Urban Mobility and Socio-Environmental Aspects in David, Panama: A Bayesian-Network Analysis

Abstract

Given that urban mobility arises from the interaction between social and environmental conditions, this study constructs a Bayesian network to represent these relationships in David, Panama, using 500 georeferenced household surveys that recorded variables related to demographics, travel behavior, infrastructure, mobility patterns and perceptions of risk, safety, and vulnerability. The Bayesian network was built and validated through a consensus-driven hybrid procedure combining structural learning and expert knowledge, resulting in a directed acyclic graph (DAG) with 127 nodes and 189 arcs; and conditional probability tables (CPTs) were learned from data. The topology of the network was analyzed with Louvain community detection, revealing eleven subsystems that group household economy and mode choice, hydrometeorological mobility barriers, congestion, public-transport quality, and safety in school travel. The inferences show gender-based differences in the risk of harassment on public transport, higher perceived vulnerability on longer trips, and elevated stress among middle-aged drivers. The model highlights potential priority interventions such as reinforcing public-transport safety, promoting self-contained trips, and encouraging short-distance active mobility, based on population perceptions. The resulting DAG functions as both an analytical and communication tool for urban management, is visually understandable to all stakeholders, and provides unprecedented evidence for Panama in a little-studied context.

1. Introduction

Urban mobility is deeply linked to the individual, to their activities, characteristics, and surrounding environment. The nature of personal movement, whether on an individual or household level, is associated with one’s particular lifestyle and reflects the structure of activity patterns [1]. The act of moving to access essential needs influences how household activities are organized, and that internal organization, in turn, has direct implications for mobility itself [2].

To describe mobility, it is necessary to move beyond a single dimension [3]. While the connection between a person and their lifestyle helps to explain mobility behavior, the intention to move is also influenced by demographic variables, the built environment, access to social goods, and perceptions of safety [4,5]. The built environment provides the contextual foundation within which human activities unfold [6], so the city plays a predominant role in shaping how and where trips occur [7], although frequency and duration are more directly related to the inherent nature of human activity.

As social, economic, and technological transformations take place in cities, they bring about the development of new models of urban mobility, which are driven by increases in the average distances traveled and lead to changes in travel patterns and the relocation of daily activities [8]. A sustainable mobility model must ensure environmental protection, social cohesion, and economic development [9], incorporating the perspectives and participation of all actors involved, especially the end user, who is ultimately the one most affected by interventions in urban environments [2,10]. In many Latin American cities, rapid urbanization has evolved alongside persistent patterns of inequality, producing forms of economic segregation [11], and visible manifestations of social exclusion that are further intensified by limited accessibility and urban planning decisions that perpetuate unequal conditions [12,13].

The city of David stands as one of the most important urban centers in the Republic of Panama, with significant commercial activity and a large portion of its mobility occurring through the use of private vehicles [14]. While the city has a regular, grid-like street layout, its peripheral areas lack connectivity and display socially unequal conditions [15]. In addition, it is a territory exposed to risks and disasters that create mobility barriers, including floods [16] and landslides [17], and it exhibits stark socio-environmental contrasts that span not only the built environment but also social, economic, and ecological dimensions.

Urban mobility functions as a bidirectional phenomenon that acts simultaneously as both cause and effect; its dynamics are closely tied to and conditioned by individual characteristics, the structure and environment of the residential unit, urban environmental conditions, and the daily practices of the population. Understanding it and making informed decisions requires a multifaceted and holistic perspective that integrates both social and environmental dimensions [18,19], which in turn enables the characterization of mobility patterns from a socio-environmental lens [20].

To study this kind of complex relationship, various multivariate statistical methods have been used, leading to relevant findings; however, the quantitative techniques that are typically applied in these studies have shown limitations when dealing with systems where variables interact in reciprocal and non-linear ways [21]. Another important issue is that traditional models often lack the capacity to visually represent complex relational structures and rarely include post hoc analytical procedures capable of transforming descriptive results into predictive tools that can support public policy. In this context, the authors of ref. [22] argue that the lack of model explainability in conventional approaches significantly limits their usefulness as instruments for decision-making in the field of mobility.

Bayesian networks provide a robust analytical framework that represents influences between variables both graphically and probabilistically, offering substantial potential for modeling complex and non-deterministic systems [23]. This approach is especially valuable for studies seeking to analyze broad and intricate social and spatial dynamics involving multiple variables [24], in contexts where the relationships between phenomena are rarely deterministic and uncertainty is an inherent element. There is growing potential in the use of machine learning for urban planning and analysis of this nature, but current applications remain geographically and methodologically unbalanced [25].

This research seeks to explore the following questions:

(i)

What is the relationship between socio-environmental conditions and mobility patterns in David, Panama?

(ii)

Which mobility profiles emerge when social, environmental, and travel variables are integrated through an explainable Bayesian network?

(iii)

What possibilities does a Bayesian network model offer for exploring complex relationships between urban mobility and socio-environmental aspects, with the potential to support decision-making processes?

To answer these questions, a hybrid structure-learning approach was implemented, combining empirical data from perception surveys with expert-reviewed probabilistic modeling. The resulting Directed Acyclic Graph (DAG) captures interdependencies among variables, offering both a visual and analytical interpretation of mobility in the city. This framework enables not only the identification of underlying behavioral patterns and vulnerability profiles but also provides a methodological tool to support planning and public policy in contexts marked by complexity and uncertainty. The following section outlines the study’s specific objectives and the hypotheses derived from its analytical design.

Research Objectives and Hypotheses

This study seeks to investigate the probabilistic interdependencies between socio-environmental conditions and urban mobility dynamics in David, Panama, using a Bayesian network model. The main objectives are:

• To map and classify the key dependencies among social, environmental, and mobility-related variables through a hybrid structure-learning process.
• To identify and interpret cohesive subsystems that reveal patterns of exclusion, risk, and behavioral adaptation using community detection techniques.
• To estimate posterior probabilities associated with mobility-related perceptions (e.g., harassment, stress, vulnerability) across diverse social profiles.
• To provide data-driven insights and modeling tools that support urban policy and planning in complex environments.

From these objectives, the following hypotheses are proposed:

H1. 

Social, environmental, and demographic variables form structured subsystems that jointly influence urban mobility patterns and behaviors.

H2. 

Gender, commute duration, and multimodality significantly affect the perception of harassment, vulnerability, and stress in daily travel.

H3. 

Bayesian network models offer an effective, interpretable, and empirically grounded framework for representing complex urban dynamics and informing mobility-related decisions.

2. Literature Review

2.1. Socio-Environmental Factors and Urban Mobility

Daily mobility is directly shaped by the individual, by their characteristics, their social context, and their environmental surroundings. Various studies in this field have found consistent associations between income, residential location, and modal choice. The study by [26] notes that individuals with higher incomes tend to live in peripheral zones [21,27], and are more likely to rely on private transport as their primary means of mobility [28,29,30]. Additionally, ref. [31] points out that income inequality intensifies the spatial segregation of travel behavior. However, it is acknowledged that this effect varies by age. On one hand, young adults tend to translate income increases into more immediate car use, whereas older individuals are more likely to sustain shorter trips, often due to health-related limitations [26,32].

Gender, a variable addressed in numerous studies, introduces additional layers of complexity. Women, often associated with caregiving responsibilities, tend to follow more spatially constrained itineraries and structure their movements differently from men [26]. Another relevant factor within this interaction system is educational attainment, which influences both purchasing power and modal preferences. Higher education levels tend to correlate with more frequent car use, while lower education levels are associated with greater dependence on public transport [30,33].

These individual characteristics are also linked to the structure of the household itself. Larger families or households with dependents increase the need for mobility and often lead to the acquisition of private vehicles [26]. Household size also conditions the choice of residential location and the length of daily trips, particularly when the search for affordable housing forces individuals to consider peripheral areas located far from employment centers [21,30,34].

Employment status similarly shapes mobility patterns. According to [35], holding a stable, full-time job is associated with more frequent and longer trips. In Lisbon, for example, contrasting social profiles were identified: high-mobility profiles consisted mostly of men with high incomes and no dependents, while low-mobility profiles were characterized by women with lower salaries and caregiving responsibilities [26]. This points to an interconnected interaction between income, gender, and domestic structure.

But it is not only social and economic factors that play a role in this system. The residential environment provides the physical support upon which these dynamics unfold. Intermediate urban densities favor what has been called self-containment, meaning the possibility of fulfilling daily needs in close proximity to the home, and they encourage the use of non-motorized modes of transport [29,36]. For instance, commuting to work may be carried out within the same neighborhood, but low-density environments increase dependence on cars, while high densities tend to generate congestion [37].

Studies on mode, duration, frequency, and distance of travel show that these dimensions are also shaped by perceptions of safety. A well-functioning transport network may increase willingness to travel, but insecurity, whether due to crime or traffic-related risks, often suppresses mobility, particularly among groups with higher levels of vulnerability [38,39].

Taken together, the literature describes a system of reciprocal relationships between socioeconomic attributes, the urban environment, and mobility patterns. However, most studies examine these factors in isolation, without adequately capturing their simultaneous interactions or their evolution under specific conditions. Given the underlying interdependence, which is difficult to represent or measure when analyzed separately. It is likely that a decision in one dimension will directly or indirectly affect many others. Yet this relationship is difficult to model using conventional technical tools and, even more so, to visualize in an integrated manner.

2.2. Bayesian Networks in Urban Systems and Decision-Making

Decision-making in matters related to urban mobility is a subject that demands a high degree of complexity and care. It is also an issue that has historically been overlooked in terms of its social impacts and the distributive effects of transport decisions [40], and it has often been addressed through approaches that fail to adequately recognize the differences between mobile subjects and their specific contexts [41], overlooking how even minor urban changes can significantly influence both mobility and individual well-being [42].

In the specific field concerning urban mobility, Bayesian networks have been used to model travel behavior [22], to analyze patterns in the use of certain transport modes based on hypothetical surveys [43], to estimate the occurrence of traffic or aviation accidents, and to assess public policies in transport planning [44,45]. These applications, which do not solely pertain to the field of urban mobility, are part of a broader spectrum that spans interdisciplinary domains such as medicine, environmental management, and risk analysis, and complex urban land-use systems, where Bayesian networks have proven to be versatile and effective tools for representing complex and uncertain systems and for supporting decision-making processes grounded in technical reasoning [44,46,47,48,49,50].

The use of Bayesian networks in urban systems can be observed in the study by [51], where the economic, social, and cultural sustainability of urban communities is evaluated by integrating both qualitative and quantitative data, analyzing multiple scenarios, and considering the formulation of predictions within highly complex systems. This study, along with others such as [47,52], combines empirical data (often drawn from surveys or census records) with expert knowledge, defines specific indicators, and uses Bayesian models to support planning and management in urban and regional contexts, thereby contributing to local governance. In [22], explainable Bayesian networks are applied to examine vulnerability in mobility from an individual perspective, modeling activity choices, transport mode selection, and trip duration. Their approach, based on travel diary data, aims to explain duration patterns as indicators of exposure to risk. Another noteworthy application appears in the study by [53], who uses Bayesian networks to model the interaction between city, transport, and environment across 75 cities. This work makes it possible to infer sustainable urban mobility profiles from complex causal relationships among urban structure, transport supply and demand, resource allocation, and externalities.

While the reviewed studies have demonstrated the potential of Bayesian networks to model complex urban systems, the present work stands out by addressing an even broader and deeply interrelated structure within a specific urban scenario, incorporating multiple social, environmental, and mobility-related dimensions from the perspective of mobile subjects. Through an explainable model based on perception data, this research seeks to advance the understanding of urban exclusion and its connections to everyday mobility, offering an analytical and communicative tool intended to support decision-making processes in unequal urban contexts.

3. Materials and Methods

3.1. Study Area: City of David

Data collection was conducted within the district of David, located in the western region of the Republic of Panama (Figure 1). This district covers an area of 892.4 km² and has a population of 156,498 inhabitants [54]. Within this district, a Sustainable Urban Mobility Plan (PIMUS) study was carried out, which revealed an urban configuration marked by low land-use mix in peripheral areas, leading to a strong dependency on the urban core. This pattern is also reflected in daily travel behavior, which is predominantly oriented toward central areas and heavily reliant on both private and collective transport. According to PIMUS, within the study area, a total of 343,640 trips are undertaken daily across various transport modes, with private motorized transport accounting for 54.4% of the modal share, followed by 29.0% for public motorized transport and 16.6% for non-motorized modes [55]. The central urban area of David attracts roughly 44.6% of all daily trips within the study area.

Socioeconomic disparities are evident across different zones of the district, particularly in terms of income, access to basic services, and housing types, while recent urban growth has been driven by the expansion of residential developments with limited connectivity. The PIMUS identified that mobility decision-making in David is highly centralized, with limited technical and operational autonomy at the local level. It also pointed to institutional weaknesses in the capacity to systematize information, prioritize interventions, and generate local evidence to support sustainable policy-making [55].

3.2. Data Collection and Survey Design

The structuring of the methodology consists of four main stages, within which a series of steps were carried out to address the scope and complexity intended by the study, as shown in Figure 2.

3.2.1. Step 1: Research Design

An extensive literature review was conducted to identify the variables of interest for this study. Through expert meetings and a review of previously used variables, a total of 128 relevant variables were identified for characterization within the research (see Appendix A). Of these, 125 correspond to variables that will be collected through georeferenced household surveys using ArcGIS Survey123, while the remaining 3 will be derived from spatial information gathered during the survey using GIS tools (ArcGIS Pro 3.5.2).

3.2.2. Step 2: The Survey Instrument

Step 2.1: Survey Design and Validation

As stated by [56], methodological decisions in social research depend both on how the phenomenon is understood and on how it is brought into the field to be measured. For data collection, residential surveys were conducted within the study area, allowing for the capture of information related to direct perceptions from the user’s perspective [39,55,57,58]. Studies such as that of [59] offer a reference framework in Panama, where surveys have been used to gather information on citizens’ perceptions of the built environment and their mobility, employing georeferenced instruments. Ref. [58] also captured population perceptions regarding urban public services through surveys designed for analysis using Bayesian networks.

The selection and structuring of variables was based on the levels of measurement defined by [60], incorporating different types of variables according to their nature and analytical purpose. For instance, some of the study variables such as housingType represent a nominal variable, coded using categories that indicate the type of housing unit (e.g., Rented room, Apartment (building), House); mobTimeHealth corresponds to an ordinal variable, with states reflecting a perceptual gradient of the physical impact of travel time (e.g., Very high, High, Moderate, Low, Very low, None); incomePerception is considered quasi-interval, as it captures a structured subjective assessment of income adequacy (e.g., Very low—Insufficient, Low—Barely sufficient, Moderate, High); and weeklyFuelCost, originally a continuous ratio variable, was reclassified into ordered brackets (e.g., ≤B/.9.99, B/.10.00–24.99, B/.25.00–49.99, B/.50.00–74.99, B/.75.00–99.99, >B/.100.00). These variables illustrate different coding approaches according to type, allowing for the breadth and complexity of the defined variables to be properly captured. The complete variable and state dictionary is presented in Appendix A. The survey was constructed following these variable considerations and was validated by experts; a pilot application was subsequently conducted to verify the questionnaire items.

Step 2.2: Survey Data Collection

A total of 500 surveys were administered using the Survey123 application, following the approach proposed by [59], with the spatial distribution shown in Figure 1, covering all the different populated areas of David. The survey captured perceptions from a sample composed of 58.4% women and 41.6% men, with recorded ages ranging from 17 to 87 years.

Step 2.3: Verification and Quality Control of Survey Data

Survey data collection and geolocation were monitored in real time to ensure coverage within the main populated areas of the study zone, encompassing the entirety of the district. During this process, responses that did not geographically align with the defined area were filtered out, and a backtracking strategy was implemented by returning to Section Step 2.2: Survey Data Collection and revisiting areas with coverage gaps in order to complete the intended spatial representation.

3.2.3. Step 3: Data Handling and Structuring

Discrete Bayesian modeling requires transforming input variables into finite categories. Since many of the variables collected in the survey did not have a predefined classification, a manual discretization process was applied by grouping states, based on expert criteria and standard references when available. The resulting set of 128 variable states was numerically encoded using an ascending order that reflects increasing estimated impact, according to the criterion defined for each variable and determined through expert judgment. Also, the final dataset was structured in a data frame for later integration into the Bayesian model. This procedure aligns with standard practices for discrete Bayesian networks, where variables are required to operate over finite state spaces and where data are typically arranged in structured data frames for model construction and parameter estimation [43].

3.2.4. Step 4: Bayesian Network Framework

Step 4.1: Bayesian Network Model Construction

The Bayesian network was constructed in Python (version 3.12.9) using the pgmpy package (version 1.0.0), based on the processed data structured in the dataframe. Since the aim was to represent the complex interaction among multiple social, environmental, and mobility dimensions, the definition of the network structure followed a collaborative process between expert knowledge and structural learning, using the HillClimbSearch algorithm [61], as proposed in the Bayesian construction procedure by [62], optimizing with a BDeu criterion with Dirichlet priors [63]. Due to the model’s magnitude and to manage the computational complexity of structure learning, the maximum number of learned parents was limited [47] to a maximum of 3 parents per node, a limit that was rarely reached within the constructed structures. This constraint improved the clarity of the resulting network.

Following a structured approach, certain arcs were predefined and induced into the learning process, derived from conceptually expected relationships in the survey through expert knowledge or prior knowledge [43]. Subsequently, the obtained structure was adjusted using the BayesianEstimator on the observed data, with an equivalent sample size of 10 [64]. The result was a directed probabilistic model through a DAG that preserves both the direction and strength of conditional relationships, allowing for the direct extraction of Conditional Probability Tables (CPTs) for further analysis and interpretation.

Step 4.2: Model Validation and Expert-Guided Structural Refinement

Based on theoretical recommendations proposed by [65] on structural learning, for a sparse Bayesian network with a limited number of parents per node, the minimum number of samples required to consistently recover the underlying structure is lower-bounded by Equation (1):

$$\Omega \left(k\mathit{log}m+{\displaystyle \frac{k^2}{m}}\right)$$

(1)

where m represents the number of variables (m = 128, in this case) and k is the maximum number of parents allowed per node (k = 3, in this case). The sample size used in this work, represented by the number of surveys applied (n = 500), satisfies this theoretical requirement, ensuring minimum conditions for structural learning.

Model validation was approached from: (1) a structural bootstrap analysis was implemented to review the accuracy estimate, which can shed light on the reliability of the results [23,66], through the stability of the learned arcs in multiple bootstrap samples [67], in this case, using 100 iterations. For each resample, a network structure was learned using the Hill-Climb Search algorithm and the BDeu score. The resulting arc frequencies were then used to construct an averaged network. Although prior studies recommend estimating optimal arc strength thresholds [67,68], we adopted fixed thresholds of 0.3, 0.5, and 0.85 for illustrative purposes. These values are commonly referenced in the literature, particularly 0.85 and 0.50, as used in [69], and serve here as a practical benchmark to visualize arc stability, rather than as a basis for model selection or inference; (2) structural fidelity was evaluated using the topological F1-score metric [64], which reached a value of 0.51, and the Jaccard index, calculated between network structures learned through five-fold cross-validation, with an average of 0.804; and (3) predictive stability, measured by the total log-likelihood under a k-fold cross-validation, yielded an average of –9418.46 with a standard deviation of ±129.82, reflecting an adequate generalization capacity to unseen data given the scale of the network. In such contexts, structure-learning methods often yield partially accurate networks, which are nonetheless useful for exploratory analysis and hypothesis generation [70].

Based on these validation results, and after being reviewed by urban mobility experts, the resulting network can be considered structurally coherent, predictively stable, and interpretable within the limitations imposed by the observed data. To ensure the transparency of the Bayesian network process, the recommendations proposed by [71] were followed.

3.3. Bayesian Network Analysis

The main analysis to be performed is a descriptive analysis of the generated DAG, the identification of relationships and connections between parents and children of the network, and the graphical representation of the robust arcs resulting from the Bootstrap allows us to describe these relationships and dependencies between variables.

For the exploratory identification of communities, the Bayesian network structure was represented as an undirected graph, which is a common practice in studies of modularity and clustering in complex networks [72,73]. This allows the identification of densely connected groups of variables, facilitating the visualization and preliminary analysis of emerging patterns. This approach was implemented through the Louvain communities function in Python [72], which evaluates the modularity gain $\Delta Q$ when considering the reassignment of a node to a different community. The formulation used to calculate this gain was proposed by [74] in their extension of the Louvain algorithm for directed networks, and is defined by the following expression in Equation (2):

$$\Delta Q={\displaystyle \frac{k_{i,\mathrm{in}}}{m}}-\gamma \left({\displaystyle \frac{k_i^{\mathrm{out}}·{\Sigma }_{\mathrm{tot}}^{\mathrm{in}}+k_i^{\mathrm{in}}·{\Sigma }_{\mathrm{tot}}^{\mathrm{out}}}{m^2}}\right)$$

(2)

where m represents the total sum of weights of the directed links in the network; $k_{i,\mathrm{in}}$ is the sum of weights of the links entering node i from the target community; $k_i^{\mathrm{out}}$ and $k_i^{\mathrm{in}}$ correspond to the weighted outbound and inbound degrees of the node, respectively; ${\Sigma }_{\mathrm{tot}}^{\mathrm{in}}$ and ${\Sigma }_{\mathrm{tot}}^{\mathrm{out}}$ are the sums of weights of the links entering and leaving the evaluated community; and $\gamma$ is the resolution parameter, set to 1.

This formulation preserves the directionality and hierarchy of a Bayesian network, which is essential given its structure as an acyclic directed graph. In this context, the authors of ref. [75] stress the relevance of adapting community detection methods specifically to DAGs, as this allows the identification of groups of nodes that share common trajectories along the network. In this way, it is possible to observe the formation of topological pattern communities within the network structure.

The data learned from the network are analyzed to propose urban profile scenarios and explore their interaction with mobility aspects, thus identifying possible profiles prone to social exclusion through inferences. For this purpose, Bayesian network factorization is used, which allows the identification of conditional dependence relationships between variables. In this framework, and as part of the construction of the model, the joint probability distribution can be expressed by means of the characteristic factorization of Bayesian networks, as shown in Equation (3):

$$P\left(X_1,\dots ,X_n\right)={\displaystyle \prod }_{i=1}^{n}P\left(X_i\mid p{a}_i\right)$$

(3)

where $\left(p{a}_i\right)$ represents the set of parents of $\left(X_i\right)$ in the DAG. This factorization allows us to efficiently represent the joint distribution by incorporating conditional independencies, characteristic of the modeled socio-environmental domain. Inferences about urban profiles and their relationship with mobility were made on the network and the learned conditional probability tables (CPTs), using inference algorithms, namely Variable Elimination in pgmpy. This process made it possible to calculate posterior probabilities of variables of interest, conditional on different configurations of evidence. In this way, it was possible to identify specific combinations of characteristics associated with a higher risk of social exclusion.

4. Results

4.1. Structure and Key Dependencies in the Learned Bayesian Network

The final consensus Bayesian Network yielded a DAG with 189 directed arcs connecting 127 nodes (global density = 0.024), as observed in Figure 3.

Table 1. Top 60 arcs with the highest bootstrap support in the final Bayesian network. The table lists |directed dependencies (Source → Target) ranked by their bootstrap frequency, which reflects the proportion of resampled networks in which each arc appeared.

Arc (Source → Target)	Bootstrap Frequency	Arc (Source → Target)	Bootstrap Frequency
activityStatus → age	0.98	kidsAtHome → maritalStatus	0.74
hhMemberSchool → hhSize	0.97	ptranspObsJS → crossFearObsJS	0.73
mainTranspMode → drives	0.94	ptranspObsJS → busStopObsJS	0.73
tallGrassbBarrRes → treesViewBarrRes	0.94	distToWork → workSubdistrict	0.73
jobType → jobSector	0.93	homeToWorkTime → distToWork	0.72
disabNightMove → disabilityType	0.93	PTFreqRes → PTQualityRes	0.72
postWorkFamTasks → activityStatus	0.92	hhSize → kidsAtHome	0.70
age → kidsAtHome	0.91	hhMSTravelTime → hhMemberSchool	0.70
eduCurrentLevel → eduLevel	0.90	floodVulnRes → floodConcernRes	0.70
workToHomeTime → homeToWorkTime	0.88	sidewalkCovHome → sidewalkConHome	0.68
carPurchasePrice → hhCars	0.87	treesViewBarrRes → adsViewBarrRes	0.68
roadConstrRes → commConstrRes	0.87	ptranspObsJS → unempDuration	0.67
hlthMobImpact → healthGeneral	0.87	laborMobilityPattern → workToHomeTime	0.67
postWorkRoutine → personalActivities	0.86	workAccessEase → workToHomeTime	0.67
age → maritalStatus	0.85	densityLevel → workSubdistrict	0.66
landslideMobRes → landslideFreqRes	0.85	mobTimeActivities → mobWeekdays	0.66
postWorkRoutine → goesHomeDirectly	0.82	hhMemberSchool → kidsAtHome	0.65
pmCongestEdu → amCongestEdu	0.82	NLBarrierRes → nightLightRes	0.65
hhMSchoolAge → hhMSWalk	0.82	densityLevel → taxiAccessRes	0.65
floodVulnRes → mobFloodRes	0.82	walkNightInsec → safetyRes	0.65
workToHomeTime → walkToWork	0.81	housingType → hhMemberSchool	0.64
treesViewBarrRes → treesRes	0.81	mainTranspMode → walks	0.64
adsViewBarrRes → adsRes	0.80	eduRouteVuln → eduRouteSafety	0.63
postWorkRoutine → stopsForShopping	0.79	otherJobs → goesHomeDirectly	0.62
personalActivities → goesHomeDirectly	0.78	hhMSTravelTime → hhMSAccessEase	0.62
taxiInsec → harassTPexp	0.77	drives → weeklyFuelCost	0.62
postWorkRoutine → otherJobs	0.76	transpCostImpact → transpCostDaily	0.61
postWorkRoutine → postWorkFamTasks	0.76	housingTenure → housingType	0.59
landslideSevRes → landslideMobRes	0.76	hhSize → disabilityType	0.58
PTFreqRes → busWaitTimeRes	0.75	disabDayMove → disabNightMove	0.58

lists some of the most stable dependencies; among the highest-frequency links are activityStatus → age (0.98), hhMemberSchool → hhSize (0.97) and mainTranspMode → drives (0.94), all consistent with plausible behavioral mechanisms. The variable with the highest number of parents (hhMemberSchool) has 3, respecting the recommended limit to avoid unobserved combinations and overfitting problems in contexts with limited samples. The variable with the highest number of direct children is (eduTravelTime), with 7 dependents, making it a central node in explaining mobility flows and their determinants.

Eight root nodes (no parents) provide the exogenous context from which the rest of the system unfolds: tallGrassbBarrRes, sidewalkCovHome, disabDayMove, hhMSchoolAge, walkNightInsec, disasterPrep, floodVulnRes, eduRouteVuln and 32 leaf nodes (no children) capture end-point outcomes such as detailed travel times or specific perceptions. The animalPresenceRes (perceived frequency of stray or wild animals) variable, was excluded from the structure-learning pipeline, as it failed to reach the 30% threshold of arc presence across bootstrap resamples and was consistently penalized by the Hill-Climb score. This variable behaves as an isolated, low-impact perception in this dataset, so the learning algorithm judged it extraneous to the core dependency structure and excluded it from the final Bayesian Network.

The final Bayesian network comprised a total of 189 directed arcs, which were categorized based on their origin and bootstrap stability. Among these, 5 arcs (2.6%) were explicitly defined through expert knowledge (highlighted in red in Figure 3). The structure also includes 63 arcs (33.4%) with a bootstrap frequency below 0.3, suggesting they were selected exclusively through the HillClimb + BDeu algorithm and thus exhibit lower empirical support (gray). A further 49 arcs (25.9%) fell within the 0.3–0.5 range (black), and 56 arcs (29.6%) within the 0.5–0.85 range (blue), both considered moderately supported. Lastly, 16 arcs (8.5%) showed high bootstrap support (≥0.85, green), indicating robust reproducibility across resampling iterations. Figure 3 presents the full Bayesian network structure, with edge colors reflecting the stability classification described above. To assess the sensitivity of the results to the choice of thresholds, alternative cut-offs were examined (lower bounds of 0.25 and 0.35; upper bounds of 0.80 and 0.90). These adjustments yielded only modest variations in the count of weak arcs (±12–13 cases), whereas the classification of moderately stable arcs remained essentially unchanged. Under the more stringent ≥0.90 criterion, the number of strongly supported arcs declined slightly (from 16 to 9), but these arcs continued to represent the most stable dependencies. Consequently, the principal findings are robust to modest alterations in threshold values.

This distribution reflects a balanced integration of expert-driven priors and data-driven structure learning (66.7%), and the remaining arcs were reviewed and deemed coherent by experts in urban mobility. The high number of arcs below the 0.3 threshold underscores the exploratory nature of the HillClimb algorithm in capturing complex dependencies, especially in data-rich but noisy urban mobility environments.

Also, Table 1 lists the top 60 most stable arcs, those with the highest bootstrap frequencies. These arcs typically represent well-established associations between demographic, behavioral, and spatial variables that define household mobility profiles and vulnerabilities in the urban context under study.

4.2. Louvain Communities in the Bayesian Network of Urban Mobility

Figure 4 presents the results of the Louvain community analysis, revealing 11 resulting communities (colored polygons) that act as intermediate meso-structures between individual arcs and the full Bayesian network. The gray lines correspond to the detected probabilistic relationships (arcs), and the eleven semi-transparent polygons indicate where interactions are densest and how the different social, environmental, and mobility aspects are interlinked within this analysis.

Community 1—see C1 in Figure 5—aggregates thirteen variables that profile the dwelling’s immediate environment and the short-range activities anchored to it: core housing attributes (housingType, housingTenure); the presence, coverage and condition of residential sidewalks (sidewalkHome, sidewalkCovHome, sidewalkConHome); active access to nearby education (walkToEdu); current activity status and personal errands (activityStatus, personalActivities, otherJobs); plus a trio of post-trip choices that reveal whether the respondent heads straight home or combines the journey with additional tasks (goesHomeDirectly, stopsForShopping, postWorkRoutine, postWorkFamTasks). The tight mesh of arcs among these variables reveals that the physical qualities of the home and its surrounding sidewalks are not isolated descriptors; they actively thread into the micro-decisions that structure a resident’s daily timetable—when to step out, whether to detour for errands, and how children reach nearby schools.

Community 2—see C2 in Figure 5—brings together twelve variables that describe who lives in the dwelling and which functional conditions may affect their day-to-day movement: household size (hhSize) and the presence, age and gender of primary-school children (hhMemberSchool, kidsAtHome, hhMSchoolGender); broad demographic descriptors such as age (age) and marital status (maritalStatus); the household’s educational attainment (eduLevel, eduCurrentLevel); and a block of functional-ability indicators that capture disability type (disabilityType) and the reported influence of sensory limitations on daytime and night-time mobility (disabDayMove, disabNightMove). A perception variable on local driving behavior (driverBehavRes) also appears, linking the family profile to the immediate traffic context. Their dense inter-connections in the DAG mean that, at the structural level, basic household composition and members’ functional capacity form a single, tightly knit sub-system.

Acting as a coherent economic cluster, Community 3 (C3 in Figure 5) brings together eleven variables that trace how household resources translate into daily mobility choices and costs. Core capacity markers—household income (hhIncome) and car ownership (hhCars)—anchor the group, while the costs of private motoring are captured by vehicle purchase price (carPurchasePrice), weekly fuel outlay (weeklyFuelCost) and the perceived ease of securing parking in the urban center of David (parkingEase). This community highlights how individuals move around, emphasizing their main transport mode (mainTranspMode) and whether they drive (drives) or walk (walks) as part of their mobility routine. This community is closely linked to the number of transport modes they use in their daily routine, or their multimodality level (multimodalityLevel), and the expenses associated with moving (transpCostDaily). Finally, disaster preparedness (disasterPrep) sits at the margin, covarying with disposable income and asset ownership. This grouping shows that financial capacity, modal choice, and the related costs form a tightly integrated subsystem that governs the affordability, diversification, and resilience of everyday mobility in the BN.

In community 4 (C4 in Figure 5), eight interrelated variables capture the hydrometeorological risks that most affect mobility in David. Flood-related indicators include event frequency (floodFreqRes), maximum water level (maxWaterLevelRes), perceived vulnerability ans disruption to mobility caused by flood (floodVulnRes, mobFloodRes); and concern about future events (floodConcernRes). Landslide risk is described by perceived severity (landslideSevRes), recurrence (landslideFreqRes), and mobility impact (landslideMobRes). Together, these nodes form a compact subsystem where both conditions and perceived threats converge, isolating hazard exposure and how it impacts how people move.

In Figure 6, Community 5 (C5) consists of seventeen variables depicting the physical streetscape and residents’ socio-perceptual lens. Environmental conditions include cleanliness (trashAccumRes, trashBarrierRes), greenery and visibility (treesRes, treesViewBarrRes, tallGrassRes, tallGrassbBarrRes), advertising presence and obstruction (adsRes, adsViewBarrRes), noise levels (noiseLevelRes), local crashes (carCrashesRes), and ongoing construction (roadConstrRes, commConstrRes). Spatial context is given by distance to the city center (distToCenter) and mobile coverage (phoneConnectivity), while behavioral and socio-cultural factors; pedestrian crossing habits (crossingBehavRes), perceived income adequacy (incomePerception), and ethnicity (ethnicity), anchor residents’ perceptions. These densely connected indicators shape a cohesive neighborhood-quality subsystem.

Converging in this sub-network, named community 6 (C6 in Figure 6), are eleven variables linking the traveler’s physical profile with the conditions encountered en route to their place of study. Anthropometric traits (gender, weight, height) define physical aspects, while class timing is set by (studyShift). The sequence of commuting when combining study and work is captured by (workToEduRoute), and the practicality of reaching the site is quantified through (eduAccessEase, eduTravelTime). Micro-environmental factors modulating this trip include the adequacy of nighttime lighting (nightLightRes), its barrier effect (NLBarrierRes), and the perceived presence of road signage and crosswalks (roadSignsRes, crosswalkRes). Their tight structural links define a subsystem where physical attributes, temporal context, and local infrastructure converge to shape perceived safety and accessibility of study commutes.

Occupying an operational niche in the network, community 7 (C7 in Figure 6) brings together twelve variables that jointly depict traffic load and the provision of collective mobility options. Perceived congestion during peak hours is captured at home and work (amCongestHome, pmCongestHome, amCongestWork, pmCongestWork), contextualized by settlement density and work location (densityLevel, workSubdistrict). Public transport experience is detailed through accessibility (PTAccessRes), frequency (PTFreqRes), overall quality (PTQualityRes), expected wait time (busWaitTimeRes), and walking time to the stop (homeTSTime), while the availability of alternatives is represented by (taxiAccessRes). This community reveals a cohesive subsystem where congestion perception, spatial structure, and public transport quality co-regulate residents’ practical mobility options.

In community 8 (C8 in Figure 6), fourteen variables depict how the travel environment and time spent commuting shape residents’ well-being. Physical and mental load is captured through general health (healthGeneral), mobility-related health impact (hlthMobImpact), and four time-exposure effects: on health (mobTimeHealth), stress (mobTimeStress), sleep (mobTimeSleep), and other activities (mobTimeActivities). Insecurity is reflected in harassment on public transport (harassTPexp), perceived taxi danger (taxiInsec), and pedestrian insecurity by day and night (walkDayInsec, walkNightInsec), alongside neighborhood safety (safetyRes) and road condition (roadConRes). Exposure intensity is anchored by weekly travel frequency (mobWeekdays) and transport cost burden (transpCostImpact). This community integrated subsystem where safety, health, and time-related burdens reinforce each other in mobility.

Serving as a mobility-barrier module (C9 in Figure 7), community 9 brings together eleven indicators of unemployment and multiple obstacles that restrict access to work or education. Central to this sub-network is the duration of unemployment (unempDuration), surrounded by perceived barriers such as absent or deteriorated streets (noStreetObsJS, condStreetObsJS), lack of private transport (vehObsJS), fear of crossing (crossFearObsJS), long walks to bus stops (busStopObsJS), and insufficient public transport (ptranspObsJS). A parallel block reflects difficulties near educational sites: congestion (amCongestEdu, pmCongestEdu) and insecurity (eduRouteSafety, eduRouteVuln). These interlinked variables form a coherent subsystem where physical, service-related, and psychological constraints intersect with joblessness, capturing a clear pattern of mobility-based exclusion.

Community 10 (C10 in Figure 7) brings together twelve variables that define the respondent’s employment profile and commuting conditions. Occupational characteristics include job type (jobType), economic sector (jobSector) and mobility pattern (laborMobilityPattern), which frame the context, while departure and return times (workDeparTime, workEndTime) set the exposure window. Spatial demands are captured by home–work travel times (homeToWorkTime, workToHomeTime) and direct distance (distToWork). Mode choice is indicated by walking (walkToWork), and route conditions are described through perceived safety (workRouteSafety), vulnerability (workRouteVuln) and ease of access (workAccessEase). The connectivity among these variables links occupational structure, scheduling, spatial separation and perceived security to shape the commuting experience.

Community 11 (C11 in Figure 7) gathers six tightly connected indicators centered on the household member who attends primary school and the conditions surrounding that daily trip. Travel duration (hhMSTravelTime) and age group (hhMSchoolAge) establish the basic parameters of the journey, while mode of travel (hhMSWalk) distinguishes whether the child walks, is escorted, or uses a vehicle. Perceived exposure to crime (hhMSRouteSafety), general vulnerability (hhMSRouteVuln) and reported ease of access (hhMSAccessEase) describe the safety and effort associated with the route. The density of connections among these variables defines a focused subsystem where time, age, mobility mode, and safety perceptions converge to describe the risks and constraints of school access within the wider Bayesian network.

4.3. Probabilistic Inference and Scenario Analysis for Decision Support

From the constructed Bayesian network, various profiles were analyzed, derived from the relationships found in the network construction itself and in the search for mobility profiles that connected the socio-environmental with aspects of mobility and perception.

Table 2. Posterior probability of perceived intensity of sexual harassment in public transport, by gender and frequency of leaving home.

Gender	Frequency of Leaving Home (mobWeekdays)	Probability of Perceived Intensity of Sexual Harassment in Public Transport (harassTPexp)
		None	Very Low	Low	Moderate	High	Very High
Female	Every weekday	36.9%	14.1%	18.3%	15.9%	10.2%	4.7%
	Some weekdays	38.7%	14.3%	18.4%	15.0%	9.6%	4.0%
	Does not leave home regularly	91.8%	1.1%	1.3%	4.3%	0.9%	0.7%
Male	Every weekday	53.1%	15.8%	19.9%	6.3%	1.5%	3.4%
	Some weekdays	55.0%	15.3%	20.2%	5.7%	1.3%	2.6%
	Does not leave home regularly	93.5%	1.7%	1.7%	1.2%	0.9%	1.1%

shows a Bayesian inference analysis that sought the probability of perceiving the intensity of sexual harassment in public transport based on evidence of sex and frequency of leaving home during the week. It is identified that the probability of perceiving harassment is closely related to leaving home, an expected condition, and the highest perception of harassment is found with evidence of greater frequency of leaving home. A marked difference in perception can be seen between men and women; women in the three states of frequency of leaving home are more likely to perceive some harassment in public transport. Figure 8 shows that a woman whose mobility involves leaving home every day has a probability of feeling harassment, regardless of the degree, of around 63%, while a man under the same conditions has a probability of perceiving harassment of 47%.

If we talk about trips made for work, in

Table 3. Posterior probability of perceived vulnerability on the commute to work, by commute duration.

Commute Duration to Work (homeToWorkTime)	Probability of Perceived Vulnerability (workRouteVuln)
	None	Very Low	Low	Moderate	High	Very High
Short (≤15 min)	21.8%	11.3%	32.7%	20.7%	9.2%	4.3%
Moderate (16–30 min)	13.8%	11.5%	31.2%	28.0%	11.7%	3.8%
Long (31–60 min)	14.0%	11.1%	27.2%	31.1%	12.7%	3.8%
Very long (>1 h)	12.6%	12.9%	24.0%	29.6%	12.9%	4.8%

we observe the association between commute duration and perceived vulnerability. While 21.8% of responders with commutes of 15 min or less report no vulnerability, this proportion drops to 12.6% for those commuting more than an hour. Conversely, the probability of reporting “Moderate” or higher vulnerability rises from 34.2% (short commute) to 47.8% (long commute) or 47.3% (very long commute). This pattern suggests that interventions aiming to reduce commute times may contribute significantly to perceived safety in daily mobility.

Figure 9 shows the perceived impact of daily commute time on stress. It is observed that stress is likely to be greatest when perceived as “Little,” “Moderate,” or “High” in all the urban profiles analyzed. The highest values for these categories are observed in middle-aged adults who work and drive, as well as in young adults with highly multimodal mobility patterns, suggesting that more demanding or complex routines are associated with a greater stress burden.

In contrast, profiles of older women and those responsible for family care tend to report lower probabilities of experiencing “High” or “Very High” stress. Furthermore, the profile of men who walk alone to school stands out for their high probability of falling into the “Don’t Know” category, which could reflect lower awareness or a different way of perceiving and reporting the impact of stress. These results show that stress related to daily commute is a widespread phenomenon, although its intensity and frequency vary across urban profiles, but maintains a similar trend.

By identifying the posterior probability of perceived health impact caused by the time a person spends commuting daily (see Figure 10), we can observe some behaviors according to the main type of transportation used and the distance at which they live from the urban center. Active modes of transportation, when combined with residences located close or very close to the city center, are those that, a posteriori, show the highest percentage of individuals reporting no negative impacts from their mobility. Increased public transportation trips show very similar behaviors regardless of the person’s distance from the center, telling us that the possibility of feeling impacted on their mobility is more linked in this case with the medium than with the distance. Finally, people who travel by private vehicle over long distances have the highest joint probability of feeling some type of impact due to their mobility.

5. Discussion

The Bayesian network constructed within this study was obtained through a hybrid procedure of structural learning and expert knowledge. It offers a probabilistic portrait consistent with the theoretical patterns described in the literature on urban mobility and socio-environmental aspects identified in the study area.

Firstly, among the dependencies identified that are supported by previous studies, we can identify the association between income and private vehicle ownership [28,29,31]; the connection between household size and the presence of school-age children, reflected in analyses of household logistics and family motorization [26]; and the influence of activity status (employment/study/unemployment) on the duration and mode of travel, as described by [21,35]. Similarly, the nodes that describe hydrometeorological risk maintain a direct relationship with the mobility barriers identified by previous studies in Latin American contexts exposed to disasters [16,17]. These consistencies not only reinforce the external validity of the model, but also underline its capacity to integrate, within a single probabilistic framework, social, environmental, and mobility dimensions that have usually been analyzed separately. This starting point opens the discussion towards emerging findings, the identification of interdependent subsystems, and the explanatory potential of the network.

The topology of the learned network shows some concentrated nodes that help explain how decisions and perceptions are articulated. The “age” node stands out, behaving as a relatively stable structural factor across resamplings, and also the “eduTravelTime” node, an axis of accessibility/service associated with education-related travel. Downstream of this latter node we can find the perception of mobility barriers due to lack of lighting associated with the duration of education-related trips, an association that was highlighted in another study conducted in Panama, where profiles associated with education-related mobility identified lighting as a highly important factor in their perception of mobility [76].

Taken together, the patterns revealed in the network show that a large part of the structural factors, for example demographic composition, constitute the backbone of the network, while qualitative factors, such as service quality, micro-level safety of the environment, and environmental conditions, modulate its day-to-day functioning, as also shown in other studies at the level of public transport [77]. The classification by bootstrap stability also allows the weighting of the confidence of the final network. Very stable edges (green arcs) inform firm conclusions; intermediate edges orient plausible hypotheses (blue and black arcs); weak edges (gray dotted arcs) are read as exploratory signals. The exclusion of marginal variables (presence of animals) indicates that the learning avoided incorporating low-impact dependencies in this context.

Turning to the second main analysis, the identification of eleven Louvain communities reflects the existence of coherent subsystems within the large and complex urban system: the immediate area of residence and family composition (C1–C2) are linked to daily routines; household income translates into modal choice and daily costs (C3); hydrometeorological risks are isolated as recurring barriers (C4); environmental quality, pedestrian infrastructure, congestion, and perceptions of health and stress interact with each other (C5–C8); and the pockets of unemployment, school insecurity, and work-related conditions converge as centers of exclusion (C9–C11). This modularity, where aspects of mobility are present in all communities, reinforces the hypothesis of bidirectional mobility, simultaneously a cause and effect of the socio-environmental structure.

Finally, the inferences drawn from the model reflect some pockets of urban exclusion: (i) gender, where women who use public transport daily have a 63% probability of experiencing harassment, which is 15% more than men under the same conditions. These results support the findings of an unequal distribution of risks and opportunities, pointed out by [11,13]; (ii) the length of the work commute, where the longer the commute, the greater the likelihood of perceived vulnerability; and (iii) the interaction between age and multimodality, which places adults aged 40–54 who drive daily as the group most likely to experience “High/Very High” stress. These posteriori distributions not only describe inequalities but also directly identify the lever variables: objective safety at bus stops and on public transport, incentives for self-containment capacity trips [29], and promotion of short-distance active mobility, such as 15 min cities [78,79].

In this context, analyzing community outcomes in conjunction with the inferences drawn, the combination of infrastructure measures (improving peripheral connectivity, lighting, drainage to minimize risks) with fare incentives for public transport could generate benefits in several modules simultaneously (C4, C7, C8). Furthermore, the findings suggest that more effective interventions could be targeted by profile. For example, safe school routes for C11 or job training and accessibility programs for C9, which would respond to “groups with certain vulnerabilities.” The concentration of risks and disadvantages in certain profiles highlights the urgency of comprehensive strategies that combine natural hazard mitigation, public transportation improvements, and gender equity policies. Moving toward a sustainable mobility model involves recognizing the multiplicity of factors: social, environmental, and infrastructure, that shape access and the quality of daily travel for the population.

This study explores Bayesian networks and their potential to represent nonlinear dependencies associated with the complex and broad mobility system and offer a visual syntax that is easily interpretable by non-technical actors. The use of structural bootstrapping, cross-validation, and expert review provides traceability, aligning with the recommendations of [71]. The resulting DAG functions as both an analytical and communication tool for urban management, visually understandable to all stakeholders, and provides unprecedented evidence for Panama in a little-studied context.

6. Conclusions

Urban mobility constitutes a complex socio-environmental system in which individual activities, domestic structures, the built environment, and natural hazards interact reciprocally. The Bayesian network demonstrates that these dimensions are articulated in subsystems connected by probabilistic relationships. Ref. [80] argues that effectively addressing urban efficiency and environmental concerns requires a comprehensive mobility-oriented urban typologization based on recent and relevant data, a dimension that can be addressed with Bayesian network models.

However, in many Latin American countries, the capacity to translate this type of knowledge into public action is limited by institutional fragmentation and the disconnect between databases, indicators, and visualization platforms, as noted by [81]. This gap favors the persistence of structural inequalities, given that travel patterns reproduce individual decisions conditioned by social and environmental factors [82]. To advance toward more efficient, equitable, and contextualized mobility policies, it is necessary to integrate complex and comprehensive models, such as those enabled by Bayesian networks [71], into cross-sector data infrastructures.

7. Limitations and Recommendations

It is important to highlight that the information collected and cross-checked in this research, for most of the variables, comes from household surveys, as previously detailed in the survey instrument section. Surveys are a valuable tool, albeit one that may involve some degree of subjectivity and potential bias. In this research, the survey was designed by experts in urban mobility, and validated by national and international reviewers, in order to minimize interpretative bias as much as possible. The survey took as reference part of the questions previously applied in the PIMUS, while also being complemented with new questions specific to this study. Even though, the use of bootstrap aggregation and expert validation further ensured that the resulting structure reflects stable relationships, minimizing the impact of atypical cases. Nevertheless, the results should be interpreted as stated perceptions and not as direct objective measurements.

Among the limitations identified in this study, although the network was built with a thorough hybrid learning and cross-validation process, internal variance remains a point of concern. The F1 score of close to 0.5 obtained indicates the presence of noise, typical of a model that integrates a high number of variables with few observations. Although k-fold cross-validation offered a reasonable overview of urban behavior and the network reflected patterns documented in the literature, to generate causal analyses or results generalizable to other case studies, greater network stability is recommended; this would require significantly expanding the sample size or, alternatively, compacting the list of variables to reduce the combinatorial burden. Furthermore, the mobility profiles analyzed were limited to representative cases in Panama, intended to demonstrate the network’s communicative potential; therefore, several specific profiles and relationships that could provide additional nuances were left out of scope.

For future work, it is recommended to compare different structural learning algorithms for large-scale urban networks to identify configurations with greater stability and less noise. Another possible line of continuation of this research would be to apply the methodology to specific subsystems (e.g., focusing on each of the axes suggested by the Louvain communities within this study). This seeks to gain deeper insights into specific causal relationships between socio-environmental variables and mobility patterns within cities.