Unobserved heterogeneity in transportation equity analysis: Evidence from a bike-sharing system in southern Tampa
Introduction
Title VI of the Civil Rights Act of 1964 requires programs, transportation programs included, that receive federal funds to bring outcomes (e.g., costs, benefits) to society non-discriminatively (Karer and Niemeier, 2013). Achieving an equitable distribution of the outcomes of transportation systems across space and different sociodemographic groups has then become a primary challenge facing urban transportation planning (Gao and Klein, 2010; Carrier et al., 2014). Regardless of enormous efforts on ensuring equity from transportation planners, assertions of inequity have been witnessed in traditional and emerging transportation systems (Noland and Lem, 2002; Guo et al., 2020). Many traditional transportation practices were known to favor automobile travel rather than other modes of transportation that are heavily relied on by socially- or economically-disadvantaged groups (Litman and Brenman, 2012). Further, research has also identified inequities in access to the emerging bike-sharing systems, with white, college-educated, and affluent people being overrepresented among the registered users of several bike-sharing systems in the United States (Ursaki and Aultman-Hall, 2015). Therefore, analyzing the equity impacts of transportation systems/policies has become an important part of transportation project design.
In the challenging mission of analyzing the equity impacts for transportation systems, a critical step is to assess the distribution of their outcomes across space and/or different demographic groups. One typical approach is to apply a mismatch analysis of simple descriptive statistics (e.g., mean) of the transportation outcome measures. This method presents the distribution of the outcome measures in maps or tables and then compares the distributions (Currie, 2004; Karn Kaplan et al., 2014; Golub and Martens, 2014; El-Geneidy et al., 2016). Mismatch analysis is quite simple and intuitive, but it cannot offer much quantitative information on equity performance. Therefore, transportation researchers have adopted inequality indexes from social science to obtain a quantitative evaluation of the overall degree of inequality. Popular inequality indicators include Gini index (Delbosc and Currie, 2011; Karn Kaplan et al., 2014; Guzman et al., 2017; Pritchard et al., 2019), Atkinson index (Levy et al., 2009), Theil's entropy index (Hamidi et al., 2019), comparative environmental risk index (Kocak, 2019), and subgroup inequality index (Gurram et al., 2015; Gurram et al., 2019; Chen et al., 2019). Another approach to quantitatively evaluating inequity, which is the focus of this paper, is statistical modeling such as the ordinary least squares regression model (Ogilvie and Goodman, 2012), the negative binomial model (Wang and Akar, 2019), and the multinomial logit model (Wang and Akar, 2019; Raux et al., 2017). In these models, the sign of the estimated coefficient on each explanatory variable indicates whether a population group with that factor is over- or under-represented in terms of the outcome they receive, while the magnitude of the coefficient is often used as a measure of the strength of the disparity (or level of inequality).
Due to their exploratory capability in describing the relationship between transportation outcomes and sociodemographic attributes, statistical models have been popularly applied for transportation equity analysis such as disparities among populations in terms of accessibility (Ogilvie and Goodman, 2012; Wang and Akar, 2019; Raux et al., 2017), exposure to emissions (Buzzelli and Jerrett, 2007; Havard et al., 2009), and safety outcomes (Harper et al., 2015; Kravetz and Noland, 2012; Morency et al., 2012). In these studies, data were usually aggregated to certain geographic scales for analysis, e.g., census tracts (Morency et al., 2012; Buzzelli and Jerrett, 2007), census blocks (Havard et al., 2009; Wang and Akar, 2019), and census block groups (Kravetz and Noland, 2012). However, data aggregation has been demonstrated to absorb individual heterogeneity in the distribution of transportation outcomes (Chen et al., 2019). Therefore, researchers have promoted the use of individual-level disaggregated data to unveil individual disparities in transportation equity analysis (Bills and Walker, 2017; Chen et al., 2019; Gurram et al., 2019). Using disaggregated data unveils individual heterogeneity that tends to be hindered by aggregated approaches and therefore offers a better interpretation of the equity impacts. Although disaggregated data contain rich information on individual sociodemographic attributes, these databases usually only cover a small fraction of the large number of elements that define individual sociodemographic status. Many other factors indeed remain unobserved to analysts. For example, the availability of credit cards has been shown to be a significant factor contributing to individual access to bike-sharing services (Shaheen et al., 2017). However, datasets providing sociodemographic information (e.g., those from the American Community Survey) do not contain such information.
These unobserved factors can introduce variations in the distribution of transportation outcomes among individuals that belong to a sociodemographic group. For instance, consider race as an unobserved factor that correlates with the distribution of transportation outcomes. Although there has been ample evidence that different racial groups benefit differently from some transportation systems in terms of their accessibility (Chen et al., 2019), there are also great variations across people of the same race, including differences in transportation needs, availability of credit cards, English proficiency and other factors that are generally unavailable to the analysts. This type of heterogeneity essentially are not captured in the dataset, and thus is called unobserved heterogeneity in the literature. It has been frequently observed in highway accident data and traffic flow data. In highway accident data, unobserved heterogeneity is found in a range of explanatory variables such as gender, age, vehicle type, traffic volume, and so on (Mannering et al., 2016). In traffic flow data, unobserved heterogeneity exists in driving styles, vehicle types, and leader-follower pair compositions (Ossen and Hoogendoorn, 2011).
However, few studies have investigated unobserved heterogeneity for transportation equity analysis. Existing studies applying exploratory statistical models for transportation equity analysis have generally assumed that parameters in the estimated model are constant across all observations; i.e., there is no unobserved heterogeneity in the collected data. However, ignoring the unobserved heterogeneity may result in misspecified models, and thus the estimated parameters will be biased and inefficient (Mannering et al., 2016). As a result, inference and policy implications based on the estimated models will be erroneous. An instance is the relationship between race and the accessibility an individual receives from a bike-sharing system. As mentioned previously, there are multiple reasons to believe that the accessibility people receive from a bike-sharing system varies from individual to individual even if they are the same race owing to unobserved individual heterogeneity. Nevertheless, if possible unobserved heterogeneity across individuals were ignored, incorrect conclusions may have been drawn from erroneous parameter estimates such as believing that all individuals in one racial group have higher accessibility than the general population. Indeed, there are possibly some individuals of that race who do not receive accessibility from the system at all because the lack of credit cards prevents them from using the services (which is not captured by the analysis dataset). This phenomenon is particularly likely when a disaggregated dataset containing a large number of samples is used for analysis. Without explicitly considering the unobserved heterogeneity, it will be difficult to determine whether this statement is true or not. Therefore, approaches to accounting for unobserved heterogeneity for analyzing transportation equity impacts are needed.
Against this background, this paper aims to apply an exploratory modeling approach to investigate whether there is unobserved heterogeneity in transportation equity impacts. To this end, we carry out a case study focusing on the distribution of individual accessibility to activity locations via bike-sharing in southern Tampa using a disaggregated dataset. The dataset includes individual bike-sharing accessibility and sociodemographic information. To allow for the investigation of possible unobserved heterogeneity in the data, three random parameters logit models are estimated using the individual-level data and data aggregated to land parcel and traffic analysis zone (TAZ) levels, respectively. The novelty of this paper lies in allowing for possible unobserved heterogeneity of random parameters and the use of heterogeneity effects in equity impact measurement for transportation equity analysis. The main contributions of this paper are threefold. First, we apply a heterogeneity modeling approach to study the equity impacts of a case study transportation system in southern Tampa using a disaggregated dataset. The use of a heterogeneity model captures the potential unobserved heterogeneity hidden in the large amount of individual-level data while traditional fixed parameters models cannot serve the same purpose. We also investigate how heterogeneity effects can be used to measure the equity impacts in transportation systems. Incorporating this unobserved heterogeneity ensures that the model is correctly specified, and thus the resultant equity interpretations are unbiased and efficient. Second, we offer a comparison between the model estimation results using disaggregated data, data aggregated to parcels, and data aggregated to TAZs. This comparison enables an in-depth understanding of the impacts of data aggregation on parameter estimates in the model, which are of special importance to transportation planners and equity analysts. It also provides insights into the presence of unobserved heterogeneity in aggregated data. Finally, the case study reveals how bike-sharing accessibility is distributed among the population and population subgroups defined by various sociodemographic attributes in southern Tampa. It also confirms the existence of unobserved heterogeneity in the investigated data, the necessity of using a heterogeneity model, and the advantage of using disaggregated data. Overall, this study offers empirical evidence to transportation equity analysts of the existence and importance of incorporating unobserved heterogeneity given the emerging use of disaggregated data in transportation equity analysis. Particularly, various equity implications and recommendations of the studied bike-sharing system provide insights that can assist bike-sharing operators in designing unobserved heterogeneity-aware equitable expansion plans in southern Tampa and beyond.
The remainder of this paper is organized as follows. Section 2 presents the materials (including the bike-sharing system, analysis area, and data collection), and the analytical method used for modeling the data. Section 3 presents and discusses the analysis results, including descriptive statistics, model estimation results using the individual-level, parcel-level, TAZ-level data, and the corresponding equity implications. Finally, Section 4 provides conclusions and potential future research directions.
Section snippets
Materials and methods
The primary goal of this study is to investigate unobserved heterogeneity in the equity impacts of transportation outcomes via a case study bike-sharing system. To this end, we first collected data on individual sociodemographic and accessibility to activity locations via a bike-sharing system in the study area. Then, a statistical modeling approach that captures unobserved heterogeneity was applied to model the data. This section presents the bike-sharing system, the analysis area, the
Results and discussion
This section discusses the results of our analyses. Section 3.1 presents the variables used for model estimation and summary statistics for bike-sharing accessibility computed by each variable that represents a population subgroup. Results from the disaggregated (i.e., individual-level) data analysis are presented in Section 3.2. Finally, Section 3.3 compares the results from the disaggregated model with those from the aggregated (i.e., parcel-level and TAZ-level) data analyses.
Conclusions
Using individual data on bike-sharing accessibility and sociodemographic in southern Tampa, this paper carries out a case study on the existence of unobserved heterogeneity in analyzing the equity impacts of the Coast Bike Share system in terms of the accessibility it brings to society. By grouping the individual accessibility values into two outcomes of having bike-sharing accessibility and not having bike-sharing accessibility, a mixed logit model was estimated to investigate the relationship
CRediT authorship contribution statement
Zhiwei Chen: Conceptualization, Methodology, Software, Formal analysis, Writing - original draft, Writing - review & editing. Xiaopeng Li: Supervision, Funding acquisition, Writing - review & editing.
Acknowledgements
This research was supported by the U.S. National Science Foundation through Grants CMMI #1634738 and CMMI #1638355. We thank Dr. Sashikanth Gurram and Dr. Amy L. Stuart for providing the disaggregated activity and demographic data necessary for this analysis. We also thank Dr. Fred Mannering for his comments on heterogeneity modeling.
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2023, Transportation Research Part B: MethodologicalCitation Excerpt :Moreover, Sama et al. (2017) incorporate the equity consideration into air traffic control at busy airports and optimize the take-off and landing operations in airports. As for the studies on bike-sharing systems, several discuss equity issues (Qian and Jaller, 2020, Dill and McNeil, 2021, Chen and Li, 2021); however, few address the equity problem. Caggiani et al. (2020) focus on the equitable stations location problem in the integration of bike and public transportation systems.
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2022, Sustainable Cities and SocietyCitation Excerpt :Since commuters with higher income are more likely to use BSS (Fishman et al., 2015), one potential way to incentivize those commuters at a lower-income range to use the service is to reduce the prices of Bicing. A price reduction can empower the groups facing socioeconomic barriers to consider Bicing as an alternative transport mode, thus contributing to closing the social equity gap concerning BSS while promoting active mobility in general (c.f., Chen & Li, 2021; Desjardins, Higgins & Páez, 2022; Lee, Sener & Jones, 2017). Furthermore, we observed that many neighborhoods with lower levels of income had experienced an improvement of bike-related infrastructure (including the implementation of tactical urbanism) during the pandemic, resulting in a noticeable increase in BSS usage.