# Families of places: report

Chapter 10.2 of ZIP Code Destiny, by Vishal Singh (NYU Stern). Generated from the chapter's data files; the reading version is at https://vishalsingh.org/zipcode/families-of-places. Table n of this report is figure n of the chapter.

## Identification

- Title: Families of places
- Label: Sorting instead of ranking
- Chapter: 10.2 (Part X, How the estimates are made; Methods and sources)
- Question: Which groups of neighborhoods share a deprivation profile, and how do the groups differ?
- Dek: Among 4 families of census tracts sorted on deprivation measures alone, life expectancy for deaths in 2010 to 2015 runs from 74.7 years in the high-poverty family to 81.7 years in the high-income family.
- Grain: neighborhoods
- Status: published
- Published: 2026-10-09
- Updated: not revised
- Data sources:
  - American Community Survey. ACS 5-year estimates 2019-2023 for 2020 tracts and counties: the 15 deprivation measures, from the staged tract file and the Census API pull of housing, occupation, income-distribution and schooling tables; years: 2019-2023 (5-year); weights: ACS 2019-2023 tract population
  - Area Deprivation Index. Area Deprivation Index 2023 (v4.0.1) national rank, tract values averaged from block groups, used to number the families and to form deciles; years: 2023 release (version 4.0.1; built on ACS 2019-2023); weights: ACS 2019-2023 tract population
  - USALEEP life expectancy. NCHS small-area life expectancy at birth, deaths in 2010 to 2015, 2020 tracts (area-weighted), institutional tracts left out; years: 2010-2015; weights: ACS 2019-2023 tract population
  - Opportunity Atlas. Adult household income rank of children born 1978 to 1983 raised in families at the 25th income percentile, 2020 tracts; years: 1978-1983 birth cohorts (2018 release); weights: ACS 2019-2023 tract population
  - CDC PLACES. CDC PLACES 2024 release (BRFSS 2022): diabetes, current smoking and fair or poor health among adults, modeled prevalence; years: 2024 release (tracts); 2025 release (ZCTAs, 2023 data year); weights: ACS 2019-2023 tract population
- Canonical URL: https://vishalsingh.org/zipcode/families-of-places
- Report: https://vishalsingh.org/zipcode/families-of-places/report
- Markdown: https://vishalsingh.org/zipcode/families-of-places/report.md
- BibTeX key: singh2026familiesofplaces

```bibtex
@misc{singh2026familiesofplaces,
  author = {Singh, Vishal},
  title = {Families of places},
  year = {2026},
  url = {https://vishalsingh.org/zipcode/families-of-places},
  note = {In ZIP Code Destiny. Published 9 October 2026.}
}
```

## Principal estimates

The facts the dek and the opening prose cite, in order of appearance.

| Estimand | Population | Period | Value | Interval | n | Weights | Source | Fact id |
| --- | --- | --- | ---: | --- | ---: | --- | --- | --- |
| definition: the number of families the chapter uses | k-means fits compared | ACS 2019-2023 | 4 |   |   | none (definition) | American Community Survey | k |
| population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | deaths in 2010 to 2015 | 74.7 | 95% CI 74.5 to 74.9 | 12,903 tracts | ACS 2019-2023 tract population | USALEEP life expectancy | f4_le |
| population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the high income family | deaths in 2010 to 2015 | 81.7 | 95% CI 81.5 to 81.8 | 16,221 tracts | ACS 2019-2023 tract population | USALEEP life expectancy | f1_le |
| count of tracts clustered | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 | 75,717 |   |   | none (full count) | American Community Survey | n_tracts |
| count of measures (definition) | deprivation measures given to k-means | ACS 2019-2023 | 15 |   |   | none (definition) | American Community Survey | n_measures |
| difference between the population-weighted mean life expectancy of the high-income and the high-poverty family, bootstrap interval over counties with shared draws | residents of tracts in the high-income and high-poverty families | deaths in 2010 to 2015 | 6.9 | 95% CI 6.7 to 7.2 | 75,717 tracts | ACS 2019-2023 tract population | USALEEP life expectancy | le_gap_14 |
| population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | deaths in 2010 to 2015 | 78.6 | 95% CI 78.1 to 79.0 | 6,587 tracts | ACS 2019-2023 tract population | USALEEP life expectancy | f2_le |
| population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the mid-range family | deaths in 2010 to 2015 | 78.6 | 95% CI 78.5 to 78.7 | 36,163 tracts | ACS 2019-2023 tract population | USALEEP life expectancy | f3_le |
| difference between the population-weighted mean ADI national rank of the mid-range and the crowded-renter family, bootstrap interval over counties with shared draws | residents of tracts in the mid-range and crowded-renter families | 2023 release on ACS 2019-2023 | 16.3 | 95% CI 8.4 to 22.6 | 75,717 tracts | ACS 2019-2023 tract population | Area Deprivation Index | adi_gap_32 |
| mean silhouette of the four families, interval from the sampling error of the sample | a seeded random sample of tracts in the frame | ACS 2019-2023 | 0.21 | 95% CI 0.21 to 0.21 | 10,000 tracts | none (each tract counts once) | American Community Survey | sil_k |
| mean silhouette of the 4-group k-means fit to simulated data with no clusters (mean of 3 draws) | a seeded random sample of tracts in the frame | ACS 2019-2023 | 0.12 |   | 10,000 tracts | none (each tract counts once) | American Community Survey | sil_null_k |
| within-group sum of squares of the best different arrangement relative to the fit that defines the families | census tracts in the frame | ACS 2019-2023 | 1.1% |   | 75,717 tracts | none (each tract counts once) | American Community Survey | alt_excess |

## Findings

K-means sorts the 75,717 census tracts of the frame into 4 families on 15 of the measures that the Area Deprivation Index (ADI) combines. The families differ by 6.9 (95% CI 6.7 to 7.2) years of life expectancy at birth between the longest-lived and the shortest-lived, for deaths in 2010 to 2015, and the sort never used life expectancy.

Two of the families show no detectable difference in life expectancy, 78.6 years for the crowded renters and 78.6 years for the mid-range family. The crowded renters also do no better on adult income rank or on modeled estimates of diabetes, smoking and self-rated health, although the ADI scores them as less deprived than the mid-range family by 16.3 (95% CI 8.4 to 22.6) points on its national rank.

The families are regions of a continuum and not separate clusters. The silhouette, a score of how well tracts fit their own group against the nearest other, is 0.21 for the four families, against 0.12 for simulated data with no clusters. A second arrangement of four groups has only 1.1% more within-group variance.

This chapter chooses the number of families, describes them, compares them with outcomes held out of the sort and with deciles of the ADI, and labels counties by the family they resemble.

Related material is in other chapters. Chapter 1.1, What the deprivation index measures (https://vishalsingh.org/zipcode/anatomy-of-deprivation) rebuilds the ADI from these measures and shows how much of its weight falls on home value. Chapter 9.2, Eight types of neighborhood (https://vishalsingh.org/zipcode/eight-types-of-neighborhood) sorts tracts on income, poverty, education, family structure, tenure, age and density, with no outcome among its inputs, so its types separate places by how they are settled as well as by their resources, while the families here use deprivation measures alone. Chapter 10.1, Gradients, slopes and variance (https://vishalsingh.org/zipcode/gradients-slopes-and-variance) covers the slopes of outcomes on the ADI and the split of variance among states, counties and tracts, and Chapter 1.2, What a county average leaves out (https://vishalsingh.org/zipcode/deprivation-at-two-zooms) repeats the index for counties.

### The measures and how they are sorted

The frame is the one that Chapter 1.1, What the deprivation index measures (https://vishalsingh.org/zipcode/anatomy-of-deprivation) uses, the 75,717 tracts of the 2020 census that have a published ADI rank, residents and all 15 measures. They hold 307.1 million residents, 93.0% of the residents of tracts with a rank in the states and the District of Columbia. Puerto Rico's 981 tracts are outside the frame, as they are in that chapter. The measures come from the American Community Survey (ACS) for 2019 to 2023. The measures of advantage are median family income, median home value, median gross rent, the monthly mortgage cost, the white-collar share of workers and the homeownership rate. The measures of hardship are the poverty rate, the near-poverty share, income disparity (the log ratio of low-income to high-income households), unemployment, the single-parent share, the share of households without a vehicle, crowding, homes without complete plumbing and the share of adults with under 9 years of schooling.

Each measure is standardized, which means subtracting its mean across tracts and dividing by its standard deviation, so that a dollar amount and a proportion count equally. K-means then places 4 centers in the space of the standardized measures so that the total squared distance from each tract to its nearest center is as small as it can be made,[1]

$$
\min_{c,\ \mu}\ \sum_{i} \lVert z_i - \mu_{c(i)} \rVert^{2},
$$

where $$z_i$$ is the vector of standardized measures for tract $$i$$, $$\mu_j$$ is the center of family $$j$$ and $$c(i)$$ is the family that tract $$i$$ is assigned to. The fit starts from many random sets of centers and keeps the best. Each tract counts once, so a family is a family of places and not of people. Residents return as weights in every profile and outcome mean below.

The ADI is not an input, but it is built from the same ACS measures, so the sort and the index share their raw material. Life expectancy, adult income rank and the health measures from PLACES are also outside the sort. They come back below as held-out outcomes.

### Four families depart most from a cloud with no clusters

The data do not say how many groups there are, and k-means returns a partition for any number. Table 1 compares fits with 2 to 10 groups on the silhouette, computed on a seeded sample of tracts.[2] The silhouette of the tract data is 0.22 for two groups, 0.21 for four and 0.15 for five, so it is no higher for four groups than for two and drops after four. Taken alone it favors two groups.

A positive silhouette does not show that groups exist, because k-means divides any cloud into parts and some of them look separate. The build therefore fits the same k-means to simulated data as well. The simulated clouds keep the distribution of each measure, including its skew and its top codes, and the correlations among measures, but their dependence is a single multivariate normal cloud with one dense core. At two groups they score 0.21, nearly the same as the tract data, which means the high silhouette at two groups comes from the shape of the cloud and not from groups in it. The sample silhouette has a margin of error of at most 0.003 either way, and the 3 simulated clouds differ from one another by at most 0.007.

At four groups the simulated score is 0.12, and the tract data exceed it by 0.09, against at most 0.03 at any other number of groups. This chapter uses four families because that is where the data depart most from a cloud without clusters. The choice is a judgment about where to draw lines on a continuum, and it does not count the kinds of neighborhood that exist.

Table 1. The tract data beat a cloud with no clusters by 0.09 in silhouette at four families, more than at any other number of families

The departure is modest. The four families hold 41.8% of the variance of the standardized measures between them, against 38.3% for four groups cut from the simulated cloud, and 13.4% of the sampled tracts have a negative silhouette, which means they sit closer to another family than to their own.

### The partition changes with weights, scale and the sample of counties

A fit can be reproducible and still have soft borders. The adjusted Rand index compares two partitions of the same tracts, with the maximum score for identical partitions and a score of zero for the agreement of random ones.[3] Refits from 6 other starting seeds agree with the families at 0.99 or higher. The result depends more on the choices in the sort. A refit that weights each tract by its population agrees at 0.74, so whether tracts or residents count changes the partition. A refit with the four dollar amounts replaced by their logs agrees at only 0.62, so the families depend on how the dollar measures are scaled, as the ADI does (Chapter 1.1, What the deprivation index measures (https://vishalsingh.org/zipcode/anatomy-of-deprivation)).

Resampling whole counties tests stability with the county as the unit of sampling, because tracts in a county resemble one another.[4] The second tab of Table 1 refits k-means on 200 resamples that draw counties with replacement, at each number of groups and with as many starts as the main fit, and assigns every tract to the nearest refit center.

The median agreement with the families at four groups is 0.88, but 17.5% (95% CI 12.9% to 23.4%) of the refits find a different arrangement, which this chapter defines as an agreement below 0.5. That is more often than at three groups, where the share is 0.0% (95% CI 0.0% to 1.9%), or at five, where it is 2.0% (95% CI 0.8% to 5.0%).

The different arrangement is in the full data too. Of 30 fits that start from a single random set of centers, 13 end there, and its within-group variance is only 1.1% higher than that of the families. It puts 76.9% of the crowded-renter tracts in one group with 47.6% of the high-poverty tracts, so a separate crowded-renter family is the least secure part of the partition.

Median agreement is between 0.88 and 0.92 up to five groups, falls to 0.80 at six and 0.54 at seven, and is 0.78 at eight. Reproducibility therefore does not favor four groups, and the benchmark above is the reason for choosing them.

### What defines each family

Table 2 shows the profile of each family on the 15 measures, and Table 3 gives the same families in the units of the measures. The four families are the high-income family, the crowded renters, the mid-range family and the high-poverty family, numbered by the mean ADI rank of their tracts from the least to the most deprived. The names describe the measures that set each family apart and are the book's labels. They say nothing about who lives in the tracts, and no measure in the sort is a race, an ethnicity or a place of birth.

Table 2. Crowded renters average 2.2 standard deviations above the mean tract on crowding, and the high-poverty family 1.4 above on poverty

The high-income family holds 76.6 million residents (24.9% of the frame) in 17,284 tracts. The mean tract median family income is 162 (95% CI 159 to 166) thousand dollars and the mean median home value 714 (95% CI 654 to 774) thousand dollars, with a poverty rate of 5.7% (95% CI 5.4% to 5.9%). Its tracts sit above the mean tract on income, housing costs and white-collar work and below it on every hardship measure, although the interval for households without a vehicle includes zero.

The crowded-renter family is the smallest, with 29.9 million residents in 6,870 tracts. Its tracts average 14.9% (95% CI 13.4% to 16.2%) of homes with more than one person per room, 43.3% (95% CI 41.0% to 46.1%) homeownership and 17.1% (95% CI 15.8% to 18.2%) of adults with under 9 years of schooling. Crowding sits 2.2 (95% CI 1.9 to 2.5) standard deviations above the mean tract.

Housing costs in the crowded-renter family are above the mean tract, with a home value of 472 (95% CI 389 to 540) thousand dollars, while family incomes are below it, at 74 (95% CI 71 to 76) thousand dollars. The family is concentrated by state, with 42.6% of its residents in California, 13.8% in New York and 11.8% in Texas.

The mid-range family is the largest, with 153.1 million residents in 37,746 tracts. Its column in Table 2 stays within 0.34 standard deviations of zero on every measure, with a family income of 95 (95% CI 94 to 95) thousand dollars and a poverty rate of 9.9% (95% CI 9.8% to 10.0%).

The high-poverty family holds 47.4 million residents in 13,817 tracts, with a poverty rate of 26.5% (95% CI 26.2% to 26.8%), a family income of 58 (95% CI 57 to 58) thousand dollars and a home value of 168 (95% CI 162 to 175) thousand dollars, so low income and low housing cost go together.

Table 3. Mean tract family income runs from 58 thousand dollars in the high-poverty family to 162 thousand dollars in the high-income family

Counting residents instead of tracts changes the profile little. Every cell of Table 2 differs from the center that k-means found, which counts each tract once, by at most 0.2 standard deviations.

### Outcomes the sort did not use

Table 4 compares the families on measures that were not inputs. Life expectancy runs from 81.7 (95% CI 81.5 to 81.8) years in the high-income family to 74.7 (95% CI 74.5 to 74.9) years in the high-poverty family, a difference of 6.9 (95% CI 6.7 to 7.2) years. The adult income rank of children raised in low-income families, which the Opportunity Atlas reports as a percentile, runs from 48.1 (95% CI 47.7 to 48.6) to 37.2 (95% CI 36.9 to 37.6). Both outcomes are older than the measures. Life expectancy is for deaths in 2010 to 2015, mobility is for children born in 1978 to 1983, and the families are drawn on conditions in 2019 to 2023. The comparison shows that present conditions line up with past outcomes, and it does not show that the families produce them.

Table 4. Life expectancy runs from 81.7 years in the high-income family to 74.7 years in the high-poverty family, and the crowded-renter and mid-range families do not differ detectably

The two middle families do not follow the ADI. The ADI scores the crowded renters at a mean rank of 38.5 (95% CI 32.0 to 46.2) and the mid-range family at 54.7 (95% CI 53.8 to 55.7), a difference of 16.3 (95% CI 8.4 to 22.6) points. Their life expectancy differs by 0.0 (95% CI −0.5 to 0.4) years, an interval that includes zero.

The adult income rank of the crowded renters is 1.9 (95% CI 1.1 to 2.7) percentiles below that of the mid-range family, and their modeled rate of fair or poor health is 8.2 (95% CI 7.2 to 9.2) points above it. The ADI follows home value closely, as Chapter 1.1, What the deprivation index measures (https://vishalsingh.org/zipcode/anatomy-of-deprivation) shows, and the crowded renters live in tracts with higher home values than the mid-range family does, 472 thousand dollars against 271 thousand dollars.

The health measures in the second tab are modeled. The PLACES model combines each survey respondent's age, sex, race and education with the poverty rate of the respondent's county. It applies the result to the age, race and sex counts of each tract. Differences among the families in that tab therefore reflect county effects and the demographic make-up of tracts, and no tract-level input of the families enters the model. Life expectancy and adult income rank are not modeled in that way. They come from death records and from tax records, interpolated from 2010 tracts to 2020 tracts by area. The intervals in the figure are bootstrap intervals over counties given the families, and they do not carry the uncertainty about the families themselves, which the refits above address.

### Deciles of the ADI mix the families

A ranking puts tracts in order, and a decile of the ranking holds whatever kinds of tract land there. Table 5 splits each decile of the ADI national rank by family. The deciles are close to equal in size, from 7,430 to 7,764 tracts, because ties in the published rank put tracts of equal rank in one decile.

In the most deprived decile, 79.2% of residents live in tracts of the high-poverty family and 16.1% in tracts of the mid-range family. The mid-range residents live 2.4 (95% CI 2.1 to 2.7) years longer than the high-poverty residents of the same decile.

No decile is a single family. The most common family holds between 50.7% and 88.3% of a decile's residents, and a second family holds at least 8.2% in every decile. Across the ten deciles, 72.0% of residents live in a tract of their decile's most common family. The crowded renters appear in every decile, from 4.7% of the most deprived decile's residents to 19.3% of the second.

Table 5. In the most deprived decile of tracts, 79.2% of residents live in high-poverty tracts and 16.1% in mid-range tracts

The mix matters for how much of the variation in outcomes a grouping carries. Ten deciles of the ADI account for 36.6% (95% CI 34.3% to 39.0%) of the variance of tract life expectancy and the four families for 33.3% (95% CI 31.4% to 35.2%). The deciles carry 3.3 (95% CI 2.0 to 4.5) points more, so four groups formed from the measures come close to ten groups formed from the rank. For adult income rank the families carry more, 27.7% (95% CI 25.6% to 30.0%) against 23.3% (95% CI 21.0% to 26.2%) for the deciles, a difference of 4.4 (95% CI 2.5 to 6.2) points.

The cells formed by decile and family account for 41.3% (95% CI 39.2% to 43.3%) of the variance of life expectancy and 30.9% (95% CI 28.7% to 33.4%) of adult income rank. The families add 4.7 (95% CI 4.1 to 5.4) points for life expectancy and 7.6 (95% CI 6.3 to 9.1) points for adult income rank to what the deciles carry, and the deciles add 8.0 (95% CI 7.3 to 8.8) and 3.2 (95% CI 2.6 to 4.0) points to what the families carry.

A grouping with more cells accounts for more variance even when it is unrelated to the outcome. If 40 cells were unrelated to life expectancy and each county counted as a single observation, which gives the most that chance could carry, they would account for 1.3%, below each of the gains above.

### At county scale the families blur

A county has one set of measures and many kinds of tract. Each of the 3,127 counties is labeled with the family whose center lies nearest the county's own measures, standardized as the tracts are. The labels give 96 high-income counties, 29 crowded-renter counties, 2,261 mid-range counties and 741 high-poverty counties (Table 6).

The distance uses 14 of the measures, without the single-parent share, because the county tables define it differently from the tract file. Each tract then takes its county's label, and the agreement between the county labels and the tract families is 0.22 on the adjusted Rand index. Across the country, 62.5% of residents live in a tract of the most common family of their county's label, and the share runs from 50.7% to 70.6% across the four labels.

Table 6. Crowded-renter tracts hold 50.7% of the residents of counties that resemble the crowded-renter family, and high-income tracts hold 34.6%

The crowded-renter and high-poverty labels are the weakest. The 29 counties with the crowded-renter label hold 21.8 million residents, and 50.7% of them live in crowded-renter tracts while 34.6% live in high-income tracts. In the 741 counties labeled high-poverty, 52.9% of residents live in high-poverty tracts.

The crowded-renter family is also not contained in its counties. 37.0% of its residents live in counties with that label, 37.2% in counties labeled mid-range and 22.3% in counties labeled high-income. A county average combines crowding, renting and costly housing with the tracts around them, so a county label does not recover the family. Chapter 1.2, What a county average leaves out (https://vishalsingh.org/zipcode/deprivation-at-two-zooms) makes the same comparison for the index itself.

### What these data cannot show

The families describe tracts, and every comparison in this chapter is ecological. The life expectancy of a family is an average over tracts, and it says little about any one resident of one tract (ecological inference). Nothing here shows that living in a family's tracts changes a person's outcome. The families are arrangements of census measures, and the outcomes that line up with them reflect selection, history, prices and policy that these data do not separate.

The number and the names of the families are choices. The silhouette favors no number of groups on its own, and the benchmark picks four by a stated rule. Refits find another arrangement more often at four groups than at three or five, and a second arrangement of four groups has only 1.1% more within-group variance than the first. Weighting by residents or rescaling the dollar measures changes the partition. The crowded-renter family depends most on those choices. The frame leaves out tracts that lack a median rent, home value or mortgage cost, which the ACS withholds for tracts with almost no renters or almost no owners, and it leaves out Puerto Rico, so none of these results describes the island.

The measures are tract estimates for 2019 to 2023 without margins of error. The tract file defines the share of single-parent households differently from the county tables, while the 819 tracts of Utah and the District of Columbia carry the county definition. Life expectancy is for deaths in 2010 to 2015 and was interpolated from 2010 to 2020 tracts by area, and the USALEEP estimates suit maps and gradients and not single tracts. Adult income rank describes children born in 1978 to 1983 and was interpolated to 2020 tracts by area. PLACES values are modeled, and the ADI averages block-group ranks over tracts without population weights. The county labels use county estimates of the same measures and treat Connecticut's planning regions as counties.

## Tables

### Table 1. The tract data beat a cloud with no clusters by 0.09 in silhouette at four families, more than at any other number of families

Mean silhouette of k-means fits to the 15 standardized deprivation measures, tract data and simulated data with no clusters, and agreement of refits on resamples of counties

#### Table 1.1. Silhouette

The tract data beat simulated data with no clusters by 0.09 at four families and by at most 0.03 at any other number

Mean silhouette by number of families, tract data and simulated data with no clusters, with 95% intervals for the sample

| conf_high | conf_low | k | n | series | silhouette |
| ---: | ---: | ---: | ---: | --- | ---: |
| 0.221 | 0.216 | 2 | 10,000 | Tract data | 0.218 |
| 0.208 | 0.205 | 2 | 10,000 | Simulated, no clusters | 0.207 |
| 0.214 | 0.207 | 3 | 10,000 | Tract data | 0.210 |
| 0.182 | 0.179 | 3 | 10,000 | Simulated, no clusters | 0.180 |
| 0.212 | 0.206 | 4 | 10,000 | Tract data | 0.209 |
| 0.122 | 0.120 | 4 | 10,000 | Simulated, no clusters | 0.121 |
| 0.153 | 0.148 | 5 | 10,000 | Tract data | 0.151 |
| 0.126 | 0.123 | 5 | 10,000 | Simulated, no clusters | 0.124 |
| 0.156 | 0.151 | 6 | 10,000 | Tract data | 0.153 |
| 0.127 | 0.124 | 6 | 10,000 | Simulated, no clusters | 0.125 |
| 0.131 | 0.126 | 7 | 10,000 | Tract data | 0.128 |
| 0.125 | 0.123 | 7 | 10,000 | Simulated, no clusters | 0.124 |
| 0.134 | 0.129 | 8 | 10,000 | Tract data | 0.132 |
| 0.122 | 0.120 | 8 | 10,000 | Simulated, no clusters | 0.121 |
| 0.140 | 0.135 | 9 | 10,000 | Tract data | 0.137 |
| 0.113 | 0.110 | 9 | 10,000 | Simulated, no clusters | 0.111 |
| 0.142 | 0.137 | 10 | 10,000 | Tract data | 0.140 |
| 0.112 | 0.109 | 10 | 10,000 | Simulated, no clusters | 0.110 |

#### Table 1.2. Agreement of refits

At four groups 17.5% of refits on resampled counties find a different arrangement, more than at three or five groups

Adjusted Rand index between the fit on all tracts and refits on resamples of counties, by number of families, median and tenth to ninetieth percentile

| k | median | p10 | p90 | refits |
| ---: | ---: | ---: | ---: | ---: |
| 2 | 0.884 | 0.738 | 0.978 | 200 |
| 3 | 0.919 | 0.855 | 0.961 | 200 |
| 4 | 0.882 | 0.352 | 0.953 | 200 |
| 5 | 0.881 | 0.753 | 0.947 | 200 |
| 6 | 0.798 | 0.645 | 0.922 | 200 |
| 7 | 0.543 | 0.467 | 0.777 | 200 |
| 8 | 0.780 | 0.677 | 0.917 | 200 |

Note: The silhouette uses a seeded random sample of tracts; the intervals show its sampling error, at most 0.003 in either direction. The simulated line is the mean of 3 draws that differ by at most 0.007 at any number of families.

Note: Simulated data are drawn from a Gaussian copula: each measure keeps its distribution in the tract data, and the dependence among measures is a single multivariate normal cloud, so k-means has no clusters to find.

Note: The band in the second tab runs from the tenth to the ninetieth percentile of the refits, each a k-means fit on a resample that draws whole counties with replacement and assigns every tract to its nearest center (replicates and seed in the methods note).

Source: ACS 2019-2023 deprivation measures, k-means fits to all tracts, silhouette on a sample of tracts; unweighted (each tract counts once)

Data: https://vishalsingh.org/zipcode/report/families-of-places/figures/number_of_families.json

### Table 2. Crowded renters average 2.2 standard deviations above the mean tract on crowding, and the high-poverty family 1.4 above on poverty

Population-weighted mean z-score of each of the 15 measures by family, tracts, ACS 2019 to 2023; zero is the mean tract

| conf_high | conf_low | family | measure | n | z |
| ---: | ---: | --- | --- | ---: | ---: |
| 1.44 | 1.29 | High income | Family income | 17,284 | 1.36 |
| −0.551 | −0.654 | Crowded renters | Family income | 6,870 | −0.599 |
| −0.121 | −0.148 | Mid-range | Family income | 37,746 | −0.134 |
| −0.942 | −0.966 | High poverty | Family income | 13,817 | −0.954 |
| 1.32 | 0.927 | High income | Home value | 17,284 | 1.12 |
| 0.553 | 0.058 | Crowded renters | Home value | 6,870 | 0.329 |
| −0.307 | −0.349 | Mid-range | Home value | 37,746 | −0.328 |
| −0.644 | −0.686 | High poverty | Home value | 13,817 | −0.666 |
| 1.36 | 1.14 | High income | Gross rent | 17,284 | 1.25 |
| 0.333 | 0.096 | Crowded renters | Gross rent | 6,870 | 0.225 |
| −0.231 | −0.315 | Mid-range | Gross rent | 37,746 | −0.273 |
| −0.644 | −0.707 | High poverty | Gross rent | 13,817 | −0.674 |
| 1.38 | 1.17 | High income | Mortgage cost | 17,284 | 1.28 |
| 0.587 | 0.166 | Crowded renters | Mortgage cost | 6,870 | 0.399 |
| −0.316 | −0.367 | Mid-range | Mortgage cost | 37,746 | −0.342 |
| −0.748 | −0.814 | High poverty | Mortgage cost | 13,817 | −0.782 |
| 1.23 | 1.10 | High income | White-collar jobs | 17,284 | 1.17 |
| −0.779 | −0.970 | Crowded renters | White-collar jobs | 6,870 | −0.877 |
| −0.061 | −0.102 | Mid-range | White-collar jobs | 37,746 | −0.082 |
| −0.776 | −0.827 | High poverty | White-collar jobs | 13,817 | −0.802 |
| 0.400 | 0.222 | High income | Homeownership | 17,284 | 0.309 |
| −0.917 | −1.15 | Crowded renters | Homeownership | 6,870 | −1.05 |
| 0.353 | 0.304 | Mid-range | Homeownership | 37,746 | 0.328 |
| −0.651 | −0.733 | High poverty | Homeownership | 13,817 | −0.692 |
| −0.722 | −0.779 | High income | Poverty | 17,284 | −0.750 |
| 0.669 | 0.492 | Crowded renters | Poverty | 6,870 | 0.572 |
| −0.307 | −0.327 | Mid-range | Poverty | 37,746 | −0.316 |
| 1.42 | 1.35 | High poverty | Poverty | 13,817 | 1.38 |
| −0.864 | −0.925 | High income | Below 150% of poverty | 17,284 | −0.895 |
| 0.821 | 0.645 | Crowded renters | Below 150% of poverty | 6,870 | 0.726 |
| −0.271 | −0.296 | Mid-range | Below 150% of poverty | 37,746 | −0.283 |
| 1.41 | 1.36 | High poverty | Below 150% of poverty | 13,817 | 1.39 |
| −0.683 | −0.806 | High income | Income disparity | 17,284 | −0.743 |
| 0.271 | 0.162 | Crowded renters | Income disparity | 6,870 | 0.217 |
| −0.086 | −0.119 | Mid-range | Income disparity | 37,746 | −0.102 |
| 0.925 | 0.890 | High poverty | Income disparity | 13,817 | 0.907 |
| −0.226 | −0.331 | High income | Unemployment | 17,284 | −0.282 |
| 0.522 | 0.366 | Crowded renters | Unemployment | 6,870 | 0.449 |
| −0.231 | −0.273 | Mid-range | Unemployment | 37,746 | −0.252 |
| 0.844 | 0.692 | High poverty | Unemployment | 13,817 | 0.764 |
| −0.538 | −0.581 | High income | Single parents | 17,284 | −0.559 |
| 0.853 | 0.631 | Crowded renters | Single parents | 6,870 | 0.735 |
| −0.120 | −0.156 | Mid-range | Single parents | 37,746 | −0.137 |
| 0.987 | 0.894 | High poverty | Single parents | 13,817 | 0.940 |
| 0.020 | −0.322 | High income | No vehicle | 17,284 | −0.174 |
| 1.29 | 0.331 | Crowded renters | No vehicle | 6,870 | 0.757 |
| −0.301 | −0.331 | Mid-range | No vehicle | 37,746 | −0.317 |
| 0.575 | 0.400 | High poverty | No vehicle | 13,817 | 0.480 |
| −0.180 | −0.304 | High income | Crowding | 17,284 | −0.241 |
| 2.49 | 1.94 | Crowded renters | Crowding | 6,870 | 2.23 |
| −0.244 | −0.284 | Mid-range | Crowding | 37,746 | −0.264 |
| 0.094 | 0.018 | High poverty | Crowding | 13,817 | 0.054 |
| −0.409 | −0.425 | High income | No plumbing | 17,284 | −0.417 |
| −0.227 | −0.290 | Crowded renters | No plumbing | 6,870 | −0.261 |
| −0.103 | −0.145 | Mid-range | No plumbing | 37,746 | −0.125 |
| 0.655 | 0.512 | High poverty | No plumbing | 13,817 | 0.580 |
| −0.382 | −0.462 | High income | Under 9 years of school | 17,284 | −0.421 |
| 2.24 | 1.83 | Crowded renters | Under 9 years of school | 6,870 | 2.05 |
| −0.235 | −0.279 | Mid-range | Under 9 years of school | 37,746 | −0.256 |
| 0.310 | 0.215 | High poverty | Under 9 years of school | 13,817 | 0.262 |

Note: Values are in standard deviations of the tract distribution of each measure, with each tract counted once, so zero is the mean tract and not the mean resident. Weighting by residents moves a cell by at most 0.2 from the k-means center.

Note: Income, home value, rent, mortgage cost, white-collar work and homeownership are measures of advantage, and the rest are measures of hardship. Intervals are 95% intervals from a bootstrap over counties, given the families.

Note: The share of single-parent households is defined differently in the tract file and in the county tables, and the tracts of Utah and the District of Columbia, which came from the Census API, follow the county definition. They are 819 of the tracts in the frame.

Source: ACS 2019-2023 deprivation measures (15) and Area Deprivation Index 2023; k-means families; population-weighted (z-scores use the unweighted mean and standard deviation across tracts)

Data: https://vishalsingh.org/zipcode/report/families-of-places/figures/family_profiles.json

### Table 3. Mean tract family income runs from 58 thousand dollars in the high-poverty family to 162 thousand dollars in the high-income family

Population-weighted means of tract values by family, in the units of each column, tracts and residents of the frame, ACS 2019 to 2023

| Family | Tracts | Residents (millions) | ADI national rank (mean) | Family income (thousands of dollars) | Home value (thousands of dollars) | Poverty (%) | Crowded homes (%) | Homeownership (%) | Adults with under 9 years of school (%) |
| --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: |
| High income | 17,284 | 76.6 | 16.9 | 162 | 714 | 5.7 | 2.3 | 72.4 | 2.3 |
| Crowded renters | 6,870 | 29.9 | 38.5 | 74 | 472 | 18.6 | 14.9 | 43.3 | 17.1 |
| Mid-range | 37,746 | 153.1 | 54.7 | 95 | 271 | 9.9 | 2.2 | 72.8 | 3.3 |
| High poverty | 13,817 | 47.4 | 79.3 | 58 | 168 | 26.5 | 3.8 | 50.9 | 6.4 |

Note: The ADI is not an input to the families. Families are numbered from least to most deprived by the population-weighted mean ADI of their tracts. The names describe the measures that define each family and are the book's labels, not categories in the data.

Note: Dollar amounts are 2019-2023 ACS medians of tracts, averaged over tracts with residents as weights; they are not medians of the family.

Source: ACS 2019-2023 deprivation measures (15) and Area Deprivation Index 2023; k-means families; population-weighted

Data: https://vishalsingh.org/zipcode/report/families-of-places/figures/family_table.json

### Table 4. Life expectancy runs from 81.7 years in the high-income family to 74.7 years in the high-poverty family, and the crowded-renter and mid-range families do not differ detectably

Population-weighted mean of tract values by family with 95% intervals from a bootstrap over counties; none of these measures was used to form the families

#### Table 4.1. Measured outcomes

Life expectancy and adult income rank are highest in the high-income family and lowest in the high-poverty family

Life expectancy at birth for deaths in 2010 to 2015 and adult income rank of children born 1978 to 1983, population-weighted family means with 95% intervals

| conf_high | conf_low | estimate | family | label | n | panel |
| ---: | ---: | ---: | --- | --- | ---: | --- |
| 81.81 | 81.50 | 81.66 | High income | High income | 16,221 | Life expectancy at birth (years) |
| 78.99 | 78.09 | 78.58 | Crowded renters | Crowded renters | 6,587 | Life expectancy at birth (years) |
| 78.67 | 78.50 | 78.59 | Mid-range | Mid-range | 36,163 | Life expectancy at birth (years) |
| 74.94 | 74.55 | 74.74 | High poverty | High poverty | 12,903 | Life expectancy at birth (years) |
| 48.57 | 47.71 | 48.13 | High income | High income | 17,256 | Adult income rank, children from low-income families (percentile) |
| 42.07 | 40.51 | 41.30 | Crowded renters | Crowded renters | 6,869 | Adult income rank, children from low-income families (percentile) |
| 43.41 | 42.98 | 43.20 | Mid-range | Mid-range | 37,728 | Adult income rank, children from low-income families (percentile) |
| 37.58 | 36.90 | 37.23 | High poverty | High poverty | 13,814 | Adult income rank, children from low-income families (percentile) |

#### Table 4.2. Modeled health measures

Diabetes, smoking and fair or poor health are lowest in the high-income family and highest in the high-poverty family

PLACES modeled prevalence among adults, population-weighted family means with 95% intervals

| conf_high | conf_low | estimate | family | label | n | panel |
| ---: | ---: | ---: | --- | --- | ---: | --- |
| 9.66 | 9.19 | 9.43 | High income | High income | 17,284 | Diabetes among adults (%) |
| 14.23 | 13.35 | 13.78 | Crowded renters | Crowded renters | 6,870 | Diabetes among adults (%) |
| 12.08 | 11.85 | 11.97 | Mid-range | Mid-range | 37,746 | Diabetes among adults (%) |
| 16.09 | 15.60 | 15.86 | High poverty | High poverty | 13,817 | Diabetes among adults (%) |
| 9.70 | 9.33 | 9.51 | High income | High income | 17,284 | Smoking among adults (%) |
| 16.53 | 15.33 | 15.83 | Crowded renters | Crowded renters | 6,870 | Smoking among adults (%) |
| 15.14 | 14.83 | 14.99 | Mid-range | Mid-range | 37,746 | Smoking among adults (%) |
| 21.09 | 20.55 | 20.82 | High poverty | High poverty | 13,817 | Smoking among adults (%) |
| 13.09 | 12.46 | 12.78 | High income | High income | 17,284 | Fair or poor health among adults (%) |
| 27.35 | 25.27 | 26.39 | Crowded renters | Crowded renters | 6,870 | Fair or poor health among adults (%) |
| 18.31 | 18.00 | 18.16 | Mid-range | Mid-range | 37,746 | Fair or poor health among adults (%) |
| 27.92 | 27.24 | 27.59 | High poverty | High poverty | 13,817 | Fair or poor health among adults (%) |

Note: Life expectancy is for deaths in 2010 to 2015 on tracts of 2020 (area-weighted from 2010 tracts), with institutional tracts left out. The adult income rank is for children born in 1978 to 1983, interpolated by land area from 2010 tracts to 2020 tracts, and tract population stands in for the number of children. Both describe the past, while the families are built on measures for 2019 to 2023.

Note: PLACES values are modeled estimates. The model combines each survey respondent's age, sex, race and education with the poverty rate of the respondent's county and applies the result to the age, race and sex counts of each tract, so differences among the families in the second tab reflect county effects and the demographic make-up of tracts, not tract-level inputs of the families. Intervals describe how the means would vary with the sample of counties, given the families, and not the choice of families.

Source: USALEEP 2010-2015, Opportunity Atlas (children born 1978 to 1983) and PLACES 2024 release; families from ACS 2019-2023; population-weighted, modeled estimates for PLACES

Data: https://vishalsingh.org/zipcode/report/families-of-places/figures/held_out_outcomes.json

### Table 5. In the most deprived decile of tracts, 79.2% of residents live in high-poverty tracts and 16.1% in mid-range tracts

Share of residents in each decile of the ADI national rank by family of their tract, percent of residents, tracts of the frame, ACS 2019 to 2023

| decile | family | share | tracts |
| --- | --- | ---: | ---: |
| 1 | High income | 88.30 | 6606 |
| 1 | Crowded renters | 11.09 | 901 |
| 1 | Mid-range | 0.378 | 39 |
| 1 | High poverty | 0.234 | 15 |
| 2 | High income | 70.94 | 5256 |
| 2 | Crowded renters | 19.28 | 1508 |
| 2 | Mid-range | 9.17 | 770 |
| 2 | High poverty | 0.617 | 54 |
| 3 | High income | 50.70 | 3698 |
| 3 | Crowded renters | 12.78 | 960 |
| 3 | Mid-range | 35.16 | 2708 |
| 3 | High poverty | 1.36 | 123 |
| 4 | High income | 18.56 | 1418 |
| 4 | Crowded renters | 10.33 | 795 |
| 4 | Mid-range | 68.03 | 5269 |
| 4 | High poverty | 3.07 | 282 |
| 5 | High income | 3.32 | 256 |
| 5 | Crowded renters | 8.23 | 589 |
| 5 | Mid-range | 82.74 | 6171 |
| 5 | High poverty | 5.72 | 477 |
| 6 | High income | 0.440 | 42 |
| 6 | Crowded renters | 8.14 | 559 |
| 6 | Mid-range | 82.69 | 6223 |
| 6 | High poverty | 8.73 | 699 |
| 7 | High income | 0.048 | 6 |
| 7 | Crowded renters | 7.61 | 516 |
| 7 | Mid-range | 77.17 | 5966 |
| 7 | High poverty | 15.18 | 1177 |
| 8 | High income | 0.015 | 1 |
| 8 | Crowded renters | 6.78 | 430 |
| 8 | Mid-range | 68.51 | 5193 |
| 8 | High poverty | 24.70 | 1806 |
| 9 | High income | 0.006 | 1 |
| 9 | Crowded renters | 5.13 | 331 |
| 9 | Mid-range | 52.11 | 4127 |
| 9 | High poverty | 42.76 | 3176 |
| 10 | High income | 0 | 0 |
| 10 | Crowded renters | 4.71 | 281 |
| 10 | Mid-range | 16.14 | 1280 |
| 10 | High poverty | 79.16 | 6008 |

Note: Shares are of residents (ACS 2019-2023 tract population) of the tracts in the frame, not of tracts. Deciles of the frame's tracts are close to equal in size, from 7,430 to 7,764 tracts, because ties in the published tract ADI national rank put tracts of equal rank in one decile. The shares are counts of ACS estimates and carry no sampling interval here.

Source: ACS 2019-2023 tract population by family; Area Deprivation Index 2023; full counts of ACS estimates

Data: https://vishalsingh.org/zipcode/report/families-of-places/figures/adi_decile_composition.json

### Table 6. Crowded-renter tracts hold 50.7% of the residents of counties that resemble the crowded-renter family, and high-income tracts hold 34.6%

Share of residents by family of their tract, in counties labeled by the nearest family center, percent of residents, ACS 2019 to 2023

| county_label | family | share |
| --- | --- | ---: |
| High-income counties | High income | 70.56 |
| High-income counties | Crowded renters | 14.05 |
| High-income counties | Mid-range | 14.06 |
| High-income counties | High poverty | 1.33 |
| Crowded-renter counties | High income | 34.63 |
| Crowded-renter counties | Crowded renters | 50.73 |
| Crowded-renter counties | Mid-range | 9.97 |
| Crowded-renter counties | High poverty | 4.67 |
| Mid-range counties | High income | 16.29 |
| Mid-range counties | Crowded renters | 5.20 |
| Mid-range counties | Mid-range | 63.01 |
| Mid-range counties | High poverty | 15.49 |
| High-poverty counties | High income | 2.91 |
| High-poverty counties | Crowded renters | 4.43 |
| High-poverty counties | Mid-range | 39.72 |
| High-poverty counties | High poverty | 52.93 |

Note: A county takes the label of the family whose center lies nearest the county's own 14 measures, standardized with the mean and standard deviation of the tract distribution, without the single-parent share, which is defined differently for counties. No clustering is run on counties. Counties include county equivalents and Connecticut's planning regions, as the ACS tables report them.

Note: Shares are of residents of the tracts in the frame and are counts of ACS estimates without a sampling interval. The county measures are medians and rates for the whole county, not averages of its tracts.

Source: ACS 2019-2023 county measures and tract population by family; labels from the nearest tract-family center; full counts of ACS estimates

Data: https://vishalsingh.org/zipcode/report/families-of-places/figures/county_group_composition.json

## All estimates

Every fact in facts.json (130), sorted by id.

| Fact id | Value | Unit | Estimand | Population | Period | Interval | n | Weights | Source | Note |
| --- | ---: | --- | --- | --- | --- | --- | ---: | --- | --- | --- |
| adi_gap_32 | 16.3 | points of the ADI national rank | difference between the population-weighted mean ADI national rank of the mid-range and the crowded-renter family, bootstrap interval over counties with shared draws | residents of tracts in the mid-range and crowded-renter families | 2023 release on ACS 2019-2023 | 95% CI 8.4 to 22.6 | 75,717 tracts | ACS 2019-2023 tract population | Area Deprivation Index |   |
| alt_cr_share | 76.9% | percent of the family's tracts | share of the family's tracts that fall in one group of the best different arrangement | tracts in the crowded-renter family | ACS 2019-2023 |   | 6,870 tracts | none (each tract counts once) | American Community Survey |   |
| alt_excess | 1.1% | percent more within-group variance | within-group sum of squares of the best different arrangement relative to the fit that defines the families | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| alt_f4_share | 47.6% | percent of the family's tracts | share of the family's tracts that fall in the same group of the best different arrangement as most crowded-renter tracts | tracts in the high-poverty family | ACS 2019-2023 |   | 13,817 tracts | none (each tract counts once) | American Community Survey |   |
| ari_boot_median | 0.88 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | median agreement with the families of refits on resamples that draw whole counties | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_cut | 0.5 | adjusted Rand index | definition: a refit whose agreement with the families is below this cutoff counts as a different arrangement of the groups | refits on resamples of counties | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| ari_k6 | 0.80 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | median agreement of refits on resamples of counties at 6 groups | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_k7 | 0.54 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | median agreement of refits on resamples of counties at 7 groups | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_k8 | 0.78 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | median agreement of refits on resamples of counties at 8 groups | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_log | 0.62 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | agreement with the families of a refit that replaces the four dollar measures by their logs | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_seed_min | 0.99 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | the lowest agreement with the families among refits with other starting seeds (10 starts each) | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_stab_hi | 0.92 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | the highest median agreement of refits on resamples of counties among two to five groups | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_stab_lo | 0.88 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | the lowest median agreement of refits on resamples of counties among two to five groups | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ari_weighted | 0.74 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | agreement with the families of a refit that weights each tract by its population | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| boot_other_share | 17.5% | percent of refits | share of refits whose agreement with the families is below the cutoff, Wilson interval that treats the refits as independent draws | refits on resamples of counties at four groups | ACS 2019-2023 | 95% CI 12.9% to 23.4% | 200 refits | none (each refit counts once) | American Community Survey |   |
| boot_other_share_k3 | 0.0% | percent of refits | share of refits whose agreement with the families is below the cutoff, Wilson interval that treats the refits as independent | refits on resamples of counties at 3 groups | ACS 2019-2023 | 95% CI 0.0% to 1.9% | 200 refits | none (each refit counts once) | American Community Survey |   |
| boot_other_share_k5 | 2.0% | percent of refits | share of refits whose agreement with the families is below the cutoff, Wilson interval that treats the refits as independent | refits on resamples of counties at 5 groups | ACS 2019-2023 | 95% CI 0.8% to 5.0% | 200 refits | none (each refit counts once) | American Community Survey |   |
| cg1_n | 96 | counties | count of counties whose measures lie nearest the center of the high income family | counties and county equivalents of the 50 states and DC with all 15 measures | ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| cg2_f1 | 34.6% | percent of the label's residents | share of the label's residents who live in tracts of the high income family | residents of tracts in the crowded-renter counties | ACS 2019-2023 |   | 29 counties | none (full count of estimates) | American Community Survey |   |
| cg2_f2 | 50.7% | percent of the label's residents | share of the label's residents who live in tracts of the crowded renters family | residents of tracts in the crowded-renter counties | ACS 2019-2023 |   | 29 counties | none (full count of estimates) | American Community Survey |   |
| cg2_n | 29 | counties | count of counties whose measures lie nearest the center of the crowded renters family | counties and county equivalents of the 50 states and DC with all 15 measures | ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| cg2_pop | 21.8 million | residents | residents of the frame who live in counties nearest the crowded-renter center | residents of tracts in counties labeled crowded-renter | ACS 2019-2023 |   | 29 counties | none (full count of estimates) | American Community Survey |   |
| cg3_n | 2,261 | counties | count of counties whose measures lie nearest the center of the mid-range family | counties and county equivalents of the 50 states and DC with all 15 measures | ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| cg4_f4 | 52.9% | percent of the label's residents | share of the label's residents who live in tracts of the high poverty family | residents of tracts in the high-poverty counties | ACS 2019-2023 |   | 741 counties | none (full count of estimates) | American Community Survey |   |
| cg4_n | 741 | counties | count of counties whose measures lie nearest the center of the high poverty family | counties and county equivalents of the 50 states and DC with all 15 measures | ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| cg_ari | 0.22 | adjusted Rand index (1 = identical partitions, 0 = chance agreement) | agreement between the tract families and the county labels, each tract taking its county's label | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| cg_diag_max | 70.6% | percent of a label's residents | the largest share, over the four county labels, of a label's residents who live in tracts of the family that the label names | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| cg_diag_min | 50.7% | percent of a label's residents | the smallest share, over the four county labels, of a label's residents who live in tracts of the family that the label names | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| cg_purity | 62.5% | percent of residents | share of residents who live in a tract of the most common tract family of their county's label | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| cr_dec_max | 19.3% | percent of residents of the decile | the largest share, over the ten deciles, of a decile's residents who live in tracts of the crowded-renter family | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| cr_dec_min | 4.7% | percent of residents of the decile | the smallest share, over the ten deciles, of a decile's residents who live in tracts of the crowded-renter family | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| cr_in_lab1 | 22.3% | percent of the family's residents | share of the crowded-renter family's residents who live in counties labeled high-income counties | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| cr_in_lab2 | 37.0% | percent of the family's residents | share of the crowded-renter family's residents who live in counties labeled crowded-renter counties | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| cr_in_lab3 | 37.2% | percent of the family's residents | share of the crowded-renter family's residents who live in counties labeled mid-range counties | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| dec10_sh_3 | 16.1% | percent of residents of the decile | share of the decile's residents who live in tracts of the mid-range family | residents of tracts in the most deprived decile of ADI ranks | ACS 2019-2023 |   | 7,569 tracts | none (full count of estimates) | American Community Survey |   |
| dec10_sh_4 | 79.2% | percent of residents of the decile | share of the decile's residents who live in tracts of the high-poverty family | residents of tracts in the most deprived decile of ADI ranks | ACS 2019-2023 |   | 7,569 tracts | none (full count of estimates) | American Community Survey |   |
| dec_modal_max | 88.3% | percent of residents of the decile | the largest share, over the ten deciles, of a decile's residents who live in tracts of its most common family | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| dec_modal_min | 50.7% | percent of residents of the decile | the smallest share, over the ten deciles, of a decile's residents who live in tracts of its most common family | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| dec_purity | 72.0% | percent of residents | share of residents who live in a tract of the most common family of their decile | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| dec_second_min | 8.2% | percent of residents of the decile | the smallest share, over the ten deciles, of a decile's residents who live in tracts of its second most common family | residents of tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| dec_tracts_max | 7,764 | tracts | the most tracts in a decile of the frame | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| dec_tracts_min | 7,430 | tracts | the fewest tracts in a decile of the frame | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| edu_years | 9 | years of schooling | definition: the schooling threshold of the measure, the share of adults who stopped before this many years | adults 25 and over | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| f1_hv | 714 | thousands of dollars of tract median home value | population-weighted mean of the tract median home value over the tracts of the family, bootstrap interval over counties | residents of tracts in the high income family | ACS 2019-2023 | 95% CI 654 to 774 | 17,284 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f1_inc | 162 | thousands of dollars of tract median family income | population-weighted mean of the tract median family income over the tracts of the family, bootstrap interval over counties | residents of tracts in the high income family | ACS 2019-2023 | 95% CI 159 to 166 | 17,284 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f1_kfr | 48.1 | percentile of the national household income rank in adulthood, children raised in families at the 25th income percentile | population-weighted mean of the tract adult income rank over the tracts of the family, bootstrap interval over counties | residents of tracts in the high income family | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 47.7 to 48.6 | 17,256 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| f1_le | 81.7 | years of life expectancy at birth | population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the high income family | deaths in 2010 to 2015 | 95% CI 81.5 to 81.8 | 16,221 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| f1_pop | 76.6 million | residents | sum of ACS 2019-2023 tract population over the tracts of the family | residents of tracts in the high income family | ACS 2019-2023 |   | 17,284 tracts | none (full count of estimates) | American Community Survey |   |
| f1_pov | 5.7% | percent of persons below the poverty line | population-weighted mean of the tract poverty rate over the tracts of the family, bootstrap interval over counties | residents of tracts in the high income family | ACS 2019-2023 | 95% CI 5.4% to 5.9% | 17,284 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f1_share | 24.9% | percent of residents of the frame | residents of the high income family as a share of residents of the frame | residents of the tracts in the frame | ACS 2019-2023 |   | 17,284 tracts | none (full count of estimates) | American Community Survey |   |
| f1_tracts | 17,284 | tracts | count of tracts in the high income family | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| f2_adi | 38.5 | points of the ADI national rank (1 least, 100 most deprived) | population-weighted mean of the tract ADI national rank, bootstrap interval over counties | residents of tracts in the crowded renters family | 2023 release on ACS 2019-2023 | 95% CI 32.0 to 46.2 | 6,870 tracts | ACS 2019-2023 tract population | Area Deprivation Index |   |
| f2_ca | 42.6% | percent of the family's residents | share of the family's residents who live in CA | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| f2_crowd | 14.9% | percent of households with more than one person per room | population-weighted mean of the tract crowding over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | ACS 2019-2023 | 95% CI 13.4% to 16.2% | 6,870 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f2_edu | 17.1% | percent of adults 25 and over with under 9 years of schooling | population-weighted mean of the tract share of adults with under 9 years of schooling over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | ACS 2019-2023 | 95% CI 15.8% to 18.2% | 6,870 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f2_hv | 472 | thousands of dollars of tract median home value | population-weighted mean of the tract median home value over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | ACS 2019-2023 | 95% CI 389 to 540 | 6,870 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f2_inc | 74 | thousands of dollars of tract median family income | population-weighted mean of the tract median family income over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | ACS 2019-2023 | 95% CI 71 to 76 | 6,870 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f2_le | 78.6 | years of life expectancy at birth | population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | deaths in 2010 to 2015 | 95% CI 78.1 to 79.0 | 6,587 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| f2_ny | 13.8% | percent of the family's residents | share of the family's residents who live in NY | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| f2_own | 43.3% | percent of occupied homes that are owner-occupied | population-weighted mean of the tract homeownership rate over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | ACS 2019-2023 | 95% CI 41.0% to 46.1% | 6,870 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f2_pop | 29.9 million | residents | sum of ACS 2019-2023 tract population over the tracts of the family | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| f2_tracts | 6,870 | tracts | count of tracts in the crowded renters family | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| f2_tx | 11.8% | percent of the family's residents | share of the family's residents who live in TX | residents of tracts in the crowded renters family | ACS 2019-2023 |   | 6,870 tracts | none (full count of estimates) | American Community Survey |   |
| f3_adi | 54.7 | points of the ADI national rank (1 least, 100 most deprived) | population-weighted mean of the tract ADI national rank, bootstrap interval over counties | residents of tracts in the mid-range family | 2023 release on ACS 2019-2023 | 95% CI 53.8 to 55.7 | 37,746 tracts | ACS 2019-2023 tract population | Area Deprivation Index |   |
| f3_hv | 271 | thousands of dollars of tract median home value | population-weighted mean of the tract median home value over the tracts of the family, bootstrap interval over counties | residents of tracts in the mid-range family | ACS 2019-2023 | 95% CI 265 to 278 | 37,746 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f3_inc | 95 | thousands of dollars of tract median family income | population-weighted mean of the tract median family income over the tracts of the family, bootstrap interval over counties | residents of tracts in the mid-range family | ACS 2019-2023 | 95% CI 94 to 95 | 37,746 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f3_le | 78.6 | years of life expectancy at birth | population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the mid-range family | deaths in 2010 to 2015 | 95% CI 78.5 to 78.7 | 36,163 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| f3_pop | 153.1 million | residents | sum of ACS 2019-2023 tract population over the tracts of the family | residents of tracts in the mid-range family | ACS 2019-2023 |   | 37,746 tracts | none (full count of estimates) | American Community Survey |   |
| f3_pov | 9.9% | percent of persons below the poverty line | population-weighted mean of the tract poverty rate over the tracts of the family, bootstrap interval over counties | residents of tracts in the mid-range family | ACS 2019-2023 | 95% CI 9.8% to 10.0% | 37,746 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f3_tracts | 37,746 | tracts | count of tracts in the mid-range family | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| f4_hv | 168 | thousands of dollars of tract median home value | population-weighted mean of the tract median home value over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | ACS 2019-2023 | 95% CI 162 to 175 | 13,817 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f4_inc | 58 | thousands of dollars of tract median family income | population-weighted mean of the tract median family income over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | ACS 2019-2023 | 95% CI 57 to 58 | 13,817 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f4_kfr | 37.2 | percentile of the national household income rank in adulthood, children raised in families at the 25th income percentile | population-weighted mean of the tract adult income rank over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 36.9 to 37.6 | 13,814 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| f4_le | 74.7 | years of life expectancy at birth | population-weighted mean of the tract life expectancy over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | deaths in 2010 to 2015 | 95% CI 74.5 to 74.9 | 12,903 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| f4_pop | 47.4 million | residents | sum of ACS 2019-2023 tract population over the tracts of the family | residents of tracts in the high poverty family | ACS 2019-2023 |   | 13,817 tracts | none (full count of estimates) | American Community Survey |   |
| f4_pov | 26.5% | percent of persons below the poverty line | population-weighted mean of the tract poverty rate over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | ACS 2019-2023 | 95% CI 26.2% to 26.8% | 13,817 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| f4_tracts | 13,817 | tracts | count of tracts in the high poverty family | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| frame_pop_share | 93.0% | percent of residents of tracts with a published ADI rank | residents of the tracts in the frame as a share of residents of tracts with a published rank | residents of tracts with a published ADI rank and residents | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| ghlth_gap_23 | 8.2 | percent of adults in fair or poor health (modeled) | difference between the population-weighted mean rate of fair or poor health of the crowded-renter and the mid-range family, bootstrap interval over counties with shared draws | residents of tracts in the crowded-renter and mid-range families | PLACES 2024 release, BRFSS 2022 | 95% CI 7.2 to 9.2 | 75,717 tracts | ACS 2019-2023 tract population | CDC PLACES |   |
| k | 4 | families | definition: the number of families the chapter uses | k-means fits compared | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| k_hi | 10 | families | definition: the most families in the comparison | k-means fits compared | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| k_lo | 2 | families | definition: the fewest families in the comparison | k-means fits compared | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| k_stab_hi | 8 | families | definition: the most families in the comparison of refits | k-means fits compared | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| kfr_gap_32 | 1.9 | percentile of the national household income rank in adulthood, children raised in families at the 25th income percentile | difference between the population-weighted mean adult income rank of the mid-range and the crowded-renter family, bootstrap interval over counties with shared draws | residents of tracts in the mid-range and crowded-renter families | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 1.1 to 2.7 | 75,717 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| le_gap_14 | 6.9 | years of life expectancy at birth | difference between the population-weighted mean life expectancy of the high-income and the high-poverty family, bootstrap interval over counties with shared draws | residents of tracts in the high-income and high-poverty families | deaths in 2010 to 2015 | 95% CI 6.7 to 7.2 | 75,717 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| le_gap_23 | 0.0 | years of life expectancy at birth | difference between the population-weighted mean life expectancy of the crowded-renter and the mid-range family, bootstrap interval over counties with shared draws | residents of tracts in the crowded-renter and mid-range families | deaths in 2010 to 2015 | 95% CI −0.5 to 0.4 | 75,717 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| le_gap_dec10 | 2.4 | years of life expectancy at birth | difference between the population-weighted mean life expectancy of the mid-range and the high-poverty family within the most deprived decile of ADI ranks, bootstrap interval over counties with shared draws | residents of tracts in the most deprived decile of tracts that belong to the mid-range and high-poverty families | deaths in 2010 to 2015 | 95% CI 2.1 to 2.7 | 75,717 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| n_adi_measures | 17 | measures | definition: count of measures in the index formula (Singh 2003, as printed in Petterson 2023), of which the chapter on what the deprivation index measures rebuilds the 15 used here | measures combined by the Area Deprivation Index | 2023 release on ACS 2019-2023 |   |   | none (definition) | Area Deprivation Index |   |
| n_boot_refits | 200 | refits | count of refits at each number of groups (definition) | refits on resamples of counties at each number of groups | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_cells | 40 | cells | count of cells (definition): ten deciles times four families | cells formed by decile and family | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_counties | 3,127 | counties | count of counties labeled | counties and county equivalents of the 50 states and DC with all 15 measures | ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| n_county_measures | 14 | measures | count of measures (definition): the 15 measures without the single-parent share | measures in the distance that labels a county | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_measures | 15 | measures | count of measures (definition) | deprivation measures given to k-means | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_null | 3 | simulated clouds | count of simulated clouds (definition) | simulated data with no clusters | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_seeds | 6 | refits | count of refits (definition) | refits with other starting seeds | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_single | 30 | fits | count of fits (definition) | single-start fits of four groups | ACS 2019-2023 |   |   | none (definition) | American Community Survey |   |
| n_single_other | 13 | fits | count of single-start fits whose agreement with the families is below one half | single-start fits of four groups | ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| n_tracts | 75,717 | tracts | count of tracts clustered | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| n_tracts_pr | 981 | tracts | count of Puerto Rico tracts, left out of the frame (the frame of the chapter on what the deprivation index measures) | census tracts of Puerto Rico | 2020 census tracts |   |   | none (full count) | American Community Survey |   |
| n_tracts_ut_dc | 819 | tracts | count of tracts of Utah and the District of Columbia in the frame, whose single-parent share follows the county definition | census tracts in the frame (2020 tracts with a published ADI rank, residents and all 15 measures) | inputs from ACS 2019-2023 |   |   | none (full count) | American Community Survey |   |
| null_draw_gap | 0.007 | silhouette (-1 to 1) | the largest difference between the highest and lowest of the simulated draws at any number of groups | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| r2_chance | 1.3% | percent of the variance of tract life expectancy | the most that 40 groups unrelated to the measure could account for by chance: groups minus one over counties minus one, which treats each county as one observation | residents of tracts with a life expectancy estimate | deaths in 2010 to 2015 |   | 3,101 counties | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| r2_kfr_add_dec | 3.2 | percentage points of the population-weighted variance of tract adult income rank | difference between the R squared of the cells formed by decile and family over the four families, bootstrap interval over counties with shared draws | residents of tracts with the measure | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 2.6 to 4.0 | 75,667 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| r2_kfr_add_fam | 7.6 | percentage points of the population-weighted variance of tract adult income rank | difference between the R squared of the cells formed by decile and family over the ten deciles, bootstrap interval over counties with shared draws | residents of tracts with the measure | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 6.3 to 9.1 | 75,667 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| r2_kfr_both | 30.9% | percent of the population-weighted variance of tract adult income rank | R squared of the group means: variance between the cells formed by decile and family over the total variance of the tract measure, bootstrap interval over counties | residents of tracts with the measure | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 28.7% to 33.4% | 75,667 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| r2_kfr_dec | 23.3% | percent of the population-weighted variance of tract adult income rank | R squared of the group means: variance between the ten deciles of the ADI rank over the total variance of the tract measure, bootstrap interval over counties | residents of tracts with the measure | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 21.0% to 26.2% | 75,667 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| r2_kfr_fam | 27.7% | percent of the population-weighted variance of tract adult income rank | R squared of the group means: variance between the four families over the total variance of the tract measure, bootstrap interval over counties | residents of tracts with the measure | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 25.6% to 30.0% | 75,667 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| r2_kfr_fam_minus_dec | 4.4 | percentage points of the population-weighted variance of tract adult income rank | difference between the R squared of the four families over the ten deciles, bootstrap interval over counties with shared draws | residents of tracts with the measure | children born 1978 to 1983, income measured around 2014 to 2015 | 95% CI 2.5 to 6.2 | 75,667 tracts | ACS 2019-2023 tract population | Opportunity Atlas |   |
| r2_le_add_dec | 8.0 | percentage points of the population-weighted variance of tract life expectancy | difference between the R squared of the cells formed by decile and family over the four families, bootstrap interval over counties with shared draws | residents of tracts with the measure | deaths in 2010 to 2015 | 95% CI 7.3 to 8.8 | 71,874 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| r2_le_add_fam | 4.7 | percentage points of the population-weighted variance of tract life expectancy | difference between the R squared of the cells formed by decile and family over the ten deciles, bootstrap interval over counties with shared draws | residents of tracts with the measure | deaths in 2010 to 2015 | 95% CI 4.1 to 5.4 | 71,874 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| r2_le_both | 41.3% | percent of the population-weighted variance of tract life expectancy | R squared of the group means: variance between the cells formed by decile and family over the total variance of the tract measure, bootstrap interval over counties | residents of tracts with the measure | deaths in 2010 to 2015 | 95% CI 39.2% to 43.3% | 71,874 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| r2_le_dec | 36.6% | percent of the population-weighted variance of tract life expectancy | R squared of the group means: variance between the ten deciles of the ADI rank over the total variance of the tract measure, bootstrap interval over counties | residents of tracts with the measure | deaths in 2010 to 2015 | 95% CI 34.3% to 39.0% | 71,874 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| r2_le_dec_minus_fam | 3.3 | percentage points of the population-weighted variance of tract life expectancy | difference between the R squared of the ten deciles over the four families, bootstrap interval over counties with shared draws | residents of tracts with the measure | deaths in 2010 to 2015 | 95% CI 2.0 to 4.5 | 71,874 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| r2_le_fam | 33.3% | percent of the population-weighted variance of tract life expectancy | R squared of the group means: variance between the four families over the total variance of the tract measure, bootstrap interval over counties | residents of tracts with the measure | deaths in 2010 to 2015 | 95% CI 31.4% to 35.2% | 71,874 tracts | ACS 2019-2023 tract population | USALEEP life expectancy |   |
| sil_half_max | 0.003 | silhouette (-1 to 1) | largest half-width of the 95% interval for the sample silhouette over the fits compared | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_k | 0.21 | silhouette (-1 to 1) | mean silhouette of the four families, interval from the sampling error of the sample | a seeded random sample of tracts in the frame | ACS 2019-2023 | 95% CI 0.21 to 0.21 | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_k2 | 0.22 | silhouette (-1 to 1) | mean silhouette of the 2-family k-means fit to the tract data, interval from the sampling error of the sample | a seeded random sample of tracts in the frame | ACS 2019-2023 | 95% CI 0.22 to 0.22 | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_k5 | 0.15 | silhouette (-1 to 1) | mean silhouette of the 5-family k-means fit to the tract data, interval from the sampling error of the sample | a seeded random sample of tracts in the frame | ACS 2019-2023 | 95% CI 0.15 to 0.15 | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_margin_k | 0.09 | silhouette (-1 to 1) | silhouette of the tract data minus the silhouette of simulated data with no clusters, four groups | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_margin_other | 0.03 | silhouette (-1 to 1) | the largest silhouette margin over simulated data at any number of groups other than four | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_neg_share | 13.4% | percent of sampled tracts | share of sampled tracts with a negative silhouette in the four families (nearer to another family than to their own) | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_null_k | 0.12 | silhouette (-1 to 1) | mean silhouette of the 4-group k-means fit to simulated data with no clusters (mean of 3 draws) | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| sil_null_k2 | 0.21 | silhouette (-1 to 1) | mean silhouette of the 2-group k-means fit to simulated data with no clusters (mean of 3 draws) | a seeded random sample of tracts in the frame | ACS 2019-2023 |   | 10,000 tracts | none (each tract counts once) | American Community Survey |   |
| ss_between | 41.8% | percent of the total variance of the standardized measures | share of the total variance of the 15 standardized measures that lies between the four families | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| ss_between_null | 38.3% | percent of the total variance of the standardized measures | share of the total variance that lies between four k-means groups in simulated data with no clusters (mean of the draws) | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| total_pop | 307.1 million | residents | sum of ACS 2019-2023 tract population over the tracts in the frame | residents of the tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (full count of estimates) | American Community Survey |   |
| z_f2_crowded | 2.2 | standard deviations above the mean tract | population-weighted mean of the tract crowding z-score over the tracts of the family, bootstrap interval over counties | residents of tracts in the crowded renters family | ACS 2019-2023 | 95% CI 1.9 to 2.5 | 6,870 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| z_f4_poverty | 1.4 | standard deviations above the mean tract | population-weighted mean of the tract poverty z-score over the tracts of the family, bootstrap interval over counties | residents of tracts in the high poverty family | ACS 2019-2023 | 95% CI 1.4 to 1.4 | 13,817 tracts | ACS 2019-2023 tract population | American Community Survey |   |
| z_gap_max | 0.2 | standard deviations | the largest difference, over families and measures, between the unweighted mean z-score (the k-means center) and the population-weighted mean z-score | census tracts in the frame | ACS 2019-2023 |   | 75,717 tracts | none (each tract counts once) | American Community Survey |   |
| z_mid_max | 0.34 | standard deviations from the mean tract | the largest absolute population-weighted mean z-score of the mid-range family over the 15 measures | residents of tracts in the mid-range family | ACS 2019-2023 |   | 37,746 tracts | ACS 2019-2023 tract population | American Community Survey |   |

## Definitions

- K-means: A method that sorts places into a chosen number of groups so that places in a group resemble one another on the measures used. The analyst sets the number of groups.
- Area Deprivation Index (ADI): A score that ranks neighborhoods by income, education, employment and housing conditions drawn from the American Community Survey. In this book a higher national percentile means a more deprived neighborhood.
- Life expectancy at birth: The average number of years a newborn would live if death rates at every age stayed as they were in the period measured. It summarizes the death rates of a period and is not a forecast for any child.
- Income rank (kfr): The position that adult children reach in the national distribution of household income, from the lowest rank to the highest, averaged over children who grew up in a place with parents at a stated income level. The Opportunity Atlas labels this measure kfr.
- Silhouette: A score for how well a place fits the group it was assigned in a clustering. Higher values mean the place sits close to its own group and far from the others.
- Modeled estimate: A figure produced by a statistical model instead of a direct count or measurement, usually for small areas where direct data are thin, borrowing strength from surveys, neighboring areas or other data. Neighboring areas can share errors, so single extremes call for caution.
- Ecological inference: Drawing conclusions about individuals from data about places or groups. A pattern across counties need not hold for the people inside them.
- USALEEP: The U.S. Small-area Life Expectancy Estimates Project, a National Center for Health Statistics release of life expectancy at birth for most census tracts. It covers deaths from 2010 to 2015 only and has not been updated.

## Methods

This chapter sorts the 75,717 census tracts of the frame into 4 families with k-means on 15 ACS 2019-2023 measures, and describes each family with outcomes that were not inputs. The fit counts each tract once and is unweighted by design, family means use tract population as weights, and the intervals resample whole counties and do not carry uncertainty about the fit. The held-out outcomes come from other periods and models: life expectancy for deaths in 2010 to 2015, adult income rank for children born 1978 to 1983, and CDC PLACES health measures that are modeled estimates. Puerto Rico's tracts are outside the frame, and county labels come from each county's nearest center, since no clustering is run on counties.

### Which tracts and measures are used

The frame is the 2020 tracts that have a published ADI rank, residents and all 15 measures (the frame of the chapter on the anatomy of a deprivation index, loaded by its loader). The 15 measures are a subset of the 17 that the Area Deprivation Index combines. Puerto Rico's tracts are not in the frame, as in that chapter.

The tracts of Utah and the District of Columbia carry the county definition of the single-parent share, which differs from the tract file's definition.  The measures are in their own units: dollars for the four dollar amounts, proportions for the other ten, and the log ratio of low-income to high-income households.

### How the families are fitted

Each measure is standardized across tracts with each tract counted once, and k-means (scikit-learn, Lloyd's algorithm, k-means++ starts, 4 groups, 20 starts, seed 12345, one thread) places the centers. The fit is unweighted by design. Families are numbered by the population-weighted mean of the published ADI, least deprived first.

### How the number of families is chosen

For 2 to 10 groups the build fits k-means with 10 starts and computes the mean silhouette on a seeded random sample of 10,000 tracts (seed 12345). The same fits are run on 3 simulated clouds of the same size that keep each measure's distribution and the correlations of normal scores among measures (a Gaussian copula, seeds 12345 to 12347) and have no clusters.

Explains Table 1.

### Held-out outcomes, deciles and county labels

Life expectancy leaves out institutional tracts (25 percent or more of residents in group quarters). Adult income rank, life expectancy and PLACES measures are not inputs. PLACES values are modeled from individual age, sex, race and education and county poverty, post-stratified to tract counts.

Deciles of the published ADI national rank are formed on the tracts of the frame and are close to equal in size, because tied ranks fall in one decile.

Each county takes the label of the family whose center lies nearest its own 14 measures (all but the single-parent share, which is defined differently for tracts and counties), standardized with the tract mean and standard deviation; no clustering is run on counties, and each tract takes its county's label.

Explains Table 4, Table 5 and Table 6.

### Means and intervals

Family means use ACS 2019-2023 tract population as weights. Intervals are 95% percentile intervals from 2,000 draws of whole counties with replacement (seed 12345); differences between two families and the variance explained by groups use the same draws. Intervals condition on the families and do not carry uncertainty about the fit.

Explains Table 2 and Table 3.

### Stability refits

Stability is tested with refits using 6 other seeds; a refit weighted by tract population; a refit with the four dollar amounts logged; 30 single-start fits to find other arrangements; and 200 refits at each number of groups from 2 to 8 (20 starts each, as many as the main fit) on resamples that draw whole counties with replacement (Connecticut tracts are assigned to its eight legacy counties; the generator of resample b is seeded with 12345 and b, and the same resamples serve every number of groups), each assigning every tract to its nearest center.

Agreement is the adjusted Rand index. The share of refits with an agreement below 0.5 has a Wilson interval that treats the refits as independent.

The refits run in worker processes; each depends only on its seed, so the result does not depend on the number of workers.

## What these data cannot show

The families describe tracts, and every comparison in this chapter is ecological. The life expectancy of a family is an average over tracts, and it says little about any one resident of one tract (ecological inference). Nothing here shows that living in a family's tracts changes a person's outcome. The families are arrangements of census measures, and the outcomes that line up with them reflect selection, history, prices and policy that these data do not separate.

The number and the names of the families are choices. The silhouette favors no number of groups on its own, and the benchmark picks four by a stated rule. Refits find another arrangement more often at four groups than at three or five, and a second arrangement of four groups has only 1.1% more within-group variance than the first. Weighting by residents or rescaling the dollar measures changes the partition. The crowded-renter family depends most on those choices. The frame leaves out tracts that lack a median rent, home value or mortgage cost, which the ACS withholds for tracts with almost no renters or almost no owners, and it leaves out Puerto Rico, so none of these results describes the island.

The measures are tract estimates for 2019 to 2023 without margins of error. The tract file defines the share of single-parent households differently from the county tables, while the 819 tracts of Utah and the District of Columbia carry the county definition. Life expectancy is for deaths in 2010 to 2015 and was interpolated from 2010 to 2020 tracts by area, and the USALEEP estimates suit maps and gradients and not single tracts. Adult income rank describes children born in 1978 to 1983 and was interpolated to 2020 tracts by area. PLACES values are modeled, and the ADI averages block-group ranks over tracts without population weights. The county labels use county estimates of the same measures and treat Connecticut's planning regions as counties.

## References

1. MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, 281-297.
2. Rousseeuw, Peter J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics 20: 53-65. https://doi.org/10.1016/0377-0427(87)90125-7
3. Hubert, Lawrence; Arabie, Phipps (1985). Comparing partitions. Journal of Classification 2(1): 193-218. https://doi.org/10.1007/BF01908075
4. Hennig, Christian (2007). Cluster-wise assessment of cluster stability. Computational Statistics & Data Analysis 52(1): 258-271. https://doi.org/10.1016/j.csda.2006.11.025

## Provenance

- Pipeline version: 0.1.0
- Build script: book2/chapters/families-of-places/build.py (sha256 fcb706d743590f60d4d04f5e5603684f782888d93d17e4f0133be0d0d400603a)
- Built on: 2026-10-07
- Site commit: c2b1ff3309cb4a10833f884da91ac0057a66ad0a

Inputs:

| File | Size (bytes) | SHA-256, first 1 MB | SHA-256, last 1 MB |
| --- | ---: | --- | --- |
| book2/chapters/anatomy-of-deprivation/deprivation.py | 18,028 | 092694cfd30446c54292ca7182d4d784e95f28766c0db63fedf53f84c7bb1b7d | 092694cfd30446c54292ca7182d4d784e95f28766c0db63fedf53f84c7bb1b7d |
| book2/chapters/families-of-places/families_data.py | 23,256 | 41dc810414ea1eccb3899088e8c6ab91a208263239defaa5b7a65305cedb7eb9 | 41dc810414ea1eccb3899088e8c6ab91a208263239defaa5b7a65305cedb7eb9 |
| data/analytic/tract_atlas.parquet | 39,659,925 | 29d5e4d943552d54aeb6ba92aadc939d9bd15bdea553c78357dbd516757be627 | 1e10d1ecf722340f23ee2212d4999a90250f85b65fa89b39e32db06d9472e22e |
| data/raw/acs/deprivation_components_2019_2023/county.parquet | 1,004,968 | c894ba6cf96378244f47cc4271a24bff087d15ba27f09e49a4ebc0a4786c6f9d | c894ba6cf96378244f47cc4271a24bff087d15ba27f09e49a4ebc0a4786c6f9d |
| data/raw/acs/deprivation_components_2019_2023/county_core.parquet | 498,878 | 8b177857027e73c1f404f7b62191ab78811e95ee54c4f07383e9e9e17da1a345 | 8b177857027e73c1f404f7b62191ab78811e95ee54c4f07383e9e9e17da1a345 |
| data/raw/acs/deprivation_components_2019_2023/tract.parquet | 13,197,793 | 5545cde2cbe96a8b56e468d65388248a241aa6bd300d3c9e325d08d3f86b11da | 5c8ec454d066988b0f1a01aaa6ed34ebfc05d162e01cf9c6bb01f9198cbaff12 |
| data/staged/adi/adi_atlas_tract2020_2023.parquet | 798,078 | 5e409bc212ff871def780fa27b4cf8b616d9da420b2b9f6455517eddcd8c1a95 | 5e409bc212ff871def780fa27b4cf8b616d9da420b2b9f6455517eddcd8c1a95 |
| data/staged/crosswalks/ct_tract2020_to_old_county.parquet | 15,842 | 961ef39f31596ef65fca2c67d5f2f63e533c5dc9b49745d3bb6437844e4b831d | 961ef39f31596ef65fca2c67d5f2f63e533c5dc9b49745d3bb6437844e4b831d |
| data/staged/life_expectancy/usaleep_tract2020.parquet | 1,316,169 | 9c9c7f103791b75eddba74e68a89804efdf2486b6b66bb4bc02a46ba5bf8bc23 | 27317107be2465d9fd5e83271dea0cd6e915ee419e2802bedc28747d0a41d38f |
| data/staged/ses/acs5_tract2020_2019_2023.parquet | 7,232,424 | 5fe6f730a35225f14d5d8abfc6b9bce58b52e545f309a7eac74f1dae74d7a31c | 7b4a2475b3852d3f91804716a04566ef8ceadacec2be9fb85f5eb642078efac6 |
| data/staged/svi/svi_tract2020_2022.parquet | 17,740,415 | cb3860d8edc2aaf1f2a02211a58f7a0b80457eb6ad9a37b5ec8abb2d5da9da10 | e371a4a696d5bed05d54ad7c5b6ca2504508805b847ec415c2322be7f66ec2b2 |

Outputs:

| File | SHA-256 |
| --- | --- |
| facts.json | 08466a4097eaac08b5d2e1dfae8c1ca703031b8ce6b3fe47fd0e305e521a3f3d |
| figures/adi_decile_composition.json | 34f80f19cbc2a4685e3de9a8a0a6c10b859ad49e65a42955f28e6629bf290e83 |
| figures/county_group_composition.json | 5d7e485b59f3d518877365296f46bd417c57461077af415982c2546771926f94 |
| figures/family_profiles.json | dba608e1df40e9909de89b387b1512a95d929d8e035cbed1e1b4ae3e1149af0c |
| figures/family_table.json | 092d8c9e5f55f7b33bc05832500e0c8e2ff1ab9ad7794e3c288b86f1edd9e4b3 |
| figures/held_out_outcomes.json | 9715ccb8c0bd1dc8215395e79723bf22944973ed875d1a7d31234d34c25696e5 |
| figures/number_of_families.json | 61ac7ef104efb337fd1cde276c8e0babe1f0855aa962fc699d1810e1433504cd |
| meta.json | bd419ebe0b487c5bec3758ecde3907369233241d8120b55436f20624942dd381 |
| refs.json | 979ce72ce7e56ad2f2fa0b196a3e6c986a3807d5b36c8a3d1d0532d742e6c62c |

## Machine formats

- Report (HTML): https://vishalsingh.org/zipcode/families-of-places/report
- Report (Markdown): https://vishalsingh.org/zipcode/families-of-places/report.md
- Every estimate (JSON): https://vishalsingh.org/zipcode/report/families-of-places/facts.json
- Table 1, figure "number_of_families" (JSON): https://vishalsingh.org/zipcode/report/families-of-places/figures/number_of_families.json
- Table 2, figure "family_profiles" (JSON): https://vishalsingh.org/zipcode/report/families-of-places/figures/family_profiles.json
- Table 3, figure "family_table" (JSON): https://vishalsingh.org/zipcode/report/families-of-places/figures/family_table.json
- Table 4, figure "held_out_outcomes" (JSON): https://vishalsingh.org/zipcode/report/families-of-places/figures/held_out_outcomes.json
- Table 5, figure "adi_decile_composition" (JSON): https://vishalsingh.org/zipcode/report/families-of-places/figures/adi_decile_composition.json
- Table 6, figure "county_group_composition" (JSON): https://vishalsingh.org/zipcode/report/families-of-places/figures/county_group_composition.json
- Index of every report: https://vishalsingh.org/zipcode/llms.txt; all reports in one file: https://vishalsingh.org/zipcode/llms-full.txt