Counterfactual mobility network embedding reveals prevalent accessibility gaps in U.S. cities

The study investigates inequality in access to urban venues arising from demographic differences in mobility behavior. Despite urbanization improving accessibility, pronounced gaps persist across gender, socioeconomic status, and ethnicity, driven by cultural, financial, and health factors. Prior work often relies on small surveys or correlation-based analyses that fail to control confounding, limiting causal interpretation and micro-level insight. The authors aim to quantify causal effects of demographics (gender, race, income, disability, education) on mobility frequency and facility accessibility across neighborhoods in six large U.S. metropolitan areas using large-scale SafeGraph mobility data (2019–2020). They further seek to move beyond aggregate statistics by developing CRANE, a counterfactual random-walks-based embedding method that disentangles confounding to reveal neighborhood- and POI-level accessibility gaps. This work addresses SDG goals by providing robust, transferable measures of inequality to inform urban policy.

The paper situates its contribution within extensive research on mobility inequalities. Gendered mobility studies show women visit fewer unique locations and travel shorter distances (Law, 1999; Gauvin et al., 2020; Ng and Acker, 2018). Socioeconomic status and age are associated with larger mobility ranges and diverse patterns (Frias-Martinez et al., 2012; Lenormand et al., 2015; Macedo et al., 2022). During COVID-19, poorer populations showed smaller reductions in mobility (Dueñas et al., 2021). Built environment factors like transit access and walkability influence mobility (Ryan et al., 2015; Sallis et al., 2018). However, many studies rely on small-scale surveys or hypothetical proximity models, introducing bias (Sharkey and Elwert, 2011; Hasthanasombat and Mascolo, 2019; Saxon, 2021). Large-scale mobility datasets (e.g., SafeGraph) enable more precise measurement (Kadar et al., 2020; Moro et al., 2021). Existing analyses are largely correlational and do not adequately account for confounding among demographic variables, limiting causal inference and micro-level understanding—gaps this study addresses via propensity score matching and the CRANE embedding approach.

Data: Demographic data come from the 2019 ACS 5-year estimates at the census block group (CBG) level, used as neighborhoods. The six MSAs studied are New York, Los Angeles, Chicago, Dallas, Houston, and Washington DC. Demographic features include female ratio, white ratio, bachelor’s degree ratio (age 25+), average household income, and disability household ratio; age structure (under 20, over 60) is also considered as covariates. Mobility data come from SafeGraph Monthly Patterns and Core Places datasets, aggregating monthly CBG-to-POI visits (workers excluded) and NAICS categories. Across MSAs, there are on average 155 million visits to 758k POIs per month. Mobility measures: For each CBG, mobility frequency (NM) is the total visits to POIs within the MSA (July–September) normalized per 100 residents. Mobility reduction (ΔM) is the change from 2019 to 2020, capturing COVID-19 impact. Facility accessibility is the proportion of a neighborhood’s visits to a given POI category (Art & Recreation, Sports, Education, Health) relative to its total visits. Propensity Score Matching (PSM): To estimate causal effects of each demographic feature T on outcomes Y (NM 2019, ΔM 2020, and category access proportions), the authors control for confounders X (other demographic features and age structure). Treatments are discretized into five equally sized levels L(T). An ordinal regression maps covariates X to a scalar propensity score b(X)=w^T X satisfying that L(T) and X are independent conditional on b(X). Neighborhoods are matched by minimizing the distance defined as the difference in propensity scores divided by the difference in treatment levels. The average treatment effect (ATE) is computed as the average difference in outcome Y across matched pairs when L(T) increases by one level. This balances covariates and isolates the effect of each demographic feature. CRANE: Counterfactual Random-Walks-based Embedding: To capture micro-level disparities and enable downstream prediction, the authors construct a heterogeneous urban mobility network with nodes for POI categories, POIs, neighborhoods, and demographic treatment levels; edges include POI-category, neighborhood-demographic, and weighted neighborhood–POI edges by visitation frequency. Counterfactual random walks sample paths Q→P→Co→o (category, POI, observed neighborhood, observed outcome) where Co is sampled proportional to its normalized visitation to P, and o is Co’s treatment level for the demographic of interest. To generate a counterfactual alternative outcome a, they sample Ca from neighborhoods with identical stratified covariates to Co (mimicking PSM) and take its treatment level. Observed outcomes are treated as positive samples; counterfactual outcomes as negatives. The embedding learning maximizes similarity among co-occurring observed components (category, POI, neighborhood, observed outcome) and minimizes similarity for alternatives, using a logistic loss over inner products. Regularization enforces spatial smoothness of neighborhood embeddings (weighted by exp(-d^2/(2σ^2)) for neighborhoods within 2.5 km) and continuity across adjacent treatment levels L(T). Embeddings are 64-dimensional; optimization uses Adam; regularization strengths are 0.0001 (spatial) and 0.01 (demographic continuity). Convergence and consistency with PSM are evaluated by comparing observed vs alternative outcome distributions and regression of proximity between category and L(T) embeddings against PSM effects.

• Mobility frequency (pre-COVID, 2019): Higher average income and higher white ratio are causally associated with higher mobility frequency across MSAs. Income has strong positive effects: a one-level increase in L(income) corresponds to about 30 more visits per 100 residents over three months. After controlling confounders, higher bachelor’s ratio shows significantly lower mobility frequency in most MSAs, reversing simple correlation results.
• Mobility reduction during COVID-19 (2020 vs 2019): Neighborhoods with higher bachelor’s ratios experienced greater mobility reductions in all six MSAs, consistent with greater telework capacity. Neighborhoods with higher white ratios had smaller mobility reductions in all six MSAs, widening pre-existing accessibility gaps.
• Facility accessibility gaps:
  • Art & Recreation: More accessed by neighborhoods with higher bachelor’s ratios; effects exceed 0.2 percentage points in New York and Washington DC.
  • Sports: More accessed by higher income, higher bachelor’s ratio, and higher white ratio neighborhoods; accessibility is lower where disability ratios are higher, indicating barriers for disabled residents.
  • Education: More accessed by higher income, higher disability ratio, and higher white ratio neighborhoods, and less by higher bachelor’s ratio neighborhoods; indicates advantages for wealthier and white populations.
  • Health: More accessed by neighborhoods with higher disability and female ratios; in Chicago, Dallas, Houston, and DC, lower-income neighborhoods have higher proportions of health visits, potentially reflecting differing healthcare needs and modalities.
• Causal vs correlational analysis: PSM corrects confounding; for example, in New York the bachelor ratio’s correlation with art access is negative, but its treatment effect becomes positive after controlling for covariates. Across 77 significant demographic-category pairs, 92.2% show consistent directions between PSM treatment effects and CRANE embedding proximity regressions.
• CRANE validation and performance:
  • Counterfactual random walk approximation converges: violations relative to PSM drop below 10% when sampling ≥100,000 walks per category; authors use 200,000.
  • Within-city prediction: CRANE embeddings improve explained variance over raw features and correlation-based embeddings in 20/24 tasks. Examples of relative improvement over raw features: New York Art & Recreation +37.18%, Chicago Art & Recreation +33.66%, Dallas Sports +7.29%. Average improvement reported is 12.57%.
  • Cross-city transfer (to Chicago): CRANE achieves best performance in 16/20 tasks, notably for Art & Recreation and Sports, indicating transferable micro-level causal structure.
  • POI-level case study (Houston): CRANE disentangles confounding between income and white ratio, retrieving sports POIs favored by high-income neighborhoods even in lower white ratio areas, which raw statistics missed.

The findings directly address the research goal of quantifying causal effects of demographics on mobility outcomes and facility access. By controlling for confounding via PSM and embedding counterfactuals into CRANE, the study reveals robust, consistent accessibility gaps: higher income and white neighborhoods enjoy higher mobility frequency and greater access to sports and education venues, while bachelor’s-heavy neighborhoods travel less generally but reduced mobility more during COVID-19. Health facility access patterns align with higher disability and female ratios, highlighting care burdens. These causal insights move beyond aggregate correlations, illuminating mechanisms at neighborhood and POI levels and enabling prediction and cross-city transfer. The results underscore structural inequities and inform policy levers such as improving affordable transportation, expanding equitable access to sports and educational facilities, and targeting support during crises to groups with limited remote-work capacity. Embedding-based representations provide a practical tool for planners to map and monitor micro-level gaps, guide POI siting, and design interventions resilient to confounding and distribution shifts.

This work contributes a causal framework for measuring urban mobility inequality using large-scale mobility traces, combining propensity score matching for MSA-level treatment effects with CRANE, a counterfactual random-walks-based network embedding that captures neighborhood- and POI-level accessibility gaps. The approach reveals consistent income and racial advantages in mobility frequency and access to sports and education, a higher COVID-19 mobility reduction among bachelor’s-heavy neighborhoods, and health access patterns tied to disability and gender. CRANE aligns with PSM, improves neighborhood-level accessibility prediction within and across cities, and uncovers POI-level causal patterns obscured by correlations. Future research directions include incorporating spatial infrastructural factors (e.g., transit networks, road structures) via natural experiments, assessing post-2021 recovery inequalities in mobility resilience, and leveraging embeddings for equitable POI recommendations and site selection to promote equal access.

• Potential omitted variables: Spatial factors such as road network structure and public transportation availability may also influence mobility and accessibility but were not included as covariates; the focus was on demographic attributes that shape residential context.
• PSM provides aggregate (MSA-level) treatment effects and relies on observed covariates; unobserved confounding cannot be fully ruled out.
• Data access limitations: SafeGraph datasets are restricted under license; although large-scale and detailed, representativeness constraints may exist. The study period centers on 2019–2020, capturing pandemic onset but not longer-term recovery dynamics.