“DEM 7263 - Calculating Indices of Residential Segregation”
Assogba Albert
10/01/2021
Getting the Tract-level Data of the Total California Population
ca_tract <- get_acs(geography = "tract",
year=2019,
output="wide",
table = "B03002",
cache_table = T,
state = "CA",
survey = "acs5",
geometry = F)## Getting data from the 2015-2019 5-year ACS## Loading ACS5 variables for 2019 from table B03002 and caching the dataset for faster future access.REcoding Variables
trt_data<- ca_tract%>%
mutate(nhwhite=B03002_003E,
nhblack=B03002_004E,
nhother= B03002_005E+B03002_006E+B03002_007E+B03002_008E+B03002_009E+B03002_010E,
hisp=B03002_012E,
total=B03002_001E,
year=2019,
cofips=substr(GEOID, 1,5))%>%
select(GEOID,nhwhite, nhblack , nhother, hisp, total, year, cofips )%>%
arrange(cofips, GEOID)
head(trt_data)## # A tibble: 6 x 8
## GEOID nhwhite nhblack nhother hisp total year cofips
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 06001400100 2317 107 578 118 3120 2019 06001
## 2 06001400200 1475 52 306 174 2007 2019 06001
## 3 06001400300 3434 459 807 351 5051 2019 06001
## 4 06001400400 2554 266 702 485 4007 2019 06001
## 5 06001400500 1874 882 998 390 4124 2019 06001
## 6 06001400600 860 358 396 131 1745 2019 06001Getting County-Level Data of the Total California Population for each race group
co_data<-trt_data%>%
group_by(cofips)%>%
summarise(co_total=sum(total),
co_wht=sum(nhwhite),
co_blk=sum(nhblack),
co_oth=sum(nhother),
cohisp=sum(hisp))Merge Tract and County Data by County FIPS Code
merged_data<-left_join(x=trt_data,
y=co_data,
by="cofips")
head(merged_data)## # A tibble: 6 x 13
## GEOID nhwhite nhblack nhother hisp total year cofips co_total co_wht co_blk
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <dbl> <dbl> <dbl>
## 1 06001~ 2317 107 578 118 3120 2019 06001 1656754 520447 171168
## 2 06001~ 1475 52 306 174 2007 2019 06001 1656754 520447 171168
## 3 06001~ 3434 459 807 351 5051 2019 06001 1656754 520447 171168
## 4 06001~ 2554 266 702 485 4007 2019 06001 1656754 520447 171168
## 5 06001~ 1874 882 998 390 4124 2019 06001 1656754 520447 171168
## 6 06001~ 860 358 396 131 1745 2019 06001 1656754 520447 171168
## # ... with 2 more variables: co_oth <dbl>, cohisp <dbl>Calculate Segregation indices for a geography of your choosing, calculate two indices of segregation.
(1) Dissimilarity Index
\[D = .5* \sum_i \left | \frac{b_i}{B} - \frac{w_i}{W} \right |\] where \(b_i\) is the number of blacks in each tract, B is the number of blacks in the county, \(w_i\) is the number of whites in the tract, and W is the number of whites in the county.
co.dis<-merged_data%>%
mutate(d.wb=abs(nhwhite/co_wht - nhblack/co_blk))%>%
group_by(cofips)%>%
summarise(dissim= .5*sum(d.wb, na.rm=T))
co.dis## # A tibble: 58 x 2
## cofips dissim
## <chr> <dbl>
## 1 06001 0.535
## 2 06003 0
## 3 06005 0.823
## 4 06007 0.509
## 5 06009 0.377
## 6 06011 0.360
## 7 06013 0.602
## 8 06015 0.386
## 9 06017 0.413
## 10 06019 0.530
## # ... with 48 more rows(2) Interaction Index
\[\text{Interaction} = \sum_i \frac{b_i}{B} * \frac{w_i}{t_i} \]
co.int<-merged_data%>%
mutate(int.bw=(nhblack/co_blk * nhwhite/total))%>%
group_by(cofips)%>%
summarise(inter_bw= sum(int.bw, na.rm=T))
co.int## # A tibble: 58 x 2
## cofips inter_bw
## <chr> <dbl>
## 1 06001 0.241
## 2 06003 0.530
## 3 06005 0.500
## 4 06007 0.658
## 5 06009 0.812
## 6 06011 0.467
## 7 06013 0.277
## 8 06015 0.576
## 9 06017 0.759
## 10 06019 0.246
## # ... with 48 more rowsIsolation Index
Next is is the isolation index for blacks. The formula is:
\[\text{Isolation} = \sum_i \frac{b_i}{B} * \frac{b_i}{t_i} \]
co.isob<-merged_data%>%
mutate(isob=(nhblack/co_blk * nhblack/total))%>%
group_by(cofips)%>%
summarise(iso_b= sum(isob, na.rm=T))
co.isob## # A tibble: 58 x 2
## cofips iso_b
## <chr> <dbl>
## 1 06001 0.228
## 2 06003 0.00866
## 3 06005 0.136
## 4 06007 0.0364
## 5 06009 0.0123
## 6 06011 0.0281
## 7 06013 0.176
## 8 06015 0.0534
## 9 06017 0.0142
## 10 06019 0.0948
## # ... with 48 more rowsWhat are the two groups you used fot the index?
For this assignment the two groups used for the Dissimilarity Index are Non Hispanic Blacks and non Hispanic Whites and i calculate segregation from non Hispanic White residents. For the interaction Index same group was used and i calculate the exposure of non Hispanic Black residents to non Hispanic White residents.
create a map of the two Segregation indices
Map of Interaction Index
ca_seg<-list(co.dis, co.int)%>% reduce (left_join, by="cofips")
options(tigris_class = "sf")
ca_counties<- counties(state="CA", cb=T, year=2010)
ca_counties$cofips<-substr(ca_counties$GEO_ID, 10,15)
ca_seg_dat<- geo_join(ca_counties, ca_seg, by_sp="cofips", by_df="cofips")## Warning: We recommend using the dplyr::*_join() family of functions instead.## Warning: `group_by_()` was deprecated in dplyr 0.7.0.
## Please use `group_by()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was generated.usa = map_data("county") # get basic map data for all USA counties
ca = subset(usa, region == "california") # subset to counties in Ohio
names(ca)## [1] "long" "lat" "group" "order" "region" "subregion"library(stringr)
ca$county = str_to_title(ca$subregion)getLabelPoint <- # Returns a county-named list of label points
function(county) {Polygon(county[c('long', 'lat')])@labpt}
centroids = by(ca, ca$county, getLabelPoint) # Returns list
centroids2 <- do.call("rbind.data.frame", centroids) # Convert to Data Frame
centroids2$county = rownames(centroids)
names(centroids2) <- c('clong', 'clat', "county")
ca_seg_dat%>%
ggplot()+geom_sf(aes(fill=inter_bw))+
scale_fill_viridis_c()+
scale_color_viridis_c()+ geom_text(data = centroids2, aes(x = clong, y = clat, label = county),
color = "darkblue", size = 2.25) + theme_map() + theme(legend.position="left")+
ggtitle("Non-Hispanic Black interaction index", subtitle = "ACS 2019")
The result of the interaction index shows that the probability of a black resident “interacting” with a white person in their neighborhood is 80% in Sierra and Nevada. Unfortunately, this also means that 80 of every 100 people a black person meets in their neighborhood will be white. Similarly, the probability of a black person interacting with a white person in their neighborhood is about 20% in Los Angeles and Imperial.
Map of Dissimilarity Index
ca_seg_dat%>%
ggplot()+geom_sf(aes(fill=dissim))+
scale_fill_viridis_c()+ scale_color_viridis_c()+
geom_text(data = centroids2, aes(x = clong, y = clat, label = county), color = "darkblue", size = 2.25) + theme_map() + ggtitle("Non-Hispanic Black Dissimilarity index", subtitle = "ACS 2019")
The results or map shows that the Dissimilarity Index for Black/White in Toulumne and Amador is 0.8. The interpretation of this value is that 80% of black residents would need to move neighborhoods to achieve a uniform distribution of black residents across neighborhoods. The map also shows the Dissimilarity index for black/white in Sierra and Alpine with a value of 0.0. This means that there is a “perfect integration” and no residential segregation of blacks and whites in these two counties in California.