Introduction

Evaluations of large public investments in transportation in the United States have demonstrated that the most vulnerable members of society are most likely to bare any negative externalities of transportation infrastructure and policy changes. These challenges have been well documented (Ward 2005; Schweitzer and Stephenson 2007; Lucas et al. 2019) and were the catalyst for federal regulations that mandate transportation equity analysis of federally funded transportation plans. Executive Order 12898 of 1994 directs federally funded agencies (including Metropolitan Planning Organizations) to assess equity impacts of all policies and activities on defined Environmental Justice communities (including low income, underrepresented, and other vulnerable groups). Further, Title VI of the Civil Rights Act of 1964 outlaws discrimination, denial of benefits, or exclusion from participation in federally funded activities, on the grounds of race, color, or national origin (Sanchez 2005; Chakraborty 2006; Marcantonio et al. 2017). Agency-level orders and directives were subsequently adopted, such as the 1999 Memorandum on Implementing Title VI Requirements in Metropolitan and Statewide Planning for the U.S. Federal Highway and Federal Transit Administrations (Williams and Golub 2017).

While equity analyses have been required for decades now, there remains a dearth of practical guidance for performing regional scale transportation equity analysis of transportation plans. Only in recent years, have we begun to see efforts to summarize and propose meaningful methods of transportation equity analysis that are appropriate for regional-level assessment. The objective of such transportation equity analyses is to evaluate how the benefits and costs of planned transportation and land-use changes are likely to be allocated among various segments of the population, particularly vulnerable communities. Notably, a study by Williams and Golub (2017) offers a comprehensive summary of the various equity analysis methods used by MPOs across the U.S. and offers two regional scale demonstrations of equity analysis using recommended approaches. Nevertheless, there remains a critical need for guidance on the application of travel demand models for regional transportation equity analysis, which are prevalent analysis tools used for a range of transportation planning activities.

A growing number of studies and regional planning efforts have applied large scale travel demand models for transportation equity analysis (Rodier et al. 2002, 2009; Castiglione et al. 2006; MTC 2001, 2013a; HGAC 2011; Oregon RTP 2018). Yet, the uptake and use of state-of-the-art activity-based travel demand models by regional planning authorities is slow. Only a hand full of efforts have implemented activity-based travel models for equity analysis (Castiglione et al. 2015; Nahmias-Biran, et al. 2017; Nahmias-Biran and Shiftan 2020). While activity-based travel demand models have the potential to support meaningful analysis of the allocation of transportation costs and benefits (Walker, 2005; Bills et al. 2012), the full exploration of the advantages of such models using real-world transportation planning scenarios is ongoing.

To help fill this void, we aim to provide a practical discussion of key features of activity-based travel models and how they can be advantageous for measuring the allocation of transportation outcomes and movement toward or away from a more equitable state. We define and test equity outcomes relative to three specific equity standards: equality, proportionality, and Rawlsian justice. Further, this study is concerned with the application of an operational activity-based travel demand models for equity analysis of regional transportation plans. A study with a similar aim (Bills and Walker 2017) presented a new framework for doing this, including distributional measure comparisons based on a logsum consumer surplus measure, and calculated from a simplified activity-based travel model. Our current study extends the work of Bills and Walker (2017) and implements their recommended framework, which includes individual-level group segmentation, calculation of disaggregate equity indicators, comparison of distributional measures across population segments, and the ranking of planning scenarios using equity-based criteria. However, our demonstration is done using a full-scale model and a set of real planning scenarios developed by a metropolitan planning organization: the San Francisco Metropolitan Transportation Commission (MTC). This is an important step toward proving the real-world benefits of such an application and exploring the nature of how transportation costs and benefits are distributed among segments of the population, based on real regional scenarios and within the context of the latest tools available to regional planning authorities. In addition, our demonstration highlights the significance of measuring equity outcomes relative to specific equity standards, for evaluating progress toward regional transportation equity. Overall, we demonstrate that fine-grained distributional measures play an important role in examining the fairness of regional transportation impacts and help to explain some underlying reasons for average measure results. Further, such measures can reveal harmful cases when disadvantaged groups are most likely to experience the disbenefits of transportation scenarios, relative to other groups. Yet each type of measure in isolation does not offer a clear story of how costs and benefits will be allocated among disadvantaged and more affluent groups. Further, our results demonstrate the significance of defining equity standards and applying the associated equity-based criteria for ranking planning scenarios, as the ranking will vary according to the evaluation criteria and as well as for different comparison groups.

Methods for regional-level transportation equity analysis

The methods used for regional transportation equity analysis have advanced considerably over the past decade. Studies have focused on how to define and identify vulnerable communities (Delbosc and Currie 2011; Gaffron 2012; Rowangould et al. 2016), indicators of transportation equity (Ramjerdi 2006; Manaugh et al. 2015; Martens et al. 2019), and definitions of transportation equity (Golub and Martens 2014; Marcantonio et al. 2017). The most common approaches for transportation equity analysis of regional plans involve the use of spatial analysis tools to map the residential proximity of vulnerable communities to proposed transportation project(s) (Amekudzi et al. 2012; Williams and Golub, 2017). These approaches measure the level of benefit to these communities, assuming that greater proximity to projects is associated with a higher-level of benefit. It is also common to measure community “costs” associated with their level of exposure to certain externalities, like air pollution and noise pollution (due to traffic congestion) (e.g. MTC 2001; Rodier et al. 2009). The challenge with these approaches, however, is that their ability to clearly represent behavioral responses to transportation and land-use changes and associate transportation gains or losses to population segments is limited.

A second approach is to model the transportation changes over time using a travel demand model. The model outputs are then processed to determine transportation gains and losses and how they compare across communities. In particular, the analysis involves first measuring the expected impacts of transportation and land use improvements on the travel behavior of defined population segments, calculating some indicators of the costs and/or benefits (due to the changes), and then comparing these costs and/or benefits across the segments to judge whether the allocation is equitable. Two important features of this analysis process are the population segmentation and equity indicator(s):

  • Population Segmentation: This refers to the definition of target and comparison groups, and requires the use of one or more variables of segmentation (e.g. income, ethnicity, gender, etc.) and a unit of segmentation (e.g. individuals, households, census blocks, travel analysis zones, etc.). Most commonly, the target group is defined in terms of “communities of concern”. These are zones or census tracks that are typically identified based on the concentration of low income and historically minoritized groups. Common variables of segmentation are income and ethnicity, and units of segmentation are typically zones or census tracts (MTC 2009, 2013b).

  • Equity Indicators: Equity indicators are variables used to measure the distribution of costs and benefits among travelers and the allocation resulting from the transportation plan. There are a range of equity indicators applied for evaluating transportation plans. For a more theoretical discussion of equity indicators, see (Ramjerdi, 2006; Manaugh et al. 2015; Martens et al. 2019), but some common indicators used in practice are work travel time, accessibility to jobs, emissions exposure, and project investments by population segment (MTC 2009; SANDAG 2011; MTC 2013a). A fundamental distinction can be drawn between some equity indicators commonly used in practice, such as commute travel time and employment accessibility (Manaugh et al. 2015) and measures that apply an explicit equity perspective or standard (Ramjerdi, 2006; Lewis et al. 2021), like the gini coefficient. In this paper, we adopt the perspective that both are relevant, and any equity indicator that captures transportation costs or benefits and can be stratified across various variables of segmentation, can serve as a measure of transportation equity when employed with an explicit equity standard.

After the population segmentation and indicator selection tasks, the allocation of costs and benefits needs to be determined. To understand conventional comparison processes for equity analyses using travel demand models, we further discuss the Metropolitan Transportation Commission’s (MTC) 2040 Regional Transportation Plans. This example is used because MTC’s methodology represents the best public practices on regional transportation equity analysis in the United States, given that they were one of the first MPO's known to have applied an activity-based travel model for regional transportation equity analysis.

MTC 2040 equity analysis (2013)

MTC’s equity analysis of their 2040 plan (MTC 2013a) assesses the impacts of five scenarios, including a No-Project scenario (business-as-usual), Project (also called Preferred) scenario, and three additional transit improvement scenarios. These scenarios were assessed using MTC’s Travel Model One, an activity-based travel demand model that replaced their legacy four-step model in early 2011. For their analysis, the target and comparison groups are defined using zones as the unit of segmentation, and variables of segmentation included income, ethnicity, english language proficiency, auto ownership, senior citizen status, disability status, number of parents in the home, and rent burden. Zones with high concentrations for at least four of these variables are classified as Communities of Concern (COCs), and a comparison is made between these Communities of Concern (target group) and the remainder of the region (comparison group). The equity indicators were average commute and non-commute travel time (for all modes), transportation/housing affordability, displacement risk, vehicle miles traveled (VMT) and emissions density (exposure to vehicle emissions).

As shown in Fig. 1, the comparison was done by taking the percent change in the indicators, compared across population segments (COCs vs. non-COCs) and across the different scenarios, using the No-Project scenario as the base case. It is also important to note that MTC’s analysis included some spatial analysis as well, where they mapped the locations of Communities of Concern relative to the planned investments in the various scenarios. Figure 1 shows the MTC results for the commute travel time indicator. From this analysis, MTC concluded that although Communities of Concern experienced a slightly smaller reduction in travel time, overall, the impacts were comparable to the Remainder of the SF Bay Region. This is because the reductions in travel costs for Communities of Concern (due to some shifting to less expensive travel modes) would likely offset the negative travel time outcomes (MTC 2013a).

Fig. 1
figure 1

MTC Equity Analysis of 2040 RTP/SCS Example: Commute Time (Minute), based on individual modes taken (MTC 2013a)

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Here our focus is not on examining the individual projects and investments included in each scenario (see MTC 2013a for a full discussion), nor do we highlight specific reasons for these results shown in Fig. 1. However, this example is sufficient for characterizing three key challenges with current applications of activity-based models for regional equity analysis. The challenges here are with (1) group segmentation, (2) equity indicators (3) and group comparisons.

(1) Group Segmentation: First, the use of zones as the unit of segmentation, while convenient, can lead to a degree of aggregation bias (Geronimus and Bound 1998), particularly in cases where the segmentation variable is person or household specific. For example, if we want to compare the impacts to low-income travelers, relative to high income travelers, there would most likely be some share of other income groups living within the target and comparison zones. It would therefore be impossible to clearly isolate the impacts to the different groups. However, it is important to note that in cases where the emphasis is on spatial comparisons, parcel or zonal segmentation units may be more appropriate. Because of the advent of population synthesis, activity-based travel models are capable of measuring equity impacts at a range of resolutions, including the individual or agent level, and this helps in mitigating issues with aggregation bias.

(2) Equity Indicators: Second, while there does not seem to be a consensus in the literature on which measures or indicators are most appropriate for reflecting equity impacts under which conditions, measures focusing solely on transportation changes (travel time, travel cost, etc.) are less comprehensive of true transportation equity impacts (Manaugh et al. 2015). While our aim here is not to recommend the “best” equity indicator, it is important to consider the extent to which the equity indicators represent true transportation-related benefits (or costs). For example, travel time indicators only capture a portion of transportation benefits, given that transportation investments generate transportation system and landuse changes, among other effects (Giuliano, 2004). Alternatively, measures of transportation accessibility can capture both land-use and transportation impacts. Accessibility measures that can also be calculated at the individual level, such as the logsum accessibility and consumer surplus measure (De Jong et al. 2007), would therefore be more sensitive to potential transportation-related impacts and desirable for transportation equity analysis.

(3) Group Comparison: Third, the use of average measures to compare indicators across population segments is particularly problematic because averages tend to mask finer-grain outcomes. The average measure may mask the reality that some groups benefit, while others are made worse off (Bills and Walker 2017).

Framework for regional transportation equity analysis

Bills and Walker (2017) developed a new framework to address many of the challenges with previous regional transportation equity analyses (outlined in the previous section). Most important here is that the framework leverages the power of activity-based travel models and calls for transportation program evaluation based on defined equity standards and comparisons of distributional measures of equity, rather than average measures. We apply their framework in our analysis, as it is inclusive of the general equity analysis practice for regional plans (Williams and Golub 2017). This process (outlined below) pays specific attention to the technical steps of performing transportation equity analysis using advanced travel demand models.

A distinction between our implementation and the framework developed by Bills and Walker (2017), is that we further elevate the significance of identifying and applying regional equity standards. The selection of equity standards is a central phase in equity analysis and must govern all aspects of the analysis, including the selection of equity measures, how they are implemented for assessment of transportation benefits and costs, as well as how transportation alternatives are ranked according to regional equity goals. Yet, there remains no agreement in the transportation planning literature on which equity standards are appropriate for addressing which transportation equity concerns. Ideally this decision would be made through a participatory planning process, including community stakeholder engagement. Lacking such a basis, in this study we demonstrate how three distinct equity standards can be employed, using metrics generated from an activity-based travel demand model, and as part of regional transportation planning activities. We demonstrate an analysis of regional transportation and landuse scenarios using Equality, Proportionality, and Rawlsian Justice standards. The selection of equity standards (implemented in step 4 of the process) is assumed to have taken place at an initial “step 0”, and steps 1 to 4 are conditioned on an initial selection of standards that aligns with the needs of the region.

Step 0:

Select an equity standard or standards that align with the region’s needs, that can be used to measure the potential for each scenario to move conditions toward (or away from) a more equitable state.

Step 1:

Segment the population (target and comparison group(s)) using an individual unit of segmentation and select comprehensive equity indicators that are sensitive to transportation changes, land-use changes, and individual-level conditions.

Step 2:

Calculate equity indicators from the activity-based travel demand model output. This involves determining the exact measures (formulas) for the selected equity indicators, and requires careful consideration given the large variety of data, choice dimensions, etc. available from activity-based models.

Step 3:

Generate and evaluate the changes of the indicators, across groups and scenarios. The “Individual Difference Density” comparison is recommended, which compares individual-level changes in the given indicator, for the different scenarios (Bills and Walker 2017). This comparison allows for a more fine-grained evaluation of benefits resulting from the transportation and land-use plans.

Step 4:

Evaluate scenarios using equity criteria (based on the equity standard(s) chosen in step 0) and rank the scenarios based on the degree to which they meet the equity criteria.

Overview of activity based modeling systems

Travel demand models generally serve as the primary transportation planning tool for measuring and forecasting changes in travel behavior that result from large scale transportation investments. These models measure the effects of transportation system and land-use changes, as well as travel and residential costs, and demographic changes on travel behavior (mode, destination, time-of-day, and other travel choices). Activity-based travel models—the latest class of travel demand models—represent the best practices in travel demand modeling and have tremendous potential for transportation equity analysis (Walker 2005; Bills et al., 2012). The synthesized population and travel choice data output from these models enable us to calculate distributional measures for transportation equity analysis, and not only identify travelers who are likely to and not benefit, but to quantify the potential for gains and losses.

Here it is important to acknowledge that the term “choice” is used throughout this and following sections and takes on a technical meaning as is often used in microeconomics and discrete choice analysis [for example, see Train (2009)]. This is despite cases that are relevant to transportation equity analysis, where some groups are constrained from freely choosing their preferred alternatives. In this study, we follow this conventional microeconomic interpretation of “choice”, which should not be taken as an assertion that all travelers have access to the same freedom in choice making.

The full modeling and analysis process using these models includes the development and estimation of the model, forecasting of the transportation and land-use scenarios, and then processing of the data. While the core contribution of this work relates to the data processing phase; it is important to review the general structure of activity-based models. The emphasis with respect to equity analysis is on capturing the heterogeneity across population segments, such that the (expected) behavioral responses to transportation and land-use changes can be modeled. These are critical for accurately measuring the differences between population segments, and therefore equity outcomes.

Activity-based travel models were developed on the basic principle that one’s travel is derived from their desire to participate in various activities (Bhat and Koppelman 1999). The structure of the model is hierarchical, with longer term choices (like work location and auto-ownership choices) higher in the model, and shorter-term choices (like mode choice) reflected at lower levels. These choice dimensions are modeled primarily as (logit) discrete choice models. Figure 2 shows a schematic for a typical activity-based travel demand model. These model components are linked together in a nested-like structure, using feedback variables. These “feedback” variables are logsums that can be generated from any (logit) choice dimension in the activity-based modeling system. These logsums are further discussed in the “Step 2: indicator calculations” section. The travel choice dimensions represented in typical activity-based models can be grouped into three sections: land-use, demand, and network-related. In addition, the modeling system includes a population synthesizer that generates a population of agents the is demographically and spatially representative of the true population.

Fig. 2
figure 2

Generic activity-based travel model schematic

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Each demand-related component of the activity-based travel demand model represents a different travel choice dimension. While a range of land-use and route/network related components feed into the model travel components, we limit our descriptions to those most relevant to generating transportation equity indicators. For a more complete review of the features of activity-based travel models, see Castiglione et al. (2015).

  1. 1.

    Population Synthesis: The purpose of the population synthesizer is to generate a sample of individual agents that is representative of the real-world population. This synthetic population is typically generated for the base year from census data, such as the American Community Survey and the U.S. Public Use Microdata Data (Guo and Bhat 2007). Each individual agent is assigned a set of characteristics (e.g., age, gender, employment status etc.) and is assigned to a household with a set of characteristics (size, number of workers, income, number of vehicles, etc.). Further, (in the absence of a residential location choice model) each household is assigned to a residential location in the region, defined as a travel analysis zone (TAZ).

  2. 2.

    Work Location Choice Model: this is a (logit) destination choice model that is a function of the amount of employment in a zone (its “size”) and the impedance associated with reaching various zones from an agent’s home location.

  3. 3.

    Auto Ownership Choice Model: this is a multinomial or nested logit model that predicts the number of automobiles owned by a household, ranging from 0 to 4 + automobiles.

  4. 4.

    Full-Day Activity Pattern Models: these models predict or assign individual as well as joint household travel patterns. This includes the travel purposes, such as to work, school, shopping, recreation, etc. Also, tour frequency (including for sub-tours), and trip-chain patterns (whether there will be stops on the out-bound and/or in-bound legs of the tour) are outcomes of these models.

  5. 5.

    Time-of-Day Choice Models: these models predict to departure and arrival times for each leg of each journey, and for each purpose class. These models are typically specified as multinomial logit.

  6. 6.

    Stop Location Choice Model: this is a destination choice model that predicts the location of stops made along each leg of the journey (given the number of stops predicted by the stop frequency model). Similar in structure to work location choice models, this model is a function of the attractiveness of the zone (as represented by the number of activities in each zone) and travel impedance.

  7. 7.

    Journey and Trip Mode Choice Models: travel mode is typically modeled at both the journey (trip chain) and trip levels. The journey mode choice model predicts the primary mode of travel for each journey (or tour), and the trip mode choice model predicts the mode of travel for each trip made along the journey (mode for travel between each stop made along the tour). The choice set for the trip mode choice model represents all possible modes of travel available to the traveler, while the choice set of journey modes is typically a set of aggregated categories of these (trip-level) modes, representing the primary mode of travel. For example, the tour level transit mode may be associated with bus, train, and ferry modes at the trip level. These models are often specified as nested logit.

Once the activity-based travel model is estimated, calibrated, and validated, it is used to forecast the travel behavior changes of the population, in response to a set of planning scenarios (such as those described in Table 1). These scenarios reflect changes in the transportation system (e.g. highway expansion, transit extension, etc.), transportation policies (e.g. fare changes, pricing schemes, etc.), and land-use policies (e.g. transit oriented development incentives, growth boundaries, etc.). To produce a scenario, changes are made by adjusting various model input data. For example, in the case of a new transit project where a rail transit alternative is made available in areas that previously did not have access to transit, this could be done by adjusting the mode choice alternative availabilities, indicating that a new transit alternative is now available for additional links in the network. Once the scenarios are developed, the activity-based model is run to generate new model outputs, in the form of transportation link volumes, number of tours taken at the individual and household levels, number of tour stops, travel purposes, travel modes, etc.

Table 1 Planning scenario descriptions
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San Francisco case study

The following sections discuss the methods and results corresponding to each of the four steps in the analysis framework for equity analysis. We start with a description of the MTC scenarios assessed in this study. As previously described, the four steps (after equity standards have been identified in Step “0”) include (1) identify of the equity indicator(s) and define of the population segments (target and comparison groups), (2) calculate the indicator(s) from the travel model output, (3) generate and compare the distributions of the equity indicators, and (4) select the equity standard(s), define the associated evaluation equity criteria, and apply them for scenario ranking.

Scenarios

MTC developed five planning scenarios for their 2013 Regional Transportation Plan evaluation; one being a “No-Project” scenario and the remaining being four “Project” scenarios that are composed of different transportation investments and land-use policy alternatives (MTC 2013b). It is important to note that all transportation projects that make up these scenarios have been specified for a 30-year planning horizon (from 2010 to 2040) and are fiscally constrained (financially feasible). The travel model data associated with each scenario included the regional forecasts for travel behavior changes due to the combinations of projects and policies represented in the scenarios. In this case study, we perform equity analysis using three of these scenarios: The No-Project, Preferred, and Transit Priority scenarios, as they are determined to be the most useful for demonstrating the range of results. These three scenarios are briefly described in Table 1, but for a more detailed discussion on all the planning scenarios, see MTC (2013b).

Step 1: population segmentation and indicators

Population segmentation

In this case study evaluation, we define the population using a single variable of segmentation: income. This is for two reasons: (1) income is modeled as a demographic characteristic (tracked over time) in Travel Model One, and other useful variables—like ethnicity—are not; and (2) the use of a single variable of segmentation in this study provides for a cleaner comparison of results and follow up discussions. This should not be taken as a recommendation that income is the only important variable of segmentation to consider in equity analysis. Further, we segment the population at the individual and household levels. The use of these disaggregate units of analysis provide for a more targeted evaluation, in comparison to zonal segmentation.

Low-income individuals/households (28.6% of the projected 2040 population) are designated as the target group (as they are the more vulnerable group), while the high-income individuals/ households (23.4% of the projected 2040 population) are the comparison group (as they are the least financially constrained). Note that low-income households are those earning less than $30,000 per year, while the high-income households are those earning greater than $100,000 While is it certainly important to consider the impacts on middle income groups, our emphasis in this case study demonstration is on presenting the results for the most and least financially constrained income groups.

Indicators

The indicators evaluated are commute tour travel time (for one direction of the tour) and logsum accessibility/consumer surplus (reflecting all work, university, high school and grade school purposes). Note that while we use commute travel purposes in this study, these equity indicators can be duplicated for other travel purposes (which may significantly affect final the results). This pair of indicators is selected because they are two of the most common indicators used in regional transportation equity analyses (MTC 2009, 2013a; SANDAG 2011) (although the more common measure for accessibility is the cumulative opportunity measure). Accessibility measurement is considered an important indicator for understanding the equity impacts of the transportation system (Lucas et al. 2016; Guthrie et al. 2017). Further, this pair of indicators will provide for a proof of concept of the usefulness of accessibility measures in comparison with a transportation service measure (i.e. travel time).

The logsum measure, in comparison to cumulative opportunity and gravity measures, is more sensitive to individual needs, which makes it suitable as an individual level measure of transportation benefits. Further, logsums can be forecasted over time, as they are an artifact of estimated changes in travel and land use attributes. The measure can be conveniently calculated from travel demand models (as detailed in Sect. Step 2: indicator calculations) and reflects both accessibility and consumer surplus. Further, the measure is sensitive to the travel attributes of multiple modes of transportation available to the traveler (including travel time and cost), and land use (employment) impacts (De Jong et al. 2007; Van Wee 2016). For these reasons, we propose that the logsum is overall desirable for fine grain equity analysis. The logsum also has a well-known challenge that requires a simplification when being applied to income classes. Given that a marginal utility of income measure is needed to calculate consumer surplus from a user’s travel utility function, and this marginal utility is systemically lower for high income travelers, this measure has the effect of biasing consumer surplus benefits in favor of higher income classes (for further discussion, see Martens 2006). For this reason, a common simplification is to apply a fixed measure of marginal utility of income across all income classes (Rosen and Small 1981; Kalmanje and Kockelman 2004). We adopt this approach to calculating logsum consumer surplus in this study (see “ Step 2: indicator calculations” section).

Step 2: indicator calculations

Here we discuss calculation of the two equity indicators: commute tour travel time and (logsum) accessibility (to employment). It is important to note here that these calculations reflect the Travel Model One specification. We do not alter the model specification in any way, and we only use data output from Travel Model One to calculate the indicators. The calculation processes using a different activity-based model may vary somewhat.

Travel time measure

We calculate the outbound tour-level commute travel times using the household location and (first) work location. We then attach the associated travel time estimate, based on the individuals travel time-of-day. These data are available from the travel model output; however, some data merging is necessary to join the relevant variables from the output files (income, travel mode, primary origin, primary destination, travel time-of-day (for the outbound travel)). Several scripts were developed to process the model files, using R Statistical and Matlab programming software.

Logsum measure

The logsum measure calculation involves the destination choice logsum calculated for mandatory tours purposes. The full sequence of calculations begins with higher-level choice dimensions (as illustrated in Fig. 2), with auto ownership, activity patterns, and time-of-day choices feeding into the mode choice models. The mode choice logsum is then used as a measure of impedance for the destination choice utilities. Our presentation of the logsum calculation begins with the mode choice model. Although Travel Model One performs many of these calculations automatically, it is useful to understand how demographic and land use variables enter the model structure. For more discussion on the model, see MTC (2011).

The Travel Model One mode choice model has a nested structure, where correlated modes are nested together. A total of 18 modes are represented in the structure, where the first level includes nests for private car, transit, and non-motorized modes, the second level splits auto modes by vehicle occupancy and transit modes by walk or drive access, and the final level splits the auto modes based on free vs. paid (tolled) mode alternatives and transit modes by specific line-haul types. These include, local bus, express bus, bus rapid transit, light rail, and heavy rail. The generalized formulation of such a nested logit logsum begins with the calculation of the mode choice logsum and is as follows:

$$mcLogsum_{ijae} = \ln \left( {\left( {\mathop \sum \limits_{l = 1}^{K} (\mathop \sum \limits_{{m \in B_{l} }} \left( {e^{{V_{ijmae} }} } \right)^{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\mu_{l} }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\mu_{l} }$}}}} } \right)^{{\mu_{l} }} } \right)$$
(1)

where \(mcLogsum_{ijae}\) is the mode choice logsum for origin i and destination alternative j, auto-ownership class \(a\), and income class e, and \(V_{ijmae}\) is the systematic utility for mode alternative m. Variables such as travel time, travel costs, and landuse variables enter into the systematic mode utilities. The travel time variables include in-vehicle and/or walk access for all modes, and access, auxiliary, egress, and wait times for transit modes. Travel costs variables include operating cost for all motorized modes, and toll and parking costs for single and high occupancy vehicle modes. There are no costs included for the non-motorized mode. Finally, the land use variables include area densityFootnote 1 and topology measures for non-motorized and transit modes. These land-use variables are not included for single and high occupancy vehicle modes.

The destination choice logsum is then calculated as follows:

$$dcLogsum_{jaep} = ln\left( {\mathop \sum \limits_{j \in D} e^{{\left( {mcLogsum_{ijae} \beta_{mcLogsum} + ln\left( {size_{jep} } \right)\beta_{size} } \right)}} } \right)$$
(2)

where \(dcLogsum_{jaep}\) is the destination choice logsum for location j, auto-ownership class \(a\), income class e, and person-type p; \(\beta_{mcLogsum}\) is the parameter associated with the mode choice logsum, and \(\beta_{size}\) is the parameter associated with the log-size term, \(\it {\text{ ln}}\left( {{\text{size}}_{{{\text{jep}}}} } \right)\). The size term is a linear-in-the-parameters function of total employment activity in zone j, split by employment sector, for workers and by school level for students. The employment sectors include trade and retail, financial and professional services, health, educational and recreational services, agricultural and natural resources, and manufacturing and transportation. Additionally, the size term (for workers only) varies by income. School levels include grade school, high school, and university levels.

The logsum measure is then calculated as follows:

$$CS_{jaep} = \left( {\frac{1}{\alpha }} \right)\left[ {dcLogsum_{jaep}^{1} - dcLogsum_{jaep}^{0} } \right]$$
(3)

where \(\alpha\) is the marginal utility of income and the superscripts 0 and 1 refer to the No-Project scenario and a project scenario, respectively. This step of calculating consumer surplus from the logsums is completed manually. Each household is then assigned a logsum value for each scenario. Finally, the change in the logsum is calculated for each household, with respect to each planning scenario.

The marginal utility of income parameter is the scaled cost parameter from the mode choice model. Because of this nested-like model structure of the mode and destination model components, it is necessary to adjust the mode choice cost parameter (or marginal utility of income) to the scale of the destination choice utilities. The expression for the marginal utility (Kalmanje and Kockelman 2005) is as follows:

$$\alpha = \beta_{mcLogsum} \beta_{OPcost}^{{}}$$
(4)

where \(\beta_{OPcost}^{{}}\) is the parameter associated with travel operation costs from the mode choice model. This formulation can be easily understood if we consider that \(\beta_{OPcost}^{{}}\) is actually multiplied by the mode choice scale parameter \(\mu_{mc}\) and \(\beta_{mcLogsum}\) is actually the ratio of the destination choice scale parameter to the mode choice scale parameter, \(\mu_{dc} /\mu_{mc}\). Therefore, Eq. (4) gives us the re-scaled mode choice cost parameter: \(\mu_{dc} \beta_{OPcost}^{*} = \mu_{mc} \beta_{OPcost}^{{}} * \mu_{dc} /\mu_{mc}\). For a full discussion of scale parameters of discrete choice models, see Train (2009).

Constraints and implications

Activity-based travel models operate on fully synthesized populations, as described in “Overview of activity based modeling systems” section. In fact, a new population is generated for each new scenario run. Given the aim to assess transportation and land-use changes at individual and household levels, it is necessary to make some constraints on the synthesized population. We use the synthetic population generated for the No-Project scenario and attach the new travel times and accessibility estimates from the Jobs-Housing and Transit Priority scenarios. The effects of these constraints are reflected in the “short-term” analysis results, where we assume that an individual’s demographic characteristics and residential location will remain the same across the three scenarios. In the “long-term” analysis results, all constraints are relaxed, meaning that the synthesized population generated for its corresponding scenario run is applied.

The types of constraints (relevant to the “short-term” analysis results) vary based on the equity indicator:

  • Travel Time Indicator: Regarding commute tour travel time, the household residential location, work location, travel mode, and travel time-of-day are constrained to be the same across model runs, for each traveler. This means that for the different scenarios, only the travel time estimate varies. The implication is that the choices of residential location, work location, travel time-of-day, and travel mode are not influenced because of transportation and land-use changes. We recognize that this is a strict assumption, as an individual may certainly choose to take rail transit to work (instead of auto), leave for work at an earlier time, or even change work locations due a new congestion pricing policy, for example. As a result, the share of travelers experiencing a reduction in travel time as well as and their magnitude of loss may be overestimated to some degree.

  • Logsum Indicator: Regarding the accessibility/consumer surplus measure, we constrain household locations to be the same across scenarios. Although this still allows for mode and destination choices to change, this restriction means that the transportation and land-use changes for each scenario have no impact on residential location choice. This may introduce a bias, as households may realistically choose to relocate due to transportation and/or land-use changes. As a result, the shares and magnitudes of losses and gains may be over or underestimated. The direction of this bias is not immediately clear and will require further investigation.

Step 3: distributional comparisons

In the following sections, we discuss the analysis of the two equity indicators—commute travel time and “mandatory” consumer surplus—for the two MTC scenarios: Transit Priority and Jobs-Housing scenarios. Note that the original data analyzed in this study is made available via MTC’s data portal (MTC ABAG 2022).

For comparison purposes, we first compute the average indicator values, under short-term and long-term conditions (Tables 2 and 3). The target and comparison groups are first segmented using MTC’s Communities-of-Concern (COC)Footnote 2. This is to represent the standard practice for regional transportation equity analysis. We also present the average indicator results for groups segmented by income class, at the zonal and individual levels (Table 2). The goal of this gradual progression from aggregate unit of segmentation to disaggregate, is to facilitate (to the extent possible) a clear discussion of the advantages of disaggregate analysis. Further, the separation between short-term and long-term results is to gauge the effect of the indicator constraints. We then discuss the results from the distributional measure comparisons (Figs. 3A–D).

Table 2 Average Commute Travel Times for Communities of Concern versus Non-Communities of Concern (Minutes)
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Table 3 Mandatory consumer surplus for low income versus high income households ($)
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Fig. 3
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A–D Individual Difference Comparisons (Logsum Consumer Surplus) Transit Priority Scenario A, Jobs-Housing Scenario B, and Individual Difference Comparisons (Commute Travel Time) for Transit Priority Scenario C and Jobs-Housing Scenario D

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Averages of equity indicators

The average commute travel times shown in Table 2 provide the baseline estimates of travel times experienced for travelers residing in COC and non-COC zones. For validation purposes, it is useful to note that these estimates for the long-term scenarios are comparable to the average commute time values from MTC’s 2013 Transportation Equity analysis (MTC 2013a). Non-COCs experience a higher average travel time compared to COCs, and the non-COCs experience a greater percent reduction in travel times, across the two scenarios. However, COCs experience a significantly greater reduction in average travel time in the Transit Priority Scenario relative to the Jobs-Housing scenario, while non-COCs experience the same change in average travel times for both scenarios. The short-term scenario estimates are largely consistent with those of the long-term estimates. The difference is that travelers would experience slightly greater reductions in average travel time, in the short term. These differences in average travel time reductions are minimal, with a range of 0.7% to 3.5% lower average travel times for the short-term estimates relative to the long-term estimates. This suggests that travel time impacts are slightly more pronounced in the short-term, given the constraints on behavior (described in “Step 2: indicator calculations” section).

The average commute travel times by zone are segmented according to low-income household density, rather than COCs versus non-COCs. That is, if a zone has 30% or more low-income households, then it is labeled as a low-income community. Low-income households are classified by MTC as households earning less than $30,000 annually, and the commute travel time averages for all households residing in low-income communities are compared with the average travel times for all remaining communities. Based on this zonal group definition, the most noticeable difference is with the low-income zones. The average travel times for all other income classes (“All Other Zones”) are very similar to that of the non-COCs, while low-income zones experience a greater percent reduction in average travel times, relative to COCs. For the short-term scenarios, the trend describing the difference between low-income communities versus all other communities is consistent with that of the travel time estimates for COCs versus non-COCs, where the average travel times and percentage changes for the vulnerable group is comparatively lower.

The average commute travel times for all low income and high-income travelers (individual segmentation) shows that low-income travelers experience commute travel times more like that of high-income travelers, as compared to the estimates from the previous segmentation definitions. The short-term estimates are particularly interesting, with low-income travelers experiencing greater percent reductions in travel time, relative to high income travelers. In the long-term, high-income travelers experience greater reductions in travel times, which is consistent with that of the previous segmentation definitions.

Lastly, the average consumer surplus estimates (Table 3) are associated with short-term and long-term conditions, for low-income and high-income households. The estimates show that both income groups experience little increase in consumer surplus in the short term (on average), while they experience significantly greater increases in the long term. This result follows the intuition that location choices are constrained in the short term, meaning that households and individuals are limited in choosing the location alternatives that would provide a greater benefit for them. Nevertheless, under these conditions both income groups experience some benefit, with high income households experiencing greater percent increases in the short term. Under long-term conditions, low-income households experience comparatively greater increases in consumer surplus.

Distributions

Figure 3A and B show the Individual Difference Density comparisons of accessibility, for the two scenarios. Data points to the right of the origin indicate increases in accessibility/consumer surplus, while points to left of the origin indicate decreases. For both scenarios, the curve for low-income households falls to the left of the curve for high income households, indicating that low-income households are more likely to experience smaller increases and greater reductions in accessibility, relative to high income households. The Transit Priority scenario distribution is bimodal for low-income households. The interpretation is that there is a density of households experiencing small increases and small decreases, with fewer experiencing no change at all. The computed shares of households experiencing loses in accessibility (shown in Table 4) show that low-income households are most likely to experience a decrease in accessibility, for both scenarios. In the most extreme case, as many as 33.3% of low-income households experience a loss in accessibility/ consumer surplus, compared to 13.4% for high income households.

Table 4 Share of households who experience a decrease in accessibility ($)
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The distributional measure comparisons in Fig. 3C and D reveal additional information about the travel time related impacts on the two income classes, beyond what is indicated by the average measures. When we compare the impacts across comparison groups, we observe that low-income travelers are less affected by the scenario changes, relative to high income commuters. The Individual Difference density comparisons reveal that the share of low-income commuters experiencing an increase in travel time is at least 19.2% for both cases, as compared to 25.5% for high income commuters (Table 5).

Table 5 Share of commuters experiencing an increase in commute travel time (%)
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Step 4: equity standards and scenario ranking

Here we present the results of applying three equity standards for ranking the two planning scenarios. Our objective here is to select the “better” option, based on the expected transportation and landuse changes from the planning scenarios. These standards include Equality, Proportionality, and Rawlsian Justice. To do this, it is necessary to interpret these theoretical concepts using reasonable numerical criteria. In fact, of the large number of equity standards found in the literature, these three standards are selected for this demonstration because of their relative ease of identifying intuitive numerical ranking criteria, given the data available in this case study. We apply these standards using the average logsum accessibility measure only, as the units of this measure can easily be translated to monetary units and more clearly represent relative costs and benefits. While individually distributed equity indicators are not extended for our implementation of these equity standards, this exercise tests the effects equity standards can have on scenario ranking outcomes.

The development of numerical criteria that aligns with a given equity standard is a non-trivial process and requires more detailed treatment that goes beyond the scope of the current paper. In the absence of more detailed treatments of theoretical equity standards, this evaluation employs simplistic criteria motivated by descriptions of the given equity standard in the available literature. For example, our use of the Rawlsian Justice standard is simplified and based on criteria that is motivated by Rawl’s 2nd principle, but deviates from Rawl’s original difference principle in this demonstration.

It is important to note that scenario ranking according to equity standards is implemented here as a part of the scenario selection. However, the process of defining the standard of equity (i.e. what equity means for the region) is a more central step, should take place initially, and should guide each step in the equity analysis framework. This process of defining transportation equity for the region should follow from an engagement process with community stakeholders, similar to what is highlighted in Karner and Marcantonio (2018).

Equality

Equality refers to an allocation that is equal for all groups of interest, regardless of need or utility (Miller 1979; Forkenbrock 2001). In this case, the allocation refers to the measured individual-level increments (positive or negative) or changes associated with the implementation of the transportation planning scenario. Yet, the equality standard is well suited for evaluating the final allocation resulting from the scenarios, which is distinguished from the increments. The decision of whether to evaluate the changes in a measure or the final allocation is tied to the overall objective of the transportation equity analysis and should be determined through the region’s community engagement process. In this study, the equality standard criteria is applied to the average per person consumer surplus, which reflects the increments associated with the planning scenarios.

Our equality criteria defines the priority scenario as the one with the smallest difference between the two income classes; the ratio of group benefits that is closest to 1. The results (Table 6) show that the Transit Priority scenario results in the ratio of benefits closest to 1 and would therefore be the top ranked scenario.

Table 6 Equality standard results
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Proportionality

Proportional equity refers to an allocation that is proportional to the share that a group represents with respect to the total population (Young 1995; Forkenbrook and Sheeley 2004, Martens et al. 2012). This standard suggests that the more equitable scenario is the one that results in the smallest difference between the groups’ share of benefits and the groups’ share of the total population. We calculate the ratio of the shares of group benefits and the group shares of the population. The results (Tables 7 and 8) show that the Transit Priority scenario results in the most proportional allocation of benefits, for both income groups, as both group’s ratios are closer to one. Yet, we also observe that the allocation is more proportional for high-income groups in both planning scenarios, relative to the low-income groups. The low-income group allocations are below the equitable proportions by 17.1% (1 − 0.829 = 0.171) and 18.7%, for the Transit Priority and Job-Housing scenarios, respectively. In comparison, the high-income groups allocation is above by 10.9% and 16.7% prospectively. While we interpret the priority scenario as the one that both groups share of benefits is most proportional, this ignores the fact that the high-income group experiences a higher proportional allocation for both scenarios. Further, one can imagine cases where the choice of priority scenario is not so straight forward; where one scenario is proportional for one group, but not the other. This implies the need for further refinement or extension of the proportionality standard to include consideration for the degree of proportionality.

Table 7 Proportionality results for the transit priority scenario
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Table 8 Proportionality results for the jobs-housing scenario
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Rawlsian justice (2nd principle)

The Rawlsian Justice standard refers to an allocation in which the greatest level of benefit is maximized for the most disadvantaged group (Oberdiek 1972). Although not a strict application of Rawls 2nd principle, our interpretation of this standard defines the low-income group as the most disadvantaged and we select the top scenario as the one in which the low-income group accrues the highest level of consumer surplus ($). In contrast to the Equality and Proportionality standards, we can see in Table 6 that the Jobs-Housing scenario results in the greatest per person consumer surplus for low-income travelers and is therefore the top ranked scenario, according to Rawlsian Justice.

Discussion

The results of this study point to four notable areas of discussion on next steps for advancing the practice of regional transportation equity analysis.

First, our results show that low-income households experience lower travel time reductions, although this can vary due to how the comparison groups are segmented (i.e. zones vs individuals/households). The distributional measures (and share of travelers experiencing reductions by individual difference comparisons) explain that this is likely due to low-income households being more likely to experience reductions in consumer surplus over time. This suggests an important complementary role of distributional measures in explaining the overall direction of benefits. The distributional measures add an additional lens by revealing more potentially harmful outcomes, where the disadvantaged travelers are most likely to experience negative outcomes of the scenarios.

Second, the results from our average comparisons, distributional measure comparisons, and scenario ranking by equity standards seem to point to different scenarios as the one most beneficial for low- and high-income travelers. We find that in most cases, the Transit Priority scenario performs better for low-income travelers while the Jobs-Housing scenario performs better for high income travelers. Although in isolation, the three sets of analyses tell different stories. If we use an implicit equality lens to evaluate measures calculated in step 3, the average travel time comparisons suggest that the Transit Priority scenario is better for low-income travelers, while the accessibility and distributional measure comparisons seem to point in the opposite direction, with both income groups more likely to experience losses from the Transit Priority scenario. In step 4, the scenario ranking by equality and proportionality standards also seem to support the Transit Priority scenario for low-income travelers, while the Rawlsian Justice standard points to the Jobs-Housing scenario. Disentangling the reasons for these results will require a more detailed breakdown of projects built into the regional plans. Among other potential differences, these varying results seem to suggest a divergence in the benefits from transportation system changes (as measured by the travel time measures) versus the benefits from land-use changes (as captured by the accessibility/consumer surplus measures).

Third, our exercise in applying equity standards for scenario ranking shows that the top ranked scenario can vary based on the standard, as well as by comparison group. Yet, our application of equity standards presents some challenges that point to a need to more rigorous review and definition of the equity standard criteria. The proportionality standard produces seemingly ambiguous results in our case. The lack of clarity on how to rank scenarios if benefits for all comparison groups do not satisfy the equity standard, suggests a need for further refinement of the proportionality standard criteria; perhaps to include consideration for the degree of proportionality. Further, investigation is warranted on how the results based on equality criteria may change of applied to the final allocation, rather than the allocation of the increments (as is done in this case).

Finally, it is important to recognize that the results from this analysis may be artifacts of the transportation projects and policies included in the two regional planning scenarios. In this study, we post-analyze scenarios that underwent a development process by MTC. For example, our explicit inclusion of equity standards (step 4) is done after calculating and evaluating equity measures based on the planning scenarios (step 3). Our adopted framework builds iteratively on existing travel demand and scenario analysis practices, however, this should not be taken as a suggestion that the integration of equity standards should be decoupled from the full planning process and conducted after scenarios are developed and measures are selected. We fall short of developing planning scenarios that align more closely with regional equity goals, but planners and practitioners should continue to consider how to further integrate equity into all planning scenarios, from the beginning of the planning process. We expect that a deeper integration of equity principles in the planning process is likely to produce more equitable results.

Conclusions

In this paper we have demonstrated how equity analysis can be conducted using an activity-based travel demand model. We use a full-scale activity-based travel modeling system and real-world transportation and land-use scenarios developed by the Metropolitan Transportation Commission of the San Francisco Bay area and evaluate the equity impacts of two planning scenarios for low-income travelers, relative to high income travelers. The indicators used to measure equity impacts include commute travel time and mandatory logsum accessibility/consumer surplus. We have discussed key features of activity-based travel models that are advantageous for equity analysis and tested equity outcomes of MTC’s planning scenarios relative to three specific equity standards: equality, proportionality, and Rawlsian justice. This case study analysis provides three important contributions to the practice of transportation planning, including a demonstration of distributional measure comparisons using realistic planning scenarios, documentation of the steps necessary for calculating distributional measures for equity analysis from an activity-based travel demand model, and evaluation of the role of equity standards in ranking planning scenarios.

Overall, our results show that comparisons of distributional measures can play a complementary role in equity analysis by helping to explain underlying reasons for average results, but each of the measures in isolation do not tell the complete story of how costs and benefits will be allocated. This suggests that distributional measures should reasonably be applied in conjunction with more general average measures. Further, the scenario ranking results confirm that the selection and application of various equity standards can have significant impacts on how plans are ranked.

Our results highlight four research directions important for advancing the practice of regional transportation equity analysis. First, further study is warranted to determine how equity analysis methods can be more tightly aligned with specific equity standards. Second, future study is warranted on how specific types of transportation-related investments may differentially affect the allocation of transportation cost and benefits, including transportation system improvements vs. land use and policy changes. Third, it is important that future studies go beyond income categories and work travel purposes and critically assess equity impacts using other segmentation variables, including ethnicity, gender, age, employment status, and education levels, as well as other non-mandatory trip purposes. Finally, it is important to determine the nature of equity analysis results based on absolute conditions vs. movement toward or away from defined equity goals.