Impact of Areal Factors on Students’ Travel Mode Choices: A Bayesian Spatial Analysis

Abstract

A preliminary analysis of the 2018/2019 Austin Travel Survey indicated that most off-campus students in Travis County, TX, tend to use cars rather than more sustainable transportation modes, significantly contributing to traffic congestion and environmental impact. This study aims to analyze the impacts of areal factors, including environmental and transportation factors, on students’ choices of travel mode in order to promote more sustainable transport behaviors. Additionally, we investigate the presence of spatial correlation and unobserved heterogeneity in travel data and their effects on students’ travel mode choices. We have proposed two Bayesian models—a basic model and a spatial model—with structured and unstructured random-effect terms to perform the analysis. The results indicate that the inclusion of spatial random effects considerably improves model performance, suggesting that students’ choices of mode are likely influenced by areal factors often ‘unobserved’ in many individual travel mode choice surveys. Furthermore, we found that the average slope, sidewalk density, and bus-stop density significantly affect students’ travel mode choices. These findings provide insights into promoting sustainable transport systems by addressing environmental and infrastructural factors in an effort to reduce car dependency among students, thereby supporting sustainable urban development.

1. Introduction

Promoting sustainable transport systems is crucial for addressing environmental challenges and supporting economic growth and community needs. These systems align with several United Nations Sustainable Development Goals, including those relating to good health and well-being, sustainable cities and communities, responsible consumption and production, and climate action. The literature (Owais and Osman 2018; Owais et al. 2021, 2015, 2013) has emphasized enhancing public transport as a key strategy for achieving sustainable mobility. However, understanding travel behavior is crucial for effectively designing and implementing transportation solutions that truly meet the needs of different populations and maximize the impacts of sustainable-mobility initiatives. This study analyzes the impacts of areal factors on students’ choice of mode to promote more sustainable transport behaviors.

Over the past decade, Travis County, Texas, and more specifically the city of Austin, has experienced significant economic and population growth. This rapid growth resulted in congested roadways coupled with the impacts of roadway construction and reduced safety and mobility throughout the county (CAMPO 2019). According to the Capital Area Metropolitan Planning Organization, the number of vehicle-miles travelled has increased by 10 million since 2010, which is a significant contributor to traffic congestion (CAMPO 2019). Furthermore, recent data from the Austin Strategic Mobility Plan indicate that, in 2018, the most common method of travel in Austin, TX was driving alone (75.40%), followed by walking (2.39%), traveling by public transport (4.01%), and other modes (18.20%) (ACC n.d.). Due to the high number of colleges and universities in Travis County, a significant portion of the total number of trips are generated by schools and students. In response to this congestion problem, the transit authorities attempted to empower students by increasing access to transit options through subsidized and reduced transit fares and shared mobility costs. However, such incentives have not been effective, in view of the continued excessive use of cars. This ongoing issue suggests that there may be underlying, “unobserved factors” influencing students’ travel behaviors.

Unobserved factors, which are not directly measured or included in the survey data, can significantly influence an individual’s choice of transport mode. Traditional approaches to travel-behavior analysis, such as generalized linear models (GLMs) and multinomial logit (MNL) models, often overlook unobserved factors. These methodologies, while useful, tend to fall short of capturing the full complexity and impacts of variables that are not directly measured, limiting their ability to fully understand the nuances of travel behavior. Furthermore, previous studies have largely focused on examining the relationship between students’ choices of mode and individual-level factors, rather than exploring areal-level influences. Our research seeks to address this gap by investigating three key questions: (1) What are the effects of areal-level transportation factors on the travel mode choices of students? (2) How do unobserved (missing) factors contribute to such choices across different regions? (3) Are these unobserved factors spatially correlated?

To explore these questions, we employ an MNL model within a Bayesian framework, which allows us to account for unobserved factors at a spatial level. This approach considers both within-zone effects that impact individuals and the potential influence of unobserved factors from neighboring zones. By integrating spatial random effects into our model, we aim to better understand and quantify the impact of these unobserved factors, leading to more accurate and nuanced insights into travel behavior. This approach provides a more comprehensive understanding of the spatial dynamics affecting students’ travel mode choices.

Our research makes several significant contributions, both academically and practically, to the understanding and implementation of sustainable transport systems. Academically, we offer insights into how transport-related and environmental factors shape students’ travel mode choices, providing a deeper understanding that can inform the design of more sustainable infrastructure. Methodologically, we advance the field by employing a Bayesian approach at the zip-code level, which allows us to capture unobserved factors. Practically, our findings equip policymakers with valuable information about the spatial distribution of travel behaviors, helping them to design more effective and sustainable transport policies.

2. Literature Review

Previous research has examined various aspects of university students’ travel behaviors, including safety perceptions and educational benefits (Babin and Kim 2001; Lu et al. 2016), daily activities (Daisy et al. 2018; Eom et al. 2009; Lee 2020; Soltani et al. 2019; Tuveri et al. 2020), tourism (Bicikova 2014; Heung and Leong 2006; Huang and Tian 2013; Shields 2011; Shoham et al. 2005; Varasteh et al. 2015; Xu et al. 2016), and behaviors relating to choice of travel mode (Cattaneo et al. 2018; Danaf et al. 2014; Henning et al. 2020; Khattak et al. 2011; Klöckner and Friedrichsmeier 2011; Mitra and Nash 2019; Tezcan 2016; Whalen et al. 2013; Zhou et al. 2018). Several factors contribute to the increasing focus on student travel behaviors over the past decade. First, these behaviors are not well understood and are often underrepresented in travel surveys, primarily due to students’ housing instability during the academic year (Khattak et al. 2011). Second, student travel mode preferences differ in key ways from those of the general population (Whalen et al. 2013). Third, and perhaps most importantly, the spatial distribution of student choices of mode varies significantly across regions Delmelle and Delmelle (2012). This highlights the need for transportation infrastructure planning that takes into account students’ distinct preferences of travel mode across different geographic areas.

However, most studies in this domain have focused on the relationship between students’ travel mode choices and individual-level factors rather than areal factors. Areal factors—such as topography, accessibility, and public transport infrastructure (Simma and Axhausen 2003)—vary considerably between regions and can significantly influence students’ travel behaviors. For instance, Tezcan (2016) examined the potential for passenger carpooling among undergraduate students, finding that females and frequent campus commuters were more inclined to carpool. Mitra and Nash (2019) explored gender differences in cycling uptake, noting higher cycling rates among men for both commuting and non-commuting trips. Henning et al. (2020) analyzed the socio-demographic factors influencing active transportation modes on campus, reporting that choices of mode were shaped by travel time, income, and marital status. Zhou et al. (2018) highlighted that college town students are more likely to walk than their urban university counterparts, and that students seeking affordable housing tend to live near bus stops, making them more likely to use buses.

Additional studies have examined the correlation between specific factors and travel behaviors. Zhan et al. (2016) found that travel distance, bicycle ownership, school location, and gender were significant determinants of travel mode choice. Haggar et al. (2019) explored how moving residences between university terms affects students’ travel mode choices, showing that movers are more likely to change their mode of transportation compared to non-movers. Other studies have noted that perceptions of gas prices, safety, and rush hour traffic also play a key role in shaping travel behavior. For example, Lidbe et al. (2020) found that higher gas prices indirectly increase walking, biking, and car usage, while Kochan et al. (2008) observed a reduction in vehicle trips due to rising fuel costs. Safety perceptions have also been shown to vary across transportation modes and demographic groups (Guo et al. 2020; Rahman et al. 2021), with a preference for private cars during peak hours and nighttime travel over public transportation (Liu et al. 2015).

Despite this body of research, few studies have incorporated spatial dimensions and areal factors into their analyses of student travel behavior. For example, Whalen et al. (2013) investigated the impact of street and sidewalk density on students’ choices of mode, and Delmelle and Delmelle (2012) examined the influence of spatial, temporal, and gender differences on transportation mode selection.

This gap in the literature highlights the need for more comprehensive spatial analysis that includes both observed and unobserved variables to better predict and understand student travel behavior. Our study addresses this gap by employing a Bayesian multinomial logit (MNL) model that integrates spatial factors, both observed and unobserved, to capture the nuanced effects of local conditions on travel behavior. While Bayesian methods and spatial analysis have been utilized in transportation research, our study stands out by focusing on latent spatial factors specific to different zones, offering a more detailed exploration of spatial effects that previous studies have largely overlooked.

3. Methodology

In this study, we applied a Bayesian logit model to analyze the factors influencing students’ choices of mode in Travis County, TX. Given that our data are hierarchical, with individual respondents clustered within geographic regions like zip codes, it was essential to account for both individual-level and spatial-level influences on travel behavior. Preliminary analyses indicated the presence of spatial autocorrelation, suggesting that students’ choices of mode are not only affected by personal and environmental factors but also by characteristics that extend across neighboring regions.

Recognizing the importance of spatial dependencies in the data, we employed a Bayesian spatial logit model that incorporates structured and unstructured spatial random effects. This model was selected to better capture the unobserved heterogeneity across space and address the limitations of simpler models. The decision to utilize a Bayesian approach was driven by several key considerations, which were as follows:

Hierarchical Data Structure: Our travel data are nested, with respondents grouped by geographic zones such as zip codes. This nesting implies that travel choices are not only influenced by individual characteristics but also by shared regional factors that may not be fully observed. A traditional logit model would fail to capture these shared influences. By incorporating spatial random effects, the Bayesian model accommodates the hierarchical nature of the data and accounts for the correlation between neighboring regions.

Spatial Correlation in Behavior: Exploratory analysis revealed spatial autocorrelation in the travel data, indicating that travel behavior in one region can influence or be influenced by that in nearby areas. Factors such as shared infrastructure or similar environmental conditions could create dependencies across regions, which a non-spatial model might overlook. The Bayesian spatial model addresses these dependencies, ensuring that spatial correlation is appropriately modeled.

Unobserved Spatial Heterogeneity: Many factors influencing travel mode choice, such as neighborhood walkability or local environmental quality, are not directly measured in our data. By incorporating spatial random effects, the Bayesian model adjusts for this unobserved spatial heterogeneity, resulting in more accurate estimates of the effects of observed explanatory variables. This adjustment helps ensure that the influence of factors like sidewalk density and bus-stop proximity is more reliably estimated.

Before delving into the specifics of our model in Section 3.4, we provide a brief review of the methodologies employed in its development, as outlined below.

3.1. Multinomial Logit Model

The multinomial logit (MNL) model is a statistical approach widely used for modeling the probability of a particular outcome when the dependent variable is categorical, with more than two mutually exclusive and exhaustive categories. This model is an extension of the binary logit model and is particularly useful in situations where individuals or decision-makers are faced with a choice among several discrete alternatives. The MNL model has been applied extensively in fields such as economics, transportation, marketing, and social sciences.

In the MNL model, the dependent variable represents the choice made by an individual or decision-maker from a set of alternatives. For example, in a transportation context, the dependent variable might represent the choice of transportation mode, such as driving, taking public transit, cycling, or walking.

The independent variables, or predictors, are the factors believed to influence the choice among the available alternatives. These can include both quantitative and qualitative attributes such as income, age, distance, cost, and specific characteristics of each alternative.

The utility $\left(U_{ik}\right)$ for individual $\left(i\right)$ choosing alternative $\left(k\right)$ is modeled as:

$$U_{ik}={\beta }_k\cdot X_i+{ϵ}_{ik}$$

(1)

where $\left(X_i\right)$ is a vector of explanatory variables for individual $\left(i\right),\left({\beta }_k\right)$ is a vector of coefficients specific to alternative $\left(k\right)$, and $\left({ϵ}_{ik}\right)$ is a random-error term that accounts for unobserved factors influencing the choice.

The probability that individual $\left(i\right)$ chooses alternative $\left(k\right)$ from a set of $\left(K\right)$ alternatives is given by the following logistic function:

$$P\left(Y_i=k\right)={\displaystyle \frac{\mathit{exp}\left({\beta }_k\cdot X_i\right)}{{\sum }_{l=1}^K\mathit{exp}\left({\beta }_l\cdot X_i\right)}}$$

(2)

This formulation ensures that the probabilities across all possible choices sum to 1, thus providing a valid probability distribution.

3.2. Bayesian MNL

In the Bayesian MNL model, the estimation of the parameters $\left({\beta }_k\right)$ is carried out within a Bayesian framework. Instead of relying solely on the data, Bayesian methods incorporate prior distributions over the parameters. The posterior distribution is then derived by combining these ‘priors’ with the likelihood of the observed data.

Mathematically, the posterior distribution of the parameters $\left({\beta }_k\right)$ given the data $\left(D\right)$ is expressed in the following form:

$$p\left(\beta |D\right)\propto p\left(D|\beta \right)p\left(\beta \right)$$

(3)

where:

-

$\left(p\left(\beta |D\right)\right)$ is the posterior distribution of the parameters.

-

$\left(p\left(D|\beta \right)\right)$ is the likelihood function of the data given the parameters.

-

$\left(p\left(\beta \right)\right)$ is the prior distribution of the parameters.

In Bayesian MNL models, it is common to assign normal priors to the coefficients $\left({\beta }_k\right)$. For instance, a normal prior might be specified as in the following:

$${\beta }_k\sim N\left({\mu }_{\beta },{\sigma }_{\beta }^2\right)$$

(4)

where $\left({\mu }_{\beta }\right)$ and $\left({\sigma }_{\beta }^2\right)$ are the mean and variance of the prior distribution, respectively. The choice of priors can significantly influence the model, especially in cases with limited data.

The posterior distribution is typically not available in closed form for Bayesian MNL models, so computational methods such as Markov-Chain Monte Carlo (MCMC) are used to approximate it. This allows for the estimation of the posterior mean and variance and credible intervals for the parameters, providing a more comprehensive understanding of the uncertainty associated with the estimates.

The Bayesian approach to MNL models offers several advantages, including the ability to incorporate prior knowledge, improved handling of small sample sizes, and the capacity to model complex hierarchical structures. It is particularly useful in cases where there is prior information about the parameters or when the data are sparse.

3.3. Conditional Autoregressive Model

The conditional autoregressive (CAR) model aims to handle spatial dependencies and account for correlations in spatial data. It is particularly useful in cases where observations are spatially structured, such as in geographical or environmental data. The CAR model provides a framework for modeling spatial correlations by specifying how the value of a variable at a given location (e.g., a zip code) is related to values at neighboring locations. The Bayesian logit model can benefit from the integration of the CAR model to account for spatial effects and dependencies. The basic idea is that the value of a variable at a specific location is influenced by the values of that variable at adjacent locations. The CAR model can be formally expressed in the following equation:

$${\varphi }_j| \{{\varphi }_l, j\ne l\} \sim N({\mu }_j,{\displaystyle \frac{{\sigma }_{\varphi }^2}{{\sum }_l{w}_{jl}}})$$

(5)

where:

-

$({\varphi }_j)$ represents the structured spatial random effect at location $\left(j\right)$;

-

$({\mu }_j)$ is the mean of the distribution, typically based on the values at neighboring locations;

-

$\left({\sigma }_{\varphi }^2\right)$ is the variance of the variable;

-

$\left(w_{jl}\right)$ is a weight that indicates whether location $\left(j\right)$ is adjacent to location $\left(l\right)$ (often binary, with 1 if adjacent and 0 otherwise).

The term $({\displaystyle \frac{{\sigma }_{\varphi }^2}{{\sum }_l{w}_{jl}}})$ denotes the conditional variance of $({\varphi }_j)$, which depends on the variance of the variable and the sum of weights associated with neighboring locations. This structure allows the CAR model to account for spatial autocorrelation by incorporating the influence of adjacent observations.

3.4. Adapted Model

In this paper, to define the principles of the multilevel MNL model in a Bayesian setting, we consider the following mode choices: car (k = 1), walking (k = 2), bus/shuttle bus (k = 3), and other modes (k = 4). By introducing new spatial random-effect terms, the utility functions corresponding to the Bayesian multinomial logit model can be expressed as follows (Zhang et al. 2021), with the bus mode (k = 3) treated as the base outcome:

$$U_{ij1}={\beta }_1{X}_{ij}+{\theta }_{j1}+{\phi }_{j1}$$

(6)

$$U_{ij2}={\beta }_2{X}_{ij}+{\theta }_{j2}+{\phi }_{j2}$$

(7)

$$U_{ij3}=0$$

(8)

$$U_{ij4}={\beta }_4{X}_{ij}+{\theta }_{j4}+{\phi }_{j4}$$

(9)

where $U_{ijk}$ refers to the utility function for student $i$ in zip code $j$ and mode $k=1,2,3,4$, $X_{ij}$ represents the deterministic part of the model; ${\beta }_k$ signifies the vector of coefficients corresponding to mode k; and ${\theta }_{jk}$ and ${\phi }_{jk}$ denote the uncorrelated and correlated heterogeneity, respectively. The variable $\beta$ is assumed to have a normal prior $N(0,10000)$. The probability that student $i$ in zip code $j$ chooses mode $k$ is represented by $p_{ijk}$ and is determined by the following expression:

$$p_{ijk}={\displaystyle \frac{\mathit{exp}(U_{ijk})}{{\sum }_{k=1}^4\mathit{exp}(U_{ijk})}}$$

(10)

The structured term has been modeled using the conditional autoregressive (CAR) model (Besag 1974) to address spatial dependencies and account for the correlation of heterogeneity terms across adjacent zip codes, as defined by the following expression:

$$\left[{\phi }_{jk}|{\phi }_{lk},j\ne l\right]~N\left({\mu }_{jk} ,{\displaystyle \frac{{\sigma }_{\phi k}^2}{{\sum }_j{w}_{jl}}}\right)$$

(11)

where

$$\begin{gathered} {\mu }_{jk}={\displaystyle \frac{{\sum }_l{\phi }_{lk}{w}_{jl}}{{\sum }_l{w}_{jl}}} \\ {w}_{jl}=1 \mathrm{if} \mathrm{zones} j \mathrm{and} l \mathrm{are} \mathrm{adjacent} \\ {w}_{jl}=0 \mathrm{otherwise} \end{gathered}$$

(12)

The variability of $\phi$ is controlled by parameter $\left(1/{\sigma }_{{\phi }_k}^2\right)$ which follows a gamma prior distribution, $Ga(0.5,0.0005)$ (Wakefield et al. 2000). Moreover, a normal prior $N(0, {\sigma }_{{\theta }_k}^2)$ is assumed for ${\theta }_k$, where $\left(1/{\sigma }_{{\theta }_k}^2\right)$ represents the precision parameter which follows a gamma prior, $Ga(0.5,0.0005)$. To assess the models’ complexity and compare different Bayesian models, we used the deviance information criterion (DIC). The DIC value is computed from the posterior distribution of the deviance, a determination which reflects the model’s fit to the observed data after updating the initial beliefs represented by the prior distribution. Lower DIC values signify a better trade-off between model fit and complexity, indicating a more suitable model for explaining the observed data. The model has been coded in WINBUGS. For more information, refer to (Goldstein n.d.).

4. Data

4.1. Study Area

The study area covers Travis County, located in Central Texas. Based on the 2020 U.S. Census, the total population of the study area is 1.3 million. The city of Austin is the study area’s population center, with approximately 1 million residents based on the latest U.S. Census population estimates.

The geographical unit of analysis is the zip code. There are a total of 56 zip-code areas within the study area, with an average population of 26,180. Within a zip code, the population shares fairly homogenous socio-economic characteristics. The data concerning the zip codes were collected from the from the Topologically Integrated Geographic Encoding and Referencing (TIGER) digital database. TIGER was developed by the U.S. Census Bureau to support its mapping needs for the decennial census and other Bureau programs. Every one to three years, the Census Bureau creates an extract from this database and releases a TIGER update. These extracts are known as TIGER/Line files. Figure 1 represents the map of the study area and its existing transportation network.

4.2. Austin Workplace Survey

This study utilized a 2018–19 workplace survey conducted in Austin to gather travel information regarding university students’ travel mode choices in Travis County, Texas, which is home to many of the universities and colleges in the state. The survey was conducted by the Transportation Planning and Programming Division of the Texas Department of Transportation in two phases (TXDOT n.d.). The first phase consisted of a telephone survey of randomly selected establishments, including local businesses and universities, to ascertain their location in the study area in terms of area type and the type of establishment—free or non-free standing. The second phase of the workplace survey involved data collection efforts (an employee survey, a student survey, and a visitor survey) at randomly selected establishments. In total, data were collected from a sample of 1490 off-campus students, including information on their annual household income, travel mode, trip origin and destination zip codes, origin-point geographical location, and other characteristics. Each zip code included in the study had at least 19 observations. Personal information, such as age and gender, was not included in the survey. Compared to other university-based surveys, the Austin workplace survey has the advantage of sampling students from different universities within the study area. As a result, it provides better insight into student travel patterns.

4.3. The Model’s Variables

The variables used in this study were obtained from various sources; however, due to the lack of data, some potential independent variables (Azimian and Jiao 2023; Azimian et al. 2021; Cheng et al. 2020; Mannering et al. 2016; Wu et al. 2020) are not included in the analysis and may therefore operate as unobserved determinants at the spatial level.

The dependent variable of interest is the travel mode choice of students for their trips to school. The four choices considered are car, bus, walking, and other modes. Given these considerations, the independent variables used for the analysis are annual household income, distance from origin (residential address) to the nearest bus stop, topographic slope, sidewalk density, 2019 annual average daily traffic (AADT), and average distance to schools. The bus stops were obtained from the State of Texas Open Data Portal (CapMetro n.d.), and the distance from each student’s origin point to the nearest bus stop was calculated using the proximity tool in ArcGIS Pro. To estimate the topographical slope, we utilized the digital elevation model from the U.S. Geological Survey (USGS n.d.). Surface analysis and a slope tool were used to create the slope raster for the entire area. Next, we made use of zonal statistics to calculate the average slope for each zip code. The sidewalk and road data were obtained from the City of Austin Open Data Portal (COA n.d.), and we estimated the sidewalk/road density by dividing the total sidewalk/road length by the zip-code area. The AADT was collected from the Texas Department of Transportation and used as a proxy for traffic congestion. We interpolated its values across the study area, and, finally, the average AADT was estimated for each zip code using a zonal statistics tool. The summary statistics and distribution of the variables used in the analysis are shown in

Table 1. Summary statistics of the variables used in the data analysis (sample size: 1490).

Independent Variable	Mean	Std. Dev.	Min	Max
Annual household income
Income < $25K	0.383	0.486	0	1
Income $25K to $65K	0.258	0.438	0	1
Income ≥ $65K	0.197	0.398	0	1
Not reported (reference)
Distance to the nearest bus stop (mile)	0.768	2.100	0	27.7
Average slope (%)	4.995	2.626	1.9	17.1
Average AADT (in thousands)	110.440	42.306	7.6	157.2
Sidewalk density (total length (mile)/zip code area (sq. mile)	15.054	6.932	0	22.8
Bus stop density (per 100 sq. mile)	834.924	590.123	0	1550.1
Road density (total length (mile)/zip code area (sq. mile)	11.142	4.988	1	38.8
Average distance to schools (mile)	4.837	5.547	0.05	28

and

Table 2. Distribution of transportation modes.

Transport Mode (Dependent Variable)	Percent
Car	58%
Bus/Shuttle	18%
Walking	17%
Other modes	7%

, respectively. Also, Figure 2 presents spatial distribution of zip-code-level variables.

5. Results

Two full Bayesian logit models are discussed in this section: a basic or non-random-effect model and a full or spatial model that includes all random-effect terms to account for the unobserved effects at the spatial level. The models were computed with the Markov-Chain Monte Carlo (MCMC) technique using the WINBUGS software (version 1.4.3). A 90% and 95% Bayesian credible interval was used to assess the significance of the covariates, and the DIC was used as a model diagnostic. To ensure the convergence of all parameters, the first 20,000 iterations were considered burn-ins and thus discarded, and the next 30,000 were used to establish the model. The MCMC chain and history plots were chosen to monitor the convergence of the parameters.

Table 3. DIC Values for the basic and spatial models.

Model	DIC
Basic model (without spatial random-effect terms)	2420
Spatial model (with spatial random-effect terms)	2362

shows the DIC values for both proposed models. The spatial model had a lower DIC than the basic model. Additionally, the difference DIC is greater than 10, which implies that including the spatial terms explained the unobserved factors affecting the students’ choices of mode and significantly contributed to the model’s accuracy (Tremblay et al. 2009). The model’s estimation results are summarized in

Table 4. Parameter estimates for the basic model (Base outcome = Bus).

Variable	Car Mean	Walking Mean	Other Modes Mean
Intercept	2.121	−7.791	−5.264
Annual household income
Income < $25K	−0.067	−0.375	0.204
Income $25K to $65K	0.423 *	−0.453	0.425
Income ≥ $65K	0.530 *	0.342	0.621
Distance to the nearest bus stop	0.153 *	0.085	−0.297
Average slope	−0.047	0.604 **	0.194 **
Average AADT (in thousands)	−0.018 **	0.013 *	−0.005
Sidewalk density	0.110 **	−0.033	0.076 **
Bus-stop density (per 100 sq. mile)	−0.001 **	0.006 **	0.002 **
Road density	0.003	−0.026	0.016
Average distance to schools	0.024	−0.569 **	0.021

Notes: * indicates significant at 90%, and ** indicates significant at 95%.

and

Table 5. Parameter estimates for the spatial model (Base outcome = Bus).

Variable	Car Mean	Walking Mean	Other Modes Mean
Intercept	3.727	−1.020	−2.294
Annual household income
Income < $25K	−0.021	−0.347	0.243
Income $25K to $65K	0.408	−0.448	0.450
Income ≥ $65K	0.540 *	0.366	0.649
Distance to the nearest bus stop	0.100	−0.362	−0.499
Average slope	−0.079 *	−0.574 *	0.084
Average AADT (in thousands)	−0.021 **	0.011 **	0.004
Sidewalk density	0.098	0.092 **	−0.132
Bus-stop density	−0.002 **	0.000	0.001 **
Road density	−0.001	−0.120	0.060
Average distance to schools	−0.021	−1.00 **	−0.065
σθ	0.842	2.645	0.811
σφ	0.140	0.138	0.188
Fraction: σθ/(σθ + σφ)	86%	95%	81%

Notes: * indicates significant at 90%, and ** indicates significant at 95%.

.

Despite the fact that the spatial model includes a small number of significant variables, they are useful for planning and practice purposes. Moreover, the insights the inclusion of spatial random effects provides are valuable: their existence highlights the need to further identify meaningful factors that can be used for planning and policy purposes. To determine such potential factors, one can turn to the findings of previous studies in the literature and explore the factors that can, in principle, have a spatial component. For example, the index and number of housing opportunities are likely to contribute to the choice of mode. However, these factors are not routinely collected in Texas. For planning and policy purposes, the findings of this case study suggest a significant spatial random effect; for this reason, we recommend that data on related factors should be collected and their effects on travel behaviors in Austin, TX should be explored.

5.1. Interpretation of Parameter Estimates

As discussed earlier, previous studies have explored few covariates at the spatial or macro level. For example, the work of Whalen et al. (2013)- investigated only street and sidewalk density, which were found to affect students’ choice of mode. To address this gap, this work examines additional macro-level factors, such as topography slope, average AADT, bus-stop density, and average distance to schools, which may contribute to students’ mode choice. To the best of our knowledge, the effects of these factors have not been evaluated before. As shown in Table 4 and Table 5, after the random-effect terms are accounted for, some variables that were insignificant in the basic model are now significant in the spatial model, and vice versa. A possible explanation for this is that the introduction of random-effect terms handles correlated data and unequal variances (SPSS Inc. 2005). This result indicates that the estimated parameters in non-random effects may not be efficient and reliable, as they are unable to capture the variability over space. Considering the parameter estimates in Table 5, taking the bus mode as a reference, having an income ≥ $65K has a significant and positive effect on students opting to travel by car. In other words, this category of students has higher odds of using a car rather than taking the bus, compared to low- and middle-income students. This finding is consistent with those of previous research (Kim and Ulfarsson 2008; Zhou et al. 2018) reporting that students with higher household income are less likely to ride transit or walk to school. The average slope was found to be negatively associated with walking and car use. These results mean that in areas with a higher topography slope (northwestern zip codes), students are more likely to use the bus rather than take the car or walk. In the literature, mixed results have been reported regarding the directionality of the slope. For example, Rodríguez and Joo (2004) claimed that slope is not a determinant factor in travel mode choice, whereas Cervero and Duncan (2003) and Nguyen et al. (2017) reported that slope significantly affects walking and the use of power-assisted bicycles.

The average AADT is negatively and positively associated with car use and walking, respectively. That is, in congested areas (central zip codes), students are more likely to travel by bus rather than car and are more likely to walk rather than take the bus than in less congested areas. This determination can be justified by the fact that parking spots may not be easily available for car users in congested areas, forcing drivers to spend additional time finding parking spaces near their destinations. Additionally, as reported by Tirachini and Hensher (2012), congestion increases bus travel time for users. Hence, walking would be a more reliable alternative for students to use to arrive at their destinations without delay.

The correlation between sidewalk density and walking is significant and has a positive sign. This means that the higher the sidewalk density (typically in central zip codes), the more students are inclined to choose to walk to campus. In a previous work, Whalen et al. (2013) also reported that sidewalk density decreases the utility of motorized modes and increases the odds of walking compared to other modes. With regard to bus-stop density, it is negatively correlated with the car mode. In other words, students in areas (central zip codes) with higher bus-stop density are more likely to use the bus than ride in a car, compared to areas with lower bus-stop densities. Interestingly, bus-stop density is found to be positively correlated with other travel modes. This is probably due to the effect of multimodal access, which accommodates and connects multiple modes (e.g., bikes or scooters) to public transportation. Specifically, in areas (central zip codes) with higher accessibility to the public transport system, students whose primary travel mode is the bicycle more frequently combine their trips with taking the bus for long-distance travels, compared to students in areas with less access to public transport. Last, the average distance to school is negatively associated with walking, suggesting that students who live farther away from schools (specifically, those living in western and, partially, eastern zip codes) are more likely to use the bus rather than walk.

5.2. Interpretation of Spatial Random-Effect Terms

The most important component in terms of planning implications consists of the spatial random-effect terms, which capture the variation across neighboring zip codes. These novel insights could be widely used by planners. As shown in Table 5, the values of σ_θ across all of the three models imply that unobserved factors (e.g., topography and land use) at the zip-code level affect student mode choice. More importantly, the values of σ_φ indicate that these determinants are slightly correlated; that is, a travel mode choice in one region is likely to be affected by unobserved factors in another area or in several other areas. Additionally, the fractions of random effects for car, walking, and other modes obtained from the spatial model are 86%, 95%, and 81%, respectively. That is, all unstructured random-effect terms explained more variations than did the structured random terms. This implies that the travel mode choice of students living in a zip-code area is significantly affected by unobserved factors within that zip code rather than those in neighboring zip-code areas. As the spatial random-effect terms reflect the unique characteristics of each area, these terms can be used to map students’ preferences of travel mode across zip codes. Incorporating spatial autocorrelation into our analysis adds substantial value by accounting for these spatial dependencies, which traditional models might miss. It enables a more precise mapping of students’ preferences of travel mode and reveals how local and adjacent factors interact to shape travel behaviors. By integrating these spatial considerations, our study provides a richer and more detailed understanding of the factors influencing student travel choices and supports the development of more targeted and effective transportation policies. Therefore, the focus on spatial autocorrelation is not merely an added complexity but a crucial aspect of enhancing the accuracy and relevance of our findings.

Figure 3 shows the students’ preferences of travel mode based on the probability estimated from the spatial random-effect terms and by holding the other predictor variables constant at zero. From the map, it is evident that in central zip codes, walking (e.g., 78703, 78752, 78705, and 78701), followed by bus (e.g., 78731 and 78722) and other modes (e.g., 78757 and 78752), are the preferred means of transport. This is fairly reasonable, as most universities are located in these zones, and off-campus housing opportunities, which represent a potential unobserved factor, are higher in central zones than in distant ones, and consequently provide accommodations for many students near the universities. Nevertheless, in many other zip codes (colored in yellow in Figure 3), students are more likely to use cars rather than other modes due to the poor public transport system or its complete absence.

5.3. Recommendations

The findings of this study highlight the presence of latent and spatially related unobserved factors that significantly influence the travel mode choices of students in Travis County. These insights suggest the need for targeted interventions and improvements in transportation planning and policy. Based on our findings, we propose the following recommendations:

• Recommendation 1: Enhance Data Granularity

This recommendation is justified, since the identification of unobserved spatial factors underscores the importance of collecting and utilizing more granular data in transportation studies. Current datasets may not capture all relevant spatial variables potentially leading to the detection of unobserved factors that impact travel behavior. To address this, we recommend the following:

• Expanded Geographic Coverage: Extend data collection efforts to cover a wider range of zones within Travis County, including both urban and rural areas. This comprehensive approach ensures that all relevant spatial attributes are captured and analyzed.
• Collect Detailed Spatial Data: Encourage transportation authorities and researchers to gather more detailed data at finer spatial scales. This includes variables related to land use, environmental factors, micro-level accessibility, and socio-economic conditions within each zone.
• Refine Survey Instruments: Update and refine travel surveys to include questions and data points that capture the nuances of spatial factors at the zone level. This can help reduce the occurrence of unobserved variables in future models.

• Recommendation 2: Develop Zone-Specific Solutions

This is justified by the study’s findings, which indicate that spatial factors are not uniform across zones, suggesting a need for customized transportation solutions that account for these differences. Policymakers should consider the following remedies:

• Implement Targeted Interventions: Develop transportation policies and infrastructure improvements that address the unique spatial challenges of each zone. For example, in areas where public transportation is underutilized due to spatial barriers, invest in infrastructure upgrades or introduce more efficient and accessible transit options.
• Zone-Specific Planning: Collaborate with local planners to design and implement transportation solutions that consider the specific spatial characteristics of each zone, such as topography, land use patterns, and proximity to amenities.

• Recommendation 3: Update the Incentive Plan

The current incentive program has proven ineffective because it does not account for the specific areal barriers faced by different zones.

• Redesign the Current Plan: Customize incentives based on the unique needs of each zone. This involves adjusting financial rewards to offset spatial barriers and enhance the attractiveness of sustainable transportation options. The goal is to increase the utility of these options in areas where existing barriers may otherwise limit their use.
• Introduce Relocation Assistance: Encourage relocation to zones with fewer spatial barriers by providing relocation assistance or housing incentives. Programs could include grants for homebuyers or rent subsidies in areas with better access to sustainable transportation. This can make living in these areas more financially attractive and encourage residents to choose locations with better access to sustainable transportation options.

By implementing these recommendations, policymakers and transportation planners can address the unobserved spatial factors identified in this study, leading to more effective and equitable transportation solutions that better serve the needs of all residents in Travis County.

6. Conclusions

This paper proposes a Bayesian logit model that analyzes students’ choices of travel mode. This type of model has not been fully exploited in the travel-behavior literature. Our results demonstrate that structured and unstructured spatial random effects considerably improve the model’s performance, as the estimated goodness-of-fit measures suggest. We examined the effects of various transport-related and environmental factors on students’ travel behavior. The variables that were found to be significant in the spatial model were reasonable and explainable. The variable of having an income ≥ $65K is positively correlated with car travel, while the average slope, average AADT, and bus-stop density were found to be significantly and negatively associated with the car mode. Moreover, the average slope is negatively correlated with walking, whereas the average AADT and sidewalk density were found to have positive impacts on walking. Lastly, among the other modes, only bus-stop density was found to be positive and significant. Although these areal-level factors were found to affect students’ choices of mode, they are likely to affect residents’ travel behaviors as well.

Our proposed spatial model offers not only improved accuracy but also additional capabilities that enhance its utility for planning and policy purposes, compared to traditionally used models. For example, the results confirmed that, in addition to individual and known areal factors, students’ choices of mode are likely to be affected by areal unobserved factors such as walkability level, transport security, and safety. This indicates that traditional models suffer from omitted variables and their parameter estimates may be biased. Moreover, the magnitude of unobserved factors and their variations across the study area highlighted the areas in which students’ preferences of travel mode differ from public transport systems, suggesting that these areas require further investigation by transit authorities to identify and address potential spatial issues that may have contributed to this undesired behavior.

While this study focuses on Travis County, Texas, the insights gained extend beyond this specific context and have broader implications for other regions with diverse socio-economic conditions, geographic characteristics, and transportation infrastructures. The Bayesian multinomial logit model used in this research provides a robust and adaptable framework that can be recalibrated for different settings. This adaptability allows for the exploration of how varying factors, such as income levels, urban density, or public transit availability, might influence travel behavior in other regions. The model’s capacity to incorporate both observed and unobserved spatial factors makes it particularly valuable for application in areas with different geographic and infrastructural characteristics.

By adjusting the model inputs to reflect region-specific factors, such as infrastructure quality and socio-economic profiles, researchers can apply our methodological approach to analyze travel behaviors in diverse settings. The core principles observed in our study, including the impacts of spatial autocorrelation and local factors on travel behavior, are likely to be relevant in various contexts. For instance, regions with similar urban or transportation challenges may exhibit comparable patterns associated with how local and neighboring factors influence travel choices. However, it is essential to account for regional variations in land use, transportation networks, and emerging transportation options like ridesharing.

Our findings also have significant implications for transportation policy beyond the specific context of Travis County. At the state or national level, these insights can inform policy decisions by highlighting the importance of incorporating spatial dynamics into transportation planning and infrastructure development. For example, understanding how local factors and neighboring areas influence travel choices can help in designing more effective transportation networks that cater to diverse needs across different regions.

Additionally, the identification of unobserved local factors such as land use and infrastructure quality underscores the need for policies that address these specific elements. State and national policymakers could use this information to prioritize investments in transportation infrastructure and services in areas where local conditions significantly impact travel behaviors. This approach could lead to more targeted and efficient transportation strategies that improve overall accessibility and sustainability.

Our research contributes to both the existing literature and practical applications in several significant ways, aligning closely with the themes of sustainable transport systems.

First, on an academic level, our study investigates the intricate relationship between transport-related and environmental factors impacting students’ travel behavior, which is crucial for sustainable development. By analyzing variables such as sidewalk availability, topography, and income, we aim to elucidate how these factors influence individuals’ transportation mode choices, including cars, walking, and bus usage. Specifically, the presence and quality of sidewalks can significantly impact pedestrian travel patterns, with well-maintained sidewalks often encouraging walking as a mode of transport, thereby reducing reliance on cars and promoting sustainability. Additionally, topographical features such as steep slopes or difficult terrain may deter walking and cycling, leading to increased car usage and subsequent environmental impacts such as air pollution and greenhouse gas emissions. By exploring these interactions between sidewalk availability, topography, and mode choice, our study provides valuable insights into designing more sustainable transportation infrastructure and promoting eco-friendly travel behaviors.

Second, from a methodological perspective, the Bayesian approach employed to capture unobserved factors at the zip-code level enhances our understanding of how local environmental and infrastructural factors influence travel mode choices. This approach is essential for developing targeted interventions to promote sustainable transport systems.

Third, we investigated the presence of spatial autocorrelation in the dataset to understand whether unobserved factors in one region are likely to affect student mode choice in neighboring regions. This spatial analysis provides insights into the geographical patterns of travel behaviors, which are crucial for designing effective and geographically targeted policy interventions.

Finally, the study offers practical contributions by providing policymakers with insights into the complex spatial distribution and conflicting effects of students’ travel behaviors across Travis County localities. Understanding these dynamics is essential for developing comprehensive and sustainable transport policies that promote environmental stewardship and support the United Nations Sustainable Development Goals.

Moreover, the study’s emphasis on the impact of unobserved local factors on travel choices suggests that future transportation policies should include more granular data collection efforts. By incorporating detailed data on local conditions, such as land use, topography, and even cultural factors, policymakers can design transportation systems that are more responsive to the needs of the population, thereby improving accessibility and reducing environmental impact

Despite the above valuable contributions, it is important to acknowledge the limitations of our study which could affect the interpretation and generalizability of our findings.

One such limitation is the use of zip code-level data as the unit of analysis, which may introduce the risk of ecological fallacies, in which aggregate-level results do not necessarily represent individual behaviors. However, considering that our study specifically targets university students—a relatively homogenous group in terms of age, educational status, and life-stage—the potential for these fallacies is somewhat mitigated. While variability within this population still exists, the commonalities provide a more stable basis for aggregated analysis. Additionally, we included household income in our analysis to add socio-economic granularity, though we recognize that this variable alone may not fully capture individual behavioral differences.

Additionally, the study faces limitations due to constraints in the available data. For example, data on access to financial resources, personal demographic information (age and gender), cultural influences, and emerging transportation options such as ridesharing were not included in the dataset provided by the Texas Department of Transportation. Although we addressed these factors to some extent—by using income as a proxy for financial resources, acknowledging the relatively homogeneous nature of the student population which minimizes the impact of age and cultural diversity, and grouping emerging transportation modes under an “other modes” category—there may be additional important variables that were not fully explored.

Given the aforementioned limitations, future research should aim to incorporate more detailed demographic data, such as individual income or car ownership, to further refine the analysis and mitigate potential ecological fallacies. Additionally, including socioeconomic and contextual factors—such as financial resources, cultural influences, and emerging transportation options—will provide a more comprehensive understanding of travel behaviors and enhance the generalizability of the findings. Future studies should also test the robustness of our results by conducting similar analyses at different levels of geographic aggregation, such as the census tract level, and by experimenting with alternative model structures. These approaches could validate our findings and uncover additional insights into the impacts of unobserved spatial factors on travel behavior.