Aggregating to Custom Geographies • urbnindicators

Census tracts are useful geographic units, but their small populations often produce estimates with large margins of error. When analyzing data, these imprecise estimates make it difficult to detect meaningful differences between areas—even when real differences exist.

calculate_custom_geographies() addresses this by aggregating tract-level (or really any level of data) data to user-defined geographies (e.g., neighborhoods, planning districts, or school zones). This aggregation increases sample sizes, reduces coefficients of variation, and enables more reliable statistical inference.

Example: DC Quadrants

We’ll demonstrate using tract-level data for Washington, DC, comparing the share of population receiving SNAP benefits across areas “quadrants”.

dc_tracts = compile_acs_data(
  years = 2024,
  tables = "snap",
  geography = "tract",
  states = "DC",
  spatial = TRUE)

Creating Custom Geographies

For illustration, we’ll create four quadrants of DC by grouping tracts based on their centroid coordinates. In practice, you would join tracts to meaningful boundaries like neighborhoods or planning areas, or you could group arbitrary numbers of adjacent tracts to form pseudo-neighborhoods with larger populations than are captured in any single tract.

# Calculate tract centroids and assign to quadrants
dc_tracts = dc_tracts %>%
  mutate(
    centroid = st_centroid(geometry),
    longitude = st_coordinates(centroid)[, 1],
    latitude = st_coordinates(centroid)[, 2],
    quadrant = case_when(
      longitude < median(longitude) & latitude >= median(latitude) ~ "Northwest",
      longitude >= median(longitude) & latitude >= median(latitude) ~ "Northeast",
      longitude < median(longitude) & latitude < median(latitude) ~ "Southwest",
      longitude >= median(longitude) & latitude < median(latitude) ~ "Southeast")) %>%
  select(-centroid, -longitude, -latitude)

# Aggregate to quadrants
dc_quadrants = calculate_custom_geographies(
  .data = dc_tracts,
  group_id = "quadrant",
  spatial = TRUE)

Comparing Precision

The maps below show the share of households receiving SNAP benefits. Notice how aggregating to quadrants produces more precise estimates with smaller coefficients of variation. Indeed, the median coefficient of variation for tract level is greater than 30, a common upper bound for “reliable” estimates.

# Tract-level map
  bind_rows(
    dc_tracts %>% mutate(geography = "Tract"),
    dc_quadrants %>% mutate(geography = "Quadrant")) %>%
  mutate(
    .by = geography,
    median_cv = round(median(snap_received_percent_CV, na.rm = TRUE)),
    label = str_c(geography, " - median CV: ", median_cv)) %>%
  ggplot() +
    geom_sf(aes(fill = snap_received_percent), color = "white", linewidth = 0.1) +
    scale_fill_continuous(palette = palette_urbn_cyan[c(3, 5, 7)], labels = scales::percent) +
    theme_urbn_map() +
    labs(fill = "SNAP Receipt (%)") +
    facet_wrap(~ label)

The quadrant-level estimates have substantially lower CVs, indicating more reliable estimates.

Detecting Statistically Significant Differences

By aggregating our tract observations, we can also calculate statistically significant differences at greater geographic scales. This enables analysis for more policy-relevant areas and helps mitigate shortcomings associated with high measures of error for smaller-population observations, which can lead to findings of no statistically significant differences.

# Calculate DC-wide SNAP rate for comparison
dc_snap_rate = sum(dc_tracts$snap_received, na.rm = TRUE) /
               sum(dc_tracts$snap_universe, na.rm = TRUE)

# Test significance at tract level
tracts_sig = dc_tracts %>%
  mutate(
    significant = tidycensus::significance(
      est1 = snap_received_percent,
      est2 = dc_snap_rate,
      moe1 = snap_received_percent_M,
      moe2 = 0.005,
      clevel = 0.9),
    difference = case_when(
      !significant ~ "Not significant",
      snap_received_percent > dc_snap_rate ~ "Higher than DC average",
      snap_received_percent < dc_snap_rate ~ "Lower than DC average"))

# Test significance at quadrant level
quadrants_sig = dc_quadrants %>%
  mutate(
    significant = tidycensus::significance(
      est1 = snap_received_percent,
      est2 = dc_snap_rate,
      moe1 = snap_received_percent_M,
      moe2 = 0.005,
      clevel = 0.9),
    difference = case_when(
      !significant ~ "Not significant",
      snap_received_percent > dc_snap_rate ~ "Higher than DC average",
      snap_received_percent < dc_snap_rate ~ "Lower than DC average"))

# Color palette
sig_colors = c(
  "Higher than DC average" = "#1696D2",
  "Lower than DC average" = "#FDBF11",
  "Not significant" = "#D2D2D2")

# Maps
map_tracts_sig = tracts_sig %>%
  ggplot() +
  geom_sf(aes(fill = difference), color = "white", linewidth = 0.1) +
  scale_fill_manual(values = sig_colors, na.value = "grey80") +
  urbnthemes::theme_urbn_map() +
  theme(legend.position = "bottom") +
  labs(fill = "", subtitle = "Tract-level", title = "")

map_quadrants_sig = quadrants_sig %>%
  ggplot() +
  geom_sf(aes(fill = difference), color = "white", linewidth = 0.3) +
  scale_fill_manual(values = sig_colors, na.value = "grey80") +
  urbnthemes::theme_urbn_map() +
  theme(legend.position = "bottom") +
  labs(fill = "", subtitle = "Quadrant-level", title = "")

gridExtra::grid.arrange(
  map_tracts_sig, map_quadrants_sig,
  ncol = 2,
  top = grid::textGrob(
    "Aggregation can mitigate challenges with small-population, high-error observations",
    gp = grid::gpar(fontsize = 12, fontface = "bold")))

Key Takeaways

Aggregation improves precision: Combining tracts into larger geographies reduces CVs and margins of error.
Better inference: More precise estimates enable detection of statistically significant differences that would otherwise be obscured by sampling error.
More relevant units of analysis: The ACS reports estimates at many geographies, but there are many others that are not supported. Think neighborhoods, wards, continuums of care, school districts, and more. To robustly calculate errors and draw reliable inferences for these other geographies is critical but challenging.