Cody Arlie ReedResearch + data
All projectsTravel communities and racial boundaries

Research project

Travel communities and racial boundaries

The questionHow are racial demographics and urban movement patterns related?

  • Large datasets
  • Network analysis
  • Fractional logit
  • Spatial inference

ApproachI built travel networks for 100 U.S. commuting zones and used fractional logits to test whether sharper changes in racial composition predict where travel-community boundaries recur across network partitions.

Overview

What I found

Sharper changes in racial composition are associated with more frequent travel-community boundaries in 52 of 100 commuting zones. Frequency here means recurrence across repeated partitions of the same travel network.

Racial gradients and travel-community boundaries

Direction of association · 100 U.S. commuting zones

PositiveIncludes zeroNegative
Combined gradient
52 positive · 47 include zero · 1 negative
Black
46 positive · 53 include zero · 1 negative
Asian
46 positive · 54 include zero · 0 negative
Hispanic
13 positive · 85 include zero · 2 negative
White
11 positive · 83 include zero · 6 negative
Multiracial / other
0 positive · 74 include zero · 26 negative
Boundary frequency is the share of 100 network partitions in which a block group borders another travel community. Bars classify its association with each racial gradient across commuting zones: positive or negative when the 95% confidence interval excludes zero.

Travel networks

Find travel communities and estimate how often their boundaries recur.

I converted 95.4 million mobile-location observations into travel networks for 100 U.S. commuting zones. Census block groups form the nodes; observed travel supplies the connections. I used the Leiden algorithm to identify groups with denser travel within them than between them.

I generated 100 partitions of each network. For each partition, a block group lies on a boundary if at least one neighboring polygon belongs to another community. Its boundary frequency is the proportion of partitions in which this occurs.

Boundary frequency and community size
bᵢ = (1 / 100) ∑ᵣ I(any neighbor of i belongs to another community in run r)

I tune the resolution toward a median community size of 50 block groups, with a maximum of 100 block groups per community and a merge step for small communities. When the target is infeasible, the tuning procedure selects the closest available result. I also compare size targets of 30 and 100 and a shorter optimization run.

Repeated partitions describe stability on the observed travel network.

Racial gradients

Estimate how racial composition changes across space.

I fit a local regression for each racial group around each block group, giving nearby places more weight. The two spatial coefficients describe how that group’s share of the local population changes toward the east and north. Together, they form a gradient: it points toward the steepest increase in that group’s population share, and its magnitude measures the rate of increase in percentage points per kilometer.

Black population share

Chicago Census block groups colored from purple for a lower Black population share to yellow for a higher share.
0%50%100%

Black racial gradient

The same Chicago area with arrows pointing toward increasing Black population share. Arrow lengths are proportional to the gradient magnitude.
Arrows point toward the steepest increase in the Black share of the local population. Longer arrows indicate steeper changes. Both maps show the same area of Chicago using 2020 Census data.
Gradients and spatial weighting
pₘ(x, y) ≈ αₘ + βₓ,ₘ x + βᵧ,ₘ y∇pₘ = (βₓ,ₘ, βᵧ,ₘ)‖∇pₘ‖ = √(βₓ,ₘ² + βᵧ,ₘ²)G = ∑ₘ ‖∇pₘ‖

Here pₘ is group m’s population share in percentage points, and x and y are local distances in kilometers. G adds the magnitudes of the five racial gradients. The Gaussian kernel uses σ = 1 km for the regression predictors and Chicago arrows, and σ = 0.5 km for the NYC map. The Chicago maps use the Census category non-Hispanic Black alone. Candidate neighbors come from the national population surface within 10 km.

The map displays G as a percentile among NYC block groups with estimates: 100 × (rank − 1) / (n − 1), using the lower rank for ties. The 90th percentile means a gradient as large as or larger than roughly 90% of NYC estimates. This rescales the map colors; the models use the underlying gradient values.

I also fit density-gradient models, which describe changes in people per unit area. Racial gradients describe changes in population shares.

New York City block groups colored from purple for lower racial-composition gradients to yellow for higher gradients, ranked within the city
More gradual changeSharper change
050100

Percentile within New York City

Where racial composition changes sharply · New York City

Colors rank the combined racial-composition gradient among NYC block groups with an estimate. Yellow indicates the sharpest local changes. Source: 2020 Census; my calculations.

Open full-size figure

Statistical modeling

Model the relationship between racial gradients and travel boundaries.

I fit fractional logits separately for 100 U.S. commuting zones, relating racial gradients to travel-boundary frequency across 138,940 block groups. I estimate standard errors with a Wendland kernel to account for spatial autocorrelation.

Results and checks

Sharper racial gradients often coincide with recurring mobility boundaries.

Sharper changes in racial composition are associated with more frequent mobility boundaries in 52 of 100 commuting zones. Black and Asian racial gradients each show this association in 46 commuting zones.

Model checks

I checked gradient and covariance calculations against independent implementations, recomputed boundary counts from saved memberships, and compared community sizes, sample coverage, and model specifications.

Download the commuting-zone model summary