1 Background & Motivation

1.1 QUESTION: Is metropolitan-level economic segregation a correlate of the pace of decline in heart disease mortality?

1.1.1 ASSUMPTIONS:

  1. Economic segregation is best measured at metropolitan (CBSA) scale.
  2. Economic segregation in 1970 is the closest ‘exposure’ period preceding county trends. In other words we are testing whether early-state economic segregation predicted subsequent slope or trend.
  3. Confounders or effect modifiers include individual (race, age), county (poverty, educational attainment), and metropolitan (population size) variables. Poverty and educational attainment are measured race-specific, and all covariates are currently in 1970 values.
  4. Data is 3-level: individual age/race groups clustered within counties clustered with CBSA’s/MSA’s

1.2 Measuring economic segregation

Economic segregation is measured at the CBSA scale using the H Index of Income Diversity1 The index quantifies the spatial separation of families according to their location in the continuous income distribution. The index ranges from 0 (complete spatial integration of families by income) to 1 (complete spatial separation of families into locally monolithic income neighborhoods).

2 Data overview

2.1 Compare measures of segregation

Economic segregation is always measured at the spatial scale of the CBSA, but is operationalized along three dimensions:

  1. When is economic segregation measured?
    • 1970
    • 2012
  2. For whom is economic segregation measured?
    • Total population
    • Only among Blacks
    • Only among Whites
  3. At what point in the income distribution is segregation (separation) conceptualized?
    • Overall income segregation considers the entire income distribution. This measure quantifies the average separation between those above and below each quantile in the continuous income distribution, averaged across incomes. This is interpreted as the overall segregation (separation) of individuals by income.
    • Poverty concentration. This measure specifically focuses on the segregation (separation) of those below versus above the 10th percentile of income in each CBSA.
    • Affluence concentration. This measure specifically focuses on the segregation (separation) of those below versus above the 90th percentile of income in each CBSA.
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2.1.1 Distribution of H values across domains

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INTERPRETATION: There has been substantial increase in the mean (and variance) of economic segregation among Blacks between 1970 and 2012. Even in 1970 there was modestly more variability in Black economic segregation than white.

2.1.2 Compare 1970 economic segregation by income cutpoint

## Warning: Removed 63 rows containing missing values (geom_point).

INTERPRETATION: This plot shows how the concentration of poverty (H10) covaries with the concentration of affluence (H90) overall and by race. We can think of overall economic segregation (H) as the aggregate of these and other patterns…so that they travel together is not a surprise. The association, however, is more linear/highly correlate among Whites than Blacks. In Blacks there are some cities where the concentration of affluence is much higher than concentration of poverty.

2.2 Distribution of county variables by quintiles of CBSA-level economic segregation, 1970

Descriptive statistics of counties stratified by CBSA quintile of economic segregation (H) in 1970
Q1 Q2 Q3 Q4 Q5 p
N Counties 81 85 126 188 226
HD % Decline (mean (sd)) 63.1 (12.9) 57.4 (12.1) 58.8 (13.4) 54.7 (14.7) 50.7 (19.3) <0.001
Total population, 1970 (mean (sd)) 137465.1 (135924.9) 166512.5 (192085.0) 166914.0 (261959.8) 193052.9 (501552.8) 170939.0 (663657.6) 0.936
% population change 1970 - 2010 (mean (sd)) 64.5 (76.9) 83.6 (135.6) 93.7 (139.0) 93.3 (104.3) 174.6 (219.8) <0.001
Total % in poverty, 1970 10.3 (4.7) 10.7 (6.1) 11.7 (8.0) 13.3 (7.5) 18.3 (9.9) <0.001
Black % in poverty, 1970 24.7 (13.1) 27.4 (15.6) 25.2 (14.1) 30.4 (17.1) 38.0 (17.4) <0.001
White % in poverty, 1970 9.9 (4.8) 9.6 (5.5) 10.2 (7.0) 10.6 (6.4) 12.3 (6.1) <0.001
Total % with college degree, 1970 8.6 (3.5) 9.8 (3.9) 8.8 (4.1) 8.4 (5.1) 8.5 (5.5) 0.270
Black % with college degree, 1970 9.2 (17.6) 5.4 (7.3) 6.0 (9.3) 4.6 (6.1) 4.1 (6.0) 0.001
White % with college degree, 1970 8.7 (3.5) 10.0 (3.9) 9.1 (4.2) 9.1 (5.7) 9.6 (6.0) 0.397

NOTE: Remember the unit of analysis in this table is the County, which is nested with the CBSA (metropolitan area). The economic segregation is measured at the CBSA level, but the outcome (percent decline in heart disease mortality and other covariates) are measured at the county level.

3 Multilevel modeling

  • Unit of analysis is county-specific demographic strata. In other words the outcome is measured for 4 demographic strata per county:
    • White, 35-64 years old
    • White, 65+
    • Black, 35-64 years old
    • Black, 65+
  • The primary exposure is overall economic segregation at the CBSA scale in 1970 (ALL70_H), although poverty concentration (ALL70_H10) and wealth concentration (ALL70_H90) are also evaluated.
  • The segregation indices are all standardized to \(N(0,1)\) for easier interpretation of regression coefficients.

3.1 Model Results

3.1.1 Unadjusted models

Models are fit for Overall H, as well as H10 (poverty concentration) and H90 (affluence concentration).
Unadjusted multilevel model follow this form:

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Here are results for unadjusted models with each of 3 segregation measures:
Compare segregation index, Unadjusted
  Overall H H10 (Poverty) H90 (Affluence)
Predictors Estimates CI p Estimates CI p Estimates CI p
(Intercept) 59.3 58.0 – 60.6 <0.001 59.5 58.0 – 60.9 <0.001 59.5 58.1 – 60.8 <0.001
H_overall -3.0 -4.2 – -1.8 <0.001
H_poverty -1.9 -3.2 – -0.5 0.007
H_affluence -2.3 -3.5 – -1.1 <0.001
Random Effects
σ2 156.29 156.27 156.27
τ00 36.59 FIPS 36.74 FIPS 36.89 FIPS
43.98 CBSA 50.45 CBSA 47.08 CBSA
ICC 0.34 0.36 0.35
N 708 FIPS 708 FIPS 708 FIPS
171 CBSA 171 CBSA 171 CBSA
Observations 2731 2731 2731
Marginal R2 / Conditional R2 0.037 / 0.365 0.014 / 0.367 0.021 / 0.363
AIC 22187.658 22202.743 22196.797

INTERPRETATION: The model is linear and the outcome is % decline - this outcome is relatively normally distributed and higher values mean faster/larger declines and smaller values mean slower. Remember also the exposure, economic segregation, is standardized so that zero = average and 1-unit is a 1-SD change. So looking at the intercepts we see that in each model for counties within CBSA’s with average economic segregation there was approximately 58-59% declines in heart disease mortality between 1970 and 2015. However for each 1-SD increase in economic segregation, declines slowed by 2-3%. One way of thinking about this is that segregation slowed the pace of progress in heart disease mortality. Comparing the different measures of segregation, the overall effect seems to be driven more by segregation of affluence than by segregation of poverty, although both are important.

3.1.2 Adjusted models

The adjusted, no interaction models are of this general form:



And here are results of adjusted (no-interaction) models for all 3 indices:

Compare segregation index, Adjusted
  Overall H H10 (Poverty) H90 (Affluence)
Predictors Estimates CI p Estimates CI p Estimates CI p
(Intercept) 21.4 2.2 – 40.6 0.029 21.9 -0.4 – 44.1 0.054 23.4 2.4 – 44.5 0.029
H_overall -4.4 -5.7 – -3.2 <0.001
White 2.7 1.6 – 3.8 <0.001 2.6 1.5 – 3.7 <0.001 2.6 1.5 – 3.7 <0.001
65+ -8.5 -9.3 – -7.7 <0.001 -8.5 -9.3 – -7.7 <0.001 -8.5 -9.3 – -7.7 <0.001
POP_CHANGE 1.8 1.4 – 2.3 <0.001 1.8 1.3 – 2.2 <0.001 1.8 1.4 – 2.2 <0.001
race_specific_poverty 2.0 -2.1 – 6.0 0.341 1.8 -2.3 – 5.8 0.386 1.9 -2.1 – 5.9 0.356
race_specific_college -1.3 -8.7 – 6.0 0.718 -1.3 -8.7 – 6.0 0.722 -1.3 -8.6 – 6.1 0.734
log(TOTPOP) 2.8 1.4 – 4.2 <0.001 2.8 1.2 – 4.4 0.001 2.7 1.2 – 4.2 <0.001
H_poverty -3.6 -5.1 – -2.1 <0.001
H_affluence -3.7 -5.0 – -2.3 <0.001
Random Effects
σ2 95.78 95.79 95.78
τ00 30.95 FIPS 30.81 FIPS 30.97 FIPS
32.00 CBSA 40.15 CBSA 38.01 CBSA
ICC 0.40 0.43 0.42
N 633 FIPS 633 FIPS 633 FIPS
139 CBSA 139 CBSA 139 CBSA
Observations 2331 2331 2331
Marginal R2 / Conditional R2 0.211 / 0.524 0.186 / 0.533 0.189 / 0.529
AIC 17902.290 17921.280 17917.526

INTERPRETATION: The deleterious effects of economic segregation are stronger with adjustment for baseline variables including race-specific poverty, population size, and population change.

3.1.3 H x Race interaction

Looking at whether the effects of overall H segregation varies by race:

## Computing p-values via Wald-statistics approximation (treating t as Wald z).
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
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Compare Interaction Models
  No Interaction Race x Seg Intxn
Predictors Estimates CI p Estimates CI p
(Intercept) 21.4 2.2 – 40.6 0.029 21.5 2.3 – 40.7 0.028
H_overall -4.4 -5.7 – -3.2 <0.001 -4.7 -6.1 – -3.4 <0.001
White 2.7 1.6 – 3.8 <0.001 2.6 1.5 – 3.7 <0.001
65+ -8.5 -9.3 – -7.7 <0.001 -8.5 -9.2 – -7.7 <0.001
POP_CHANGE 1.8 1.4 – 2.3 <0.001 1.8 1.4 – 2.3 <0.001
race_specific_poverty 2.0 -2.1 – 6.0 0.341 2.0 -2.1 – 6.0 0.340
race_specific_college -1.3 -8.7 – 6.0 0.718 -1.4 -8.8 – 5.9 0.703
log(TOTPOP) 2.8 1.4 – 4.2 <0.001 2.8 1.4 – 4.2 <0.001
H_overall:raceWhite 0.5 -0.3 – 1.3 0.226
Random Effects
σ2 95.78 95.77
τ00 30.95 FIPS 30.92 FIPS
32.00 CBSA 31.99 CBSA
ICC 0.40 0.40
N 633 FIPS 633 FIPS
139 CBSA 139 CBSA
Observations 2331 2331
Marginal R2 / Conditional R2 0.211 / 0.524 0.212 / 0.524
AIC 17902.290 17902.725

INTERPRETATION: There is no evidence for a \(race*segregation\) interaction.

3.1.4 H x Age interaction

Looking at whether the effects of overall H segregation varies by race:

## Computing p-values via Wald-statistics approximation (treating t as Wald z).
## Computing p-values via Wald-statistics approximation (treating t as Wald z).
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Compare Interaction Models
  No Interaction Age x Seg Intxn
Predictors Estimates CI p Estimates CI p
(Intercept) 21.4 2.2 – 40.6 0.029 21.4 2.2 – 40.6 0.029
H_overall -4.4 -5.7 – -3.2 <0.001 -4.5 -5.8 – -3.2 <0.001
White 2.7 1.6 – 3.8 <0.001 2.7 1.6 – 3.8 <0.001
65+ -8.5 -9.3 – -7.7 <0.001 -8.5 -9.3 – -7.7 <0.001
POP_CHANGE 1.8 1.4 – 2.3 <0.001 1.8 1.4 – 2.3 <0.001
race_specific_poverty 2.0 -2.1 – 6.0 0.341 2.0 -2.1 – 6.0 0.343
race_specific_college -1.3 -8.7 – 6.0 0.718 -1.4 -8.7 – 6.0 0.713
log(TOTPOP) 2.8 1.4 – 4.2 <0.001 2.8 1.4 – 4.2 <0.001
H_overall:age65+ 0.2 -0.6 – 1.0 0.688
Random Effects
σ2 95.78 95.82
τ00 30.95 FIPS 30.95 FIPS
32.00 CBSA 31.99 CBSA
ICC 0.40 0.40
N 633 FIPS 633 FIPS
139 CBSA 139 CBSA
Observations 2331 2331
Marginal R2 / Conditional R2 0.211 / 0.524 0.211 / 0.524
AIC 17902.290 17904.052

INTERPRETATION: There is no evidence for a \(age*segregation\) interaction.

3.1.5 H x Race x Age interaction

Compare Segregation Indices, Intxn Model
  No Interaction (H) Race x Age x Seg Intxn (H) Race x Age x Seg Intxn (H10) Race x Age x Seg Intxn (H90)
Predictors Estimates CI p Estimates CI p Estimates CI p Estimates CI p
(Intercept) 21.4 2.2 – 40.6 0.029 20.7 1.5 – 39.9 0.034 21.3 -1.0 – 43.5 0.061 22.8 1.7 – 43.8 0.034
H_overall -4.4 -5.7 – -3.2 <0.001 -3.1 -4.6 – -1.7 <0.001
White 2.7 1.6 – 3.8 <0.001 3.4 2.0 – 4.7 <0.001 3.4 2.1 – 4.7 <0.001 3.3 1.9 – 4.6 <0.001
65+ -8.5 -9.3 – -7.7 <0.001 -7.6 -8.8 – -6.5 <0.001 -7.6 -8.8 – -6.4 <0.001 -7.7 -8.9 – -6.5 <0.001
POP_CHANGE 1.8 1.4 – 2.3 <0.001 1.8 1.4 – 2.3 <0.001 1.8 1.3 – 2.2 <0.001 1.8 1.4 – 2.2 <0.001
race_specific_poverty 2.0 -2.1 – 6.0 0.341 2.5 -1.5 – 6.4 0.227 2.3 -1.7 – 6.3 0.270 2.2 -1.8 – 6.2 0.281
race_specific_college -1.3 -8.7 – 6.0 0.718 -0.9 -8.1 – 6.4 0.812 -0.9 -8.1 – 6.4 0.811 -0.7 -8.0 – 6.5 0.844
log(TOTPOP) 2.8 1.4 – 4.2 <0.001 2.9 1.5 – 4.2 <0.001 2.8 1.2 – 4.4 0.001 2.7 1.2 – 4.3 <0.001
H_overall:raceWhite -2.6 -3.7 – -1.5 <0.001
H_overall:age65+ -3.4 -4.6 – -2.2 <0.001
raceWhite:age65+ -1.4 -2.9 – 0.2 0.092 -1.5 -3.1 – 0.1 0.061 -1.3 -2.9 – 0.3 0.115
H_overall:raceWhite:age65+ 6.4 4.8 – 8.0 <0.001
H_poverty -2.7 -4.3 – -1.0 0.002
H_poverty:raceWhite -2.0 -3.1 – -0.9 <0.001
H_poverty:age65+ -2.7 -3.9 – -1.5 <0.001
H_poverty:raceWhite:age65+ 5.4 3.8 – 7.0 <0.001
H_affluence -2.6 -4.1 – -1.0 0.001
H_affluence:raceWhite -2.3 -3.4 – -1.1 <0.001
H_affluence:age65+ -2.9 -4.1 – -1.6 <0.001
H_affluence:raceWhite:age65+ 5.6 3.9 – 7.3 <0.001
Random Effects
σ2 95.78 92.58 93.33 93.46
τ00 30.95 FIPS 31.61 FIPS 31.37 FIPS 31.44 FIPS
32.00 CBSA 32.04 CBSA 40.12 CBSA 38.02 CBSA
ICC 0.40 0.41 0.43 0.43
N 633 FIPS 633 FIPS 633 FIPS 633 FIPS
139 CBSA 139 CBSA 139 CBSA 139 CBSA
Observations 2331 2331 2331 2331
Marginal R2 / Conditional R2 0.211 / 0.524 0.224 / 0.540 0.196 / 0.545 0.198 / 0.540
AIC 17902.290 17843.660 17877.043 17875.232

INTERPRETATION: Using the AIC model fit statistic as a guide, there is evidence for a \(race\x age\x segregation\) interaction. Because it is hard to interpret the interaction models, here are plots of the segregation x race x age effects for ALL70_H, the overall segregation index (results are similar for H10 and H90, the indices of poverty and affluence segregation respectively).

3.1.6 Interaction plot of segregation x race x age

4 Conclusion

  1. Best fitting model is 3-way interaction (race x age x segregation) for overall H.
  2. While the interaction model fits best, the heterogeneity in slope is modest. All sub-groups have inverse association between % decline and economic segregation but steepest slope is for older Blacks and younger whites.
  3. Overall H fits best, although segregation of affluence seems relatively more important than segregation of poverty.

  1. Reardon SF, Bischoff K. Income Inequality and Income Segregation. Am J Sociol. 2011 Jan;116(4):1092–153.↩