EPID 684

Spatial Epidemiology

4/12/2022

Jon Zelner

`[email protected]`

`epibayes.io`

Discuss the qualitative dimensions of residential segregation.

Looking at interacting dimensions of risk using the index of concentration at the extremes (đź§Š).

Using a hierarchical approach to characterize multi-level patterns of residential segregation.

Smoothing pt. 2 (if âŹ°â€¦)

Take a look at the map of county-level segregation here.

Read some of the (short) regional segregation stories.

Pick an area that you are interested in/feel knowledgable about.

Look at patterns of change over time.

How does changing the scale impact what you see/learn from the map?

A function of local and regional dynamics.

Reflects the independent and interacting effects of racial discrimination and economic disparities (1).

Huge regional differences in the nature, causes, and intensity of residential segregation.

Obviously these dynamics stretch the ability of very reductive approaches to show us much that is meaningful.

Capture the impact of extremes

For wealth: \[\text{ICE}_i = \frac{A_i - P_i}{T_i}\]

Where, \(P_i\) = number of poor people in area \(i\), \(A_i\) number of affluent people, and \(T_i\) is total number.

Ranges from -1 to 1

Can be extended to multiple groupings, i.e. number of wealthy individuals in advantaged race/ethnic group - number of poor individuals in disadvantaged race/ethnic group.

What does the ICE let us learn in the Feldman (2) piece that we wouldnâ€™t have otherwise?

Dissimilarity & Isolation only characterize variation

*within*the lowest levels observed.Moranâ€™s I includes information on

*proximity*or*adjacency*but is also only focused on lowest-level relationships.Lichter and Parisi (3) use the Thiel index - an entropy-based measure - to characterize the overall intensity and scale of residential segregation.

Entropy (\(E\)) is a measure of uncertainty

Maximum value \(\to\) Maximum Uncertainty

Minimum value Minimum Uncertainty

For two groups: \[E = p \frac{1}{p} + (1-p)\frac{1}{1-p}\]

Not limited to binary comparisons

A weighted average of differences in entropy between different levels.

If \(H=0\), the entropy within all lower-level units is equivalent to the population-level entropy.

In other words, all variation is within-unit.

If \(H=1\), the total amount of population-level entropy is explained by between-unit variation.

\[ H_{B \in M} = \frac{1}{N_M E_M} \sum_{b=1}^{B}N_B(E_M-E_b) \]

Where:

- \(N_M\) is the total population
- \(E_M\) is the entropy for the whole population
- \(N_b\) is the population of small area \(b\)
- \(E_b\) is the entropy of small area \(b\)

\(H\) is a sum over neighborhood-level differences from the population entropy.

To see what the contribution of a given level is to the overall H, we just look at the sum over all smallest-level units in the one we care about.

This lets us ask what proportion of the total \(H\) in an area can be attributed to variation within and between different types of units within a metro area.

Can theses approaches help us pick more relevant scales of analysis? (Figure from (4))

1.

Bruch EE, Mare RD. Neighborhood Choice and Neighborhood Change. *American Journal of Sociology* [electronic article]. 2006;112(3):667â€“709. (http://www.journals.uchicago.edu/doi/full/10.1086/507856). (Accessed April 11, 2022)

2.

Feldman JM, Waterman PD, Coull BA, et al. Spatial social polarisation: Using the Index of Concentration at the Extremes jointly for income and race/ethnicity to analyse risk of hypertension. *J Epidemiol Community Health* [electronic article]. 2015;69(12):1199â€“1207. (http://jech.bmj.com/content/69/12/1199). (Accessed March 31, 2022)

3.

Lichter DT, Parisi D, Taquino MC. Toward a New Macro-Segregation? Decomposing Segregation within and between Metropolitan Cities and Suburbs. *American Sociological Review* [electronic article]. 2015;80(4):843â€“873. (https://doi.org/10.1177/0003122415588558). (Accessed March 13, 2020)

4.

PetroviÄ‡ A, Manley D, van Ham M. Freedom from the tyranny of neighbourhood: Rethinking sociospatial context effects. *Progress in Human Geography* [electronic article]. 2020;44(6):1103â€“1123. (https://doi.org/10.1177/0309132519868767). (Accessed February 14, 2021)

5.

Glanz J, Carey B, Holder J, et al. Where America Didnâ€™t Stay Home Even as the Virus Spread. *The New York Times* [electronic article]. 2020;(https://www.nytimes.com/interactive/2020/04/02/us/coronavirus-social-distancing.html). (Accessed April 11, 2022)