explicit econometric approaches. It begins with conventional ordinary least squares (OLS) models to identify initial relationships between speeding degree and explanatory variables, while noting any limitations that emerge from non-spatial assumptions. After establishing the OLS baseline, spatial diagnostics is applied to confirm whether spatial autocorrelation is present, justifying the need for spatial models. Then, the appropriate spatial econometric model—either a spatial lag model (SLM) or a spatial error model (SEM)—based on these diagnostics will be selected. Finally, the results of the spatial model will be interpreted, linking road design features, enforcement measures, and network properties to core concepts in transport geography.

5.1. Establishing the Baseline and Identifying Potential Spatial Limitations

The first step involves estimating a baseline OLS model to understand how traditional non-spatial approaches perform and to reveal initial patterns, as well as anomalies, that might suggest spatial interdependencies. As shown in

Table 2. Estimation results of basic OLS, OLS with interaction variables, and OLS with only enforcement camera variable.

Category	Variable	OLS (Model 0)				OLS with Interaction Variable (Model 1)				Model Comparison	VIF
		Estimate	Std. Error	t-Statistics	p-Value	Estimate	Std. Error	t-Statistics	p-Value
-	Intercept	41.362	0.404	102.346	0.0000 ***	41.539	0.405	102.659	0.0000 ***	+/+	-
Link- related variables	Number of lanes	−0.885	0.048	−18.573	0.0000 ***	−0.877	0.048	−18.409	0.0000 ***	−/−	2.616
	Speed limit	−0.719	0.004	−169.595	0.0000 ***	−0.724	0.004	−168.844	0.0000 ***	−/−	1.553
	Presence of one-way lanes	4.365	0.286	16.221	0.0000 ***	4.689	0.286	16.411	0.0000 ***	+/+	1.114
	Presence of median	8.620	0.121	71.391	0.0000 ***	8.592	0.121	71.148	0.0000 ***	+/+	1.810
	Presence of bus dedicated lane	−13.331	0.258	−51.660	0.0000 ***	−13.371	0.258	−51.822	0.0000 ***	−/−	1.305
	Presence of on-street parking lot	−6.993	0.248	−28.188	0.0000 ***	−7.021	0.248	−28.305	0.0000 ***	−/−	1.043
	Number of bus station	−0.037	0.043	−0.868	0.3860	−0.034	0.043	−0.799	0.0420	·/·	1.067
	Presence of school zone	−4.678	0.118	−39.784	0.0000 ***	−4.651	0.118	−39.545	0.0000 ***	−/−	1.094
	Presence of silver zone	−0.931	0.177	−5.264	0.0000 ***	−0.858	0.177	−4.846	0.0000 ***	−/−	1.047
Node- related variables	Road property change points	1.928	0.105	18.330	0.0000 ***	1.964	0.105	18.656	0.0000 ***	+/+	2.445
	Presence of traffic lights	−4.381	0.176	−24.932	0.0000 ***	−4.338	0.176	−24.685	0.0000 ***	−/−	1.079
	Presence of speed enforcement camera	1.524	0.230	6.628	0.0000 ***	−8.562	1.292	−6.627	0.0000 ***	+/−	1.018
	Closeness centrality	−287.841	12.767	−22.546	0.0000 ***	−285.219	12.767	−22.340	0.0000 ***	−/−	1.511
	Betweenness centrality	61.891	1.694	36.538	0.0000 ***	62.377	1.694	36.812	0.0000 ***	+/+	1.749
Interaction variable	Speed limit × Presence of speed enforcement camera	-	-	-	-	0.157	0.020	7.933	0.000 ***	·/+	-
Goodness of fit		Multiple R-squared: 0.3033, Adjusted R-squared: 0.3032, F-statistic: 3105 on 14 and 99,836 DF, p-value: <2.2 × 10−16 Log-likelihood = −402,481.5 AIC = 804,993, BIC = 805,135.7				Multiple R-squared: 0.3037, Adjusted R-squared: 0.3036, F-statistic: 2904 on 15 and 99,835 DF, p-value: <2.2 × 10−16 Log-likelihood = −402,450.0 AIC = 804,932, BIC = 805,084.2
OLS with only enforcement camera variable (Model 0-1)
Category		Variable			Estimate	Std. Error		t-statistics		p-value
-		Intercept			−8.842	0.053		−167.980		0.000 ***
Node-related variables		Presence of speed enforcement camera			−1.387	0.273		−5.076		0.000 ***
Goodness of fit					Multiple R-squared: 0.000258, Adjusted R-squared: 0.000248, F-statistic: 25.77 on 1 and 99,849 DF, p-value: 3.856 × 10−07 Log-likelihood = −420,512.0 AIC = 841,028, BIC = 841,047

***: Statistically significant at the 0.001 level. +/−: Positive/negative parameter and statistically significant at the 0.001 level. ·: Non statically significant ant the 0.05 level.

, the initial OLS model (Model 0) presents an unexpected positive parameter for the ‘presence of speed enforcement camera’ variable. This implies that roads with cameras are associated with increased speeding degree. This finding contradicts conventional expectations and previous literature [84,85,86], indicating that additional complexities may be at play.

To expand these results, a simplified OLS model (Model 0-1) focusing solely on the speed camera variable was estimated. Here, the coefficient for camera presence turned negative and significant, aligning better with anticipated behavior (i.e., cameras reducing speeding degree). The discrepancy between Model 0 and Model 0-1 suggests that interaction effects or subtle variable interrelationships influence the initial results. While all variables’ variance inflation factors (VIF) remain below 10, indicating no severe multicollinearity [87], the reversal of the camera effect highlights that a single global OLS model may be insufficient to capture the full complexity of the speed-behavior relationship.

In response to this complexity, an OLS model incorporating an interaction term (speed limit × speed enforcement camera) was constructed (Model 1), drawing on the results from [88] which used the same Jeju C-ITS data. This interaction-based OLS model improved model fit, as evidenced by better R-squared, Log-likelihood, AIC, and BIC values compared to Model 0. By including this interaction term, this paper founds that the influence of speed enforcement cameras may depend on the prevailing speed limit environment.

However, despite these refinements, OLS models inherently assume that observations are independent of one another, ignoring potential spatial spillover effects. The irregularities uncovered in the baseline OLS analysis—such as unexpected coefficient signs and the need for interaction terms—motivate the next analytical step: testing for spatial autocorrelation. If spatial patterns are present, a spatial econometric approach (e.g., SLM or SEM) can more adequately represent the interconnected nature of vehicle speeds, aligning with transport geography’s emphasis on spatial interdependencies.

In summary, these baseline OLS analyses serve as a benchmark, revealing complexities and hinting at underlying spatial structures that OLS cannot fully address. The next subsection will employ spatial diagnostics to confirm these questions and guide the selection of an appropriate spatial model.

5.2. Spatial Diagnostics and Model Results

Having established a baseline with OLS models and identified potential complexities that may arise from ignoring spatial interdependencies, the next step is to formally assess whether spatial autocorrelation is present in the data. Spatial autocorrelation suggests that speeds observed at one location are systematically related to speeds observed at nearby locations—an essential consideration given the transport geography context, where road environments and driver behaviors often cluster geographically.

To begin, Moran’s I statistic, introduced earlier in this paper with a value of 0.302, provided initial evidence of moderate positive spatial autocorrelation in the speeding degree. A Moran’s I value greater than zero indicates that similar values of the dependent variable (whether high or low speeding degrees) tend to cluster in space, rather than being randomly distributed. This clustering is consistent with the notion that driver behavior is influenced not only by local conditions but also by the characteristics of adjacent road segments, reflecting spatial spillover effects and the interconnected nature of transportation networks [76].

To further confirm and quantify spatial dependence, Lagrange multiplier (LM) tests were performed for the two spatial autocorrelation models. Specifically, both LM-lag and LM-error tests assessed whether spatially lagged dependent variables or spatially correlated disturbances, respectively, should be included in the model specification. As shown in

Table 3. Construction results of OLS model and spatial autocorrelation model.

Category	Variable	OLS with Interaction Variable (Model 1)				Spatial Lag Model (Model 2)				Spatial Error Model (Model 3)
		Estimate	Std. Error	t-Statistics	p-Value	Estimate	Std. Error	z-Statistics	p-Value	Estimate	Std. Error	z-Statistics	p-Value
-	Intercept	41.539	0.405	102.659	0.000 ***	30.577	0.435	70.314	0.000 ***	52.690	4.189	12.577	0.000 ***
Link- related variables	Number of lanes	−0.877	0.048	−18.409	0.000 ***	−0.059	0.047	−1.250	0.211	2.323	0.072	32.039	0.000 ***
	Speed limit	−0.724	0.004	−168.844	0.000 ***	−0.606	0.005	−131.024	0.000 ***	−0.794	0.005	−155.511	0.000 ***
	Presence of one-way lanes	4.689	0.286	16.411	0.000 ***	5.148	0.267	19.265	0.000 ***	4.507	0.288	15.660	0.000 ***
	Presence of median	8.592	0.121	71.148	0.000 ***	6.612	0.122	50.307	0.000 ***	4.404	0.145	30.332	0.000 ***
	Presence of bus dedicated lane	−13.371	0.258	−51.822	0.000 ***	−9.117	0.255	−35.731	0.000 ***	−5.865	0.302	−19.400	0.000 ***
	Presence of on-street parking lot	−7.021	0.248	−28.305	0.000 ***	−5.216	0.235	−22.241	0.000 ***	−1.754	0.292	−6.001	0.000 ***
	Number of bus station	−0.034	0.043	−0.799	0.000	0.005	0.040	−0.134	0.893	0.172	0.049	3.544	0.004 **
	Presence of school zone	−4.651	0.118	−39.545	0.000 ***	−3.057	0.114	−26.754	0.000 ***	−1.017	0.137	−7.431	0.000 ***
	Presence of silver zone	−0.858	0.177	−4.846	0.000 ***	−1.152	0.166	−6.952	0.000 ***	−1.838	0.224	−8.206	0.000 ***
Node- related variables	Road property change points	1.964	0.105	18.656	0.000 ***	1.869	0.098	18.989	0.000 ***	1.918	0.109	17.551	0.000 ***
	Presence of traffic lights	−4.338	0.176	−24.685	0.000 ***	−3.465	0.165	−20.981	0.000 ***	−2.148	0.164	−13.070	0.000 ***
	Presence of speed enforcement camera	−8.562	1.292	−6.627	0.000 ***	−5.086	1.210	−4.205	0.000 ***	3.036	1.334	2.276	0.028 ***
	Closeness centrality	−285.219	12.767	−22.340	0.000 ***	−65.364	12.686	−5.152	0.000 ***	−607.236	133.473	−4.550	0.000 ***
	Betweenness centrality	62.377	1.694	36.812	0.000 ***	33.676	1.681	20.038	0.000 ***	−18.481	2.474	−7.470	0.000 ***
Interaction variable	Speed limit x Presence of speed enforcement camera	0.157	0.020	7.933	0.000 ***	0.099	0.019	5.353	0.000 ***	−0.044	0.021	−2.100	0.036 **
Spatial model related	ρ					0.446	0.009	51.084	0.000 ***
	λ									0.973	0.004	243.579	0.000 ***
Lagrange Multiplier & Robust Lagrange Multiplier		-				LM VALUE: 44,288.674 Prob: 0.0000 **** Robust LM Value: 620.573 Prob: 0.0000 ****				LM VALUE: 358,543.599 Prob: 0.0000 **** Robust LM Value: 314,875.497 Prob: 0.0000 ****
Goodness of fit		Multiple R-squared: 0.3037, Adjusted R-squared: 0.3036, F-statistic: 2904 on 15 and 99,835 DF, p-value: <2.2 × 10−16 Log-likelihood = −402,450.0 AIC = 804,932, BIC = 805,084.2				Pseudo R-squared: 0.3936 Log-likelihood = −395,719.5 AIC = 791,473, BIC = 791,634.7				Pseudo R-squared: 0.2238 Log-likelihood = −425,311.2 AIC = 850,656.4, BIC = 850,818.1

****: Statistically significant at the 0.001 level. ***: Statistically significant at the 0.01 level. **: Statistically significant at the 0.05 level.

, the LM tests produced statistically significant results for both LM-lag and LM-error. This outcome implies that both a spatial lag model (SLM), which incorporates spatial dependencies directly into the dependent variable, and a spatial error model (SEM), which accounts for spatial correlation among the error terms, could theoretically improve upon the OLS baseline.

Based on these diagnostics, the next step is to estimate and compare the spatial econometric models (SLM and SEM) against the OLS baseline. While both LM-lag and LM-error tests indicated potential improvements over OLS, the ultimate choice must rest on both statistical performance and theoretical alignment with transport geography concepts of spatial interaction.

Choosing between SLM and SEM involves considering the theoretical underpinnings of speed-related behaviors as well as the empirical fit to the data. If speeding degree in one location directly influences speeding degrees in adjacent areas—perhaps through drivers perceiving the prevailing speeds around them or through shared road design features—a spatial lag model is often more appropriate. Conversely, if spatial autocorrelation arises from unobserved contextual factors (e.g., enforcement intensity or environmental conditions) that cluster geographically, an SEM might be favored.

As shown in Table 3, when directly estimated, the SLM outperforms both OLS and SEM in several respects. The SLM achieves a pseudo R-squared of approximately 0.3936, surpassing the OLS model’s R-squared of around 0.3037 (from Model 1) and the SEM’s pseudo R-squared of 0.2238. Additionally, log-likelihood, AIC, and BIC values indicate that the SLM provides a better fit to the data. Figure 6 offers a visual comparison of observed versus predicted speeding degrees for the OLS, SLM, and SEMs. In this scatter plot, points lying closer to the 1:1 line represent better predictive accuracy. As depicted, the SLM’s predictions cluster more tightly around the line than those of the OLS and SEMs, visually confirming the improved fit and reduced residual variability indicated by the statistical measures. This visual evidence further reinforces the notion that spatially modeling driver behavior aligns more closely with the underlying spatial structure of vehicle speeds. This improvement suggests that incorporating the spatially lagged dependent variable—representing the influence of nearby speeds—more accurately captures the complex spatial structure underlying speeding degree.

From a theoretical standpoint, the superior performance of the SLM supports the notion that speeding degree at one location is influenced not only by local conditions but also by the speed patterns of neighboring road segments. This aligns with the idea that drivers perceive and respond to the broader spatial environment, including cues from adjacent areas. In contrast, the SEM’s poorer fit and the emergence of multiple inverted parameter signs—particularly for the “Presence of speed enforcement camera” variable—indicate that modeling spatial dependence solely through spatially correlated errors does not fully reflect the observed patterns of driver behavior. The SLM, however, corrects the anomalies encountered in the OLS baseline, such as the counterintuitive positive association between cameras and speeding degree, by explicitly modeling the spatial diffusion of speeds.

In essence, the SLM better reconciles the empirical results with transport geography principles, recognizing that driver speed choices are not made in isolation but are part of a dynamic spatial milieu. By acknowledging spatial spillovers, the SLM provides a richer interpretation of how road design features, enforcement measures, and network connectivity shape speeding degree. The next subsection will delve deeper into variable interpretation, situating these findings within theoretical frameworks and drawing implications for policy and road safety strategies.

5.3. Variable Interpretation Within a Transport Geography Framework

Building on the results of the spatial lag model (SLM), this subsection interprets the key variables by grouping them into thematic clusters that resonate with transport geography principles. Rather than addressing variables one-by-one, this approach highlights broader conceptual linkages and informs more nuanced policy strategies.

5.3.1. Road Geometry and Design Features

Several variables relate directly to road geometry and physical design aspects. The presence of median barriers, for instance, was found to positively correlate with speeding degree, suggesting that when lanes are physically separated, drivers perceive fewer immediate risks and may travel faster. This finding aligns with literature indicating that certain design cues can inadvertently encourage slowing down if they perceive danger [66,89,90,91,92]. Similarly, the positive impact of one-way lanes on speeding degree—especially on segments with modestly lower limits—implies that simplified traffic flows and reduced oncoming conflicts can embolden drivers to exceed speed limits. In contrast, bus-only lanes exert a decelerating influence, as these visually distinct and functionally different lanes likely signal to drivers that they should exercise caution, reflecting how certain design elements can effectively act as traffic-calming measures.

It should be noted that these coefficients are interpreted as associations conditional on included covariates, not causal effects. For example, the positive coefficient for medians may capture co-occurring design characteristics (e.g., wider cross-sections, fewer interruptions), while the effect of road property change points may reflect unobserved factors such as adjacent land use or traffic composition. These findings therefore warrant cautious interpretation and further investigation.

Additionally, the number of lanes, initially significant at the 1% level in the OLS model, loses significance in the SLM once spatial dependence is accounted for. Roads with more lanes are often clustered in urban centers, and when the spatial term (ρ) incorporates these spatial patterns, the standalone effect of lane number diminishes. This indicates that what appeared as a lane-based influence under OLS partly reflected underlying spatial clustering. Moreover, in contrast to prior studies [22,25] that found a positive relationship between the number of lanes and vehicle speed, this paper’s OLS model showed a negative correlation for the speeding degree measure. This discrepancy arises from defining the dependent variable as speeding degree (speed minus limit) rather than absolute speed. Roads with higher speed limits (and more lanes) yield lower speeding degrees relative to their limits. Indeed, correlations confirm that while the number of lanes positively correlates with raw speed, it correlates negatively with the speeding degree, reconciling these findings with previous literature.

The interplay between lane configurations and speeding degree illustrates how road layout and surface conditions extend beyond simple engineering measures; they inform driver perceptions of risk, comfort, and appropriate speeds. By recognizing these influences, policymakers and planners can consider implementing design changes—such as narrower lanes, strategically placed medians, or visually salient bus lanes—to naturally guide drivers toward safer speeds, a concept widely discussed in self-explaining roads literature.

5.3.2. Regulatory and Enforcement Attributes

Variables linked to regulation and enforcement offer insights into how formal interventions shape driver responses. The negative relationship between speed enforcement cameras and speeding degree observed in the SLM confirms their deterrent effect on speeding degree when properly modeled. Moreover, the interaction between speed enforcement cameras and speed limits highlights the complexity of driver behavior: while enforcement cameras generally reduce speeding degree, their influence intensifies under higher speed limits due to drivers accounting for penalty thresholds. This phenomenon reflects a form of risk compensation, where drivers consider the likelihood of sanctions and adapt their speed accordingly.

Further quantifying this dynamic, the interaction variable (speed limit × presence of speed enforcement camera) reveals that for every 1 km/h increase in the speed limit, the speeding degree rises by approximately 10%. This suggests drivers exploit a known enforcement tolerance, commonly understood as leniency up to around 10% above the posted limit. For instance, on a 100 km/h road, fines may not apply until 110 km/h, enabling drivers to maintain higher speeds without incurring penalties. Such behavior underscores how even subtle policy thresholds can shape driver responses to enforcement measures.

At first glance, this regression finding may seem inconsistent with the descriptive statistics in Figure 2, which show that speeding violations occur most frequently in zones with excessively low limits (e.g., 20–50 km/h). However, these two results capture different aspects of speeding behavior. Figure 2 reflects the frequency of violations across speed-limit categories, whereas the regression result highlights the conditional effect of speed limits on the magnitude of speeding degree, particularly under enforcement conditions. In other words, low-speed zones record more frequent violations in terms of counts, but in camera-enforced high-speed zones, the extent of speeding degree deviations increases because drivers exploit tolerance thresholds. Thus, the descriptive and regression results are complementary rather than contradictory, together illustrating how both low- and high-limit contexts create distinct forms of speeding risk.

In addition, the negative impacts of school zones and silver zones validate targeted regulatory strategies designed to protect vulnerable road users. School zones, in particular, exhibit a stronger decelerating effect than silver zones, underscoring societal emphasis on child safety. The diverging magnitudes of these effects support the broader notion that transport regulations must be context-specific and culturally informed. This resonates with transport geography’s emphasis on human-environment interactions and the importance of locally tailored interventions.

5.3.3. Network Connectivity and Structure

Centrality measures—closeness and betweenness—capture the structural significance of nodes within the road network and thus influence speed patterns. The negative association of closeness centrality with speeding degree suggests that in densely connected urban cores, frequent intersections and complex road networks encourage slower speeds due to heightened driver vigilance. Conversely, the positive association between betweenness centrality and speeding degree indicates that arterial roads, serving as primary connectors within the network, facilitate higher speeds. These patterns align with transport geography insights that network hierarchy and connectivity play a pivotal role in shaping mobility behavior. The fact that spatial dependence reduced the magnitude and significance of these centrality measures in the SLM implies that part of their initial explanatory power was due to spatial clustering effects. Nonetheless, the structural properties of the road network remain critical for understanding variations in driver behavior.

Beyond centrality measures, node-level characteristics also matter. For example, ‘road property change points’—segments without intersections, endpoints, or U-turn nodes—were found to elevate vehicle speeds by allowing uninterrupted travel. Such continuous stretches reduce driver vigilance and encourage sustained, higher-speed driving, illustrating another facet of how network topology influences behavior.

5.3.4. Surrounding Environment

Finally, the presence of on-street parking and bus stops offers clues about how the immediate roadside environment affects drivers. The negative relationship between on-street parking and speeding degree illustrates how increased roadside activity and the potential for unpredictable pedestrian or vehicle maneuvers encourage caution. Similarly, while the number of bus stations was less influential, the complexity added by these pick-up/drop-off points can foster more conservative driving. Such environmental cues enhance the “friction” of the streetscape and resonate with the idea that mixed-use, pedestrian-friendly environments contribute to safer speeds, consistent with principles of livable streets and complete streets approaches [34,93,94,95].

Moreover, previous research has already demonstrated a positive correlation between parking space density in residential areas and lower driving speeds [96]. This aligns with the present findings in this paper, reinforcing that the availability or absence of on-street parking significantly influences speed reduction, as drivers anticipate more frequent pedestrian or vehicular interactions.

5.3.5. Summary of Variable Interpretation

By grouping variables into these thematic categories—road design, regulatory measures, network structure, and surrounding environment—this paper moves beyond simple variable-level interpretation. Instead, it presents an integrated narrative where drivers respond to a combination of design cues, enforcement policies, network layouts, and environmental interactions. This approach echoes holistic understanding of mobility, where both physical infrastructure and social regulations converge to shape travel behavior.

6. Conclusions

This paper contributes to the understanding of vehicle speeding behavior by incorporating spatial autocorrelation models at a fine spatial scale. Moving beyond conventional analyses using aggregated zone-level data, it employs point-level speed observations and uses “speeding degree” (speed minus limit), rather than absolute speed, as the dependent variable. This approach provides granular insights into how localized road features, enforcement measures, and spatial contexts shape driver speed choices.

Several key findings emerge. First, Moran’s I statistic confirmed the presence of moderate positive spatial autocorrelation, underscoring that drivers’ speeding degree patterns are not independent but influenced by nearby conditions. Traditional OLS models, which ignore these spatial dependencies, produced anomalous results—such as counterintuitive associations between enforcement cameras and speeding degree. Incorporating spatial autocorrelation via the spatial lag model (SLM) rectified these issues, improving model fit and aligning the results more closely with transport geography principles. This finding demonstrates that spatial econometric models are vital for capturing the inherent spatial interconnections in traffic behavior.

Second, the SLM’s superior performance relative to the spatial error model (SEM), despite the latter’s favorable Lagrange multiplier tests, illustrates the importance of assessing multiple diagnostic criteria. The SLM not only provided better goodness-of-fit measures but also produced more theoretically consistent parameter signs. This outcome highlights the need to look beyond simple diagnostic tests and incorporate both empirical and conceptual considerations when selecting a spatial model.

Third, the analysis revealed that multiple dimensions of the transport environment interact to influence speeding degree. Road geometry and design cues—such as median barriers and one-way lanes—can inadvertently encourage higher speeds by reducing perceived risk. Conversely, features like bus-only lanes and on-street parking add “friction” that prompts drivers to slow down. Regulatory and enforcement measures, including school zones, silver zones, and enforcement cameras, generally reduce speeding degree. However, the interaction between speed limits and camera enforcement is complex, with drivers seemingly exploiting known tolerance thresholds. Additionally, network connectivity metrics (closeness and betweenness centrality) and the presence of uninterrupted road segments (“road property change points”) further demonstrate that speed behaviors are intertwined with how roads are organized in space.

These insights suggest that focusing solely on lowering speed limits is insufficient. Effective speed management must combine targeted enforcement, carefully considered road geometry, and context-specific regulatory measures. For instance, altering median designs or integrating visually salient bus lanes can shape drivers’ speed choices toward safer levels without solely relying on strict enforcement.

Previous before-and-after studies have also demonstrated that speed limit interventions alone are insufficient, and that complementary measures such as enforcement or road design changes are necessary to achieve meaningful speed reductions. Our findings are consistent with this body of work. However, unlike prior studies that relied primarily on temporal comparisons, the present research applies spatial econometric models to point-level ADAS speed data. This approach provides a novel perspective by quantifying spatial spillovers and contextual influences on speed choice, thereby confirming existing knowledge through a different methodological lens. In conclusion, this paper reinforces the importance of considering spatial spillovers, road design, environmental cues, and regulatory frameworks together. By employing spatial autocorrelation models at the point level, it offers a more nuanced comprehension of drivers’ speed choices and speeding dynamics.

These findings offer valuable insights for policymakers but have several limitations. First, temporal variations in speeding—such as seasonal or time-of-day effects—were not examined, though patterns may differ across seasons and peak hours. Future work should incorporate temporal dimensions including day-of-week patterns and time-series weather conditions for better understanding. Second, the sample is largely rental vehicles driven by non-local visitors; while this reduces local bias, it limits external validity, highlighting the need to compare visitor and resident drivers. Third, the data did not allow clear separation of free-flow and congested speeds; richer trajectory data and headway-based methods could address this. Finally, while this study has advanced the understanding of spatial and environmental determinants of speeding degree, we did not conduct a global sensitivity analysis to systematically evaluate the relative importance and interactions of these factors. Global sensitivity analysis techniques, as discussed in prior studies (e.g., [97,98]), provide a powerful framework for quantifying parameter influence. Incorporating such methods could further strengthen future investigations by offering a more rigorous assessment of how spatial and environmental variables jointly shape speeding behavior. Future research should also consider the role of pedestrian and cycling infrastructure—such as sidewalks, crossings, and bike lanes—in shaping vehicle speeds, thereby linking traffic safety outcomes more directly to sustainability objectives.

Beyond Jeju Island, applying these findings to other regions requires attention to both infrastructural and contextual differences. For example, the relative influence of design features (e.g., medians, bus lanes) and enforcement strategies may vary depending on road hierarchies, traffic compositions, and cultural driving norms. Future research should therefore test the framework in diverse geographical and temporal settings to establish the extent of generalizability and to guide context-specific policy design.

Despite these limitations, policymakers and planners are encouraged to adopt a holistic perspective, implementing integrated strategies that recognize the complex interplay between infrastructure, environment, enforcement, and human behavior. In practice, this may include targeted traffic calming interventions such as the installation or relocation of speed cameras at identified hot spots, the redesign of median barriers or intersections to reduce excessive speed, and the incorporation of visually salient features like bus lanes, pedestrian crossings, and bike facilities. By aligning these interventions with the spatial factors identified in this study, policymakers can design safer and more sustainable road environments.