Ben Elbers - Did Residential Racial Segregation in the U.S. Really Increase?

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Ben Elbers - Did Residential Racial Segregation in the U.S. Really Increase?

https://elbersb.com/public/posts/2021-07-23-segregation-increase/

[jkaucic]

Dear Ben Elbers,

I have a question concerning aggregate, but also local, values of the H and M indexes as compared to the D index. I have used your segregation package on two different datasets, and always the aggregate H index was in the range of 0.0x, while the D index was 0.x; ranging from a difference factor 3 up to factor 10. So the interpretation of both indices, which are normalized between 0 and 1, would differ completely (H index saying 'segregation close to zero', while D index indicating some level of segregation).

I have tested this with the R code and dataset related to your paper mentioned in this blog post and also found metro areas where D is ten times larger than H for specific racial group comparisons. E.g. it came up in the Hispanic-White comparison in Springfield, MO 1990 & Houma-Thibodaux, LA 1990 & Daphne-Fairhope-Foley, AL 1990 - all characterized by an average 100 times larger White population than Hispanic population across tracts. Is it the case that the H (and M index, i guess) are going towards zero, if one of the groups is significantly smaller than the other group? Or am I missing something completely different?

I am looking forward to your kind reply,
kind regards,
Jiannis

[jkaucic]

Thank you for your reply. My neighborhood definition are 100x100m grid cells with between 30 and 263 households. I guess that's very small and therefore I'd rather not use the local segregation scores? Would you have a suggestion how I could measure local segregation instead? (I am looking for a variable to measure micro-segregation across these 100m grid cells)

I do not follow the argument that local segregation scores of any unit or group should not be correlated with group size. Isn't local segregation measuring the deviation between the makeup of the city versus that of individuals' local neighborhood? And therefore, If I measure the segregation between high income groups and low income groups, shouldn't those neighborhoods with high (or low) shares of either group show high segregation values as opposed to neighborhoods with a group distribution close to the city mean? Otherwise, I am fundamentally misunderstanding the theory behind segregation scores and very sorry to bother you with this.

Best regards

[elbersb]

Yeah, that sounds indeed rather small. There's a bootstrap function built in the segregation package (Use se=TRUE when you call mutual_local). You could try to see how variable the local scores are. But if you don't have enough data, there won't be a magic bullet to solve this problem. As always in statistics, when you have little data, you need to make more assumptions.

My argument was about unit local segregation not being correlated with unit size (and the same for the correlation between group scores and group size). I guess in general I find it hard to reason about the correlation between the unit score and the group size, because the unit score is a summary of the distribution of all the groups simultaneously. Are you using a multi group measure or are you computing two-group measures?

[jkaucic]

Two-group measure

[elbersb]

So for a two-group measure the correlation would depend on the specific circumstances, but in general you would expect the correlation to be fairly small. Deviations from the global average are measured in both directions. So if you have two groups, then those neighborhoods where a group is underrepresented will have a high ls score, and neighborhoods where a group is overrepresented will have a high ls score. So you have more of a U shape (segregation is high when there's very few AND a lot of members of the group in question).

[jkaucic]

That makes perfect sense. Thank you so much for clarifying that!

Best regards!

[jimenezanalia]

Dear Benjamin Elbers,

Hello! I'm demography PhD student and I'm beggining to study about segregation and the R package that you created. A question arised as I finished to read your paper "A Method for Studying Differences in Segregation Across Time and Space" and this particular publication:

Is there a way to compare local segregation across time? And if so, could you be so kind to refer me to a paper o publication where that is explained, please?

[elbersb]

Hi! There isn't really a good answer to this, as these scores are not used very much in the literature. Two things that you could look at:
a) The segregation package allows for the computation of margins-adjusted local segregation scores - the idea is that these measure just the "structural" change as defined in the paper. You can find an FAQ entry about that here: https://elbersb.github.io/segregation/articles/faq.html#how-can-i-compute-margins-adjusted-local-segregation-scores
b) I also wrote up some thought on local segregation scores here: https://osf.io/preprints/socarxiv/3juyc/ Maybe that's helpful too.

[jimenezanalia]

Thank you very much for your reply! I was a little lost as to where to look some answers. Now thanks to you, I can give it a try again :)

[aferna08]

Hi Dr. Elbers,

I have a quick question about the behavior of the shapley decomposition method in the two-group context. When comparing changes in local scores over time using the mutual_difference command, it's my understanding that the "total" for each geographic sub-unit should sum to the overall structural change in M. This, for example, is the case in the Brooklyn example you show in your paper.

I've been having some issues with getting this to behave correctly in my own research, which involves comparing tract level changes in local black-white segregation for different CBSAs. I noticed in the replication materials for your Brooklyn example if you filter to any two-group race pair the local totals also do not sum exactly to the overall structural change (although they are much closer in than in my case). Perhaps something behaves differently in the two-group case than in the multi-group case? Or perhaps I'm misunderstanding how these local scores behave, and I shouldn't expect them to sum to the structural component?

Thank you so much for your time and contribution to this work! As a PhD student my research wouldn't be possible without the work you've done.

Best,
Aaron

[elbersb]

Hi, could you share some code? If you look at eq 10 in the paper, then that's the (exact) decomposition you can do for the unit local scores. Note that you need to apply the weights. A sum of local differences will not add up to the total change.

[aferna08]

Thanks for the quick reply! I have to admit I get a bit lost with the equation notation at times, so it's definitely possible I'm mistaking which package commands correspond to which equations. My understanding is the components coded as ls_diff_mean are the margins adjusted local difference and total is the weighted difference that should sum to overall structural change.

As far as code, here is an example from the replication materials of the Brooklyn example. After loading in the LTDB data, I simply added another filter to your mutual_difference command to restrict it to a two-group race pair. For example:

diff <- mutual_difference(filter(d, year == 2000 & race %in% c("nhwhite", "hispanic")), filter(d, year == 2010 & race %in% c("nhwhite", "hispanic")), group = "race", unit = "GEOID", weight = "n", method = "shapley_detailed")

In this case sum(diff$est[diff$stat == "structural"]) returns -0.05179928 and sum(diff$est[diff$stat == "total"]) returns -0.05631622. These values are obviously close but not exactly the same, which led me to believe I was missing something about their mathematical relationship. In my own research with tracts in the entire New York CBSA I get a larger difference. I'm happy to share that work in more detail over email if it would be useful.

Thanks so much,
Aaron

[elbersb]

Looking at the documentation (I'm also not quite firm on the exact details here any more), it says that

The changes in local linkage are given by ls_diff1 and ls_diff2, and their average is given by ls_diff_mean. The row named total summarizes the contribution of the unit towards structural change using the formula .5 * p1 * ls_diff1 + .5 * p2 * ls_diff2. The sum of all "total" components equals structural change.

So "total" is what is referred to as delta_u,structural in the paper (eq. 10). The values are not agreeing completely because of simulation uncertainty due to the IPF procedure. Try using the precision parameter in your example:

> diff <- mutual_difference(filter(d, year == 2000 & race %in% c("nhwhite", "hispanic")),  filter(d, year == 2010 & race %in% c("nhwhite", "hispanic")), group = "race", unit = "GEOID", weight = "n", method = "shapley_detailed", precision = 0.000000001) 
> sum(diff$est[diff$stat == "structural"])
[1] -0.05635925
> sum(diff$est[diff$stat == "total"])
[1] -0.05635927

If you use a very low precision parameter, are the values closer in your dataset?

[aferna08]

That fixed it! And makes complete sense with the IPF procedure—I should have read more into how that works. Thank you again for your time—I really appreciate it.