Unobserved heterogeneity in transportation equity analysis: Evidence from a bike-sharing system in southern Tampa

Abstract

Assessing the equity impacts of transportation systems/policies has become a crucial component in transportation planning. Existing statistical modeling approaches for transportation equity analysis have typically assumed that parameter estimates are constant across all observations and used data aggregated to certain geographic units for the analysis. Such methods cannot capture unobserved factors that are not contained in the dataset, i.e., unobserved heterogeneity, which is likely to be present in the increasingly popular disaggregated datasets. To investigate whether there is unobserved heterogeneity in transportation equity impacts, this study carries out an empirical study focusing on the distribution of individual accessibility to activity locations via bike-sharing in southern Tampa. A disaggregated dataset containing information on individual bike-sharing accessibility and socio-economic factors is modeled with a random parameters logit model that allows for the investigation of possible unobserved heterogeneity. Further, models are estimated using data aggregated to parcel- and TAZ-levels to explore the impacts of data aggregation on model estimation results. The models unveil the unobserved heterogeneity in bike-sharing accessibility among populations in different groups defined by different sociodemographic factors in southern Tampa. These results shed insights into how the inconsistent disparity direction of transportation outcomes across individuals in a population group can be measured from the heterogeneity effects. Finally, a comparison between different models show that to capture such inconsistency, the use of disaggregated data with heterogeneity models is highly recommended for transportation equity analysis.

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.