Cluster Analysis Pt. 3
Riya Sharma
2024-
## This code will not be evaluated automatically.
## (Notice the eval = FALSE declaration in the options section of the
## code chunk)
my_packages <- c("tidyverse", "broom", "coefplot", "cowplot",
"gapminder", "GGally", "ggrepel", "ggridges", "gridExtra",
"here", "interplot", "margins", "maps", "mapproj",
"mapdata", "MASS", "quantreg", "rlang", "scales",
"survey", "srvyr", "viridis", "viridisLite", "devtools")
install.packages(my_packages, repos = "http://cran.rstudio.com")Set Up Project and Load Libraries
To begin we must load some libraries we will be using. If we do not load them, R will not be able to find the functions contained in these libraries. The tidyverse includes ggplot and other tools. We also load the socviz and gapminder libraries.
Load Health Opportunity Index Data
I’ll join the HOI column to the SVI dataframe for cluster analysis purposes
# load HOI dataset
hoi = read_csv("/Users/riyasharma/Documents/GitHub/24Spr_RSharma_DATS4001/data/bigdata/VA HOI Data/Health_Opportunity_Index_20240203.csv")## Rows: 1875 Columns: 20
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (1): Rural~Urban
## dbl (19): Census Tract, Access to Care, Employment Accessibility, Affordabil...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# get county and tract values from tidycensus
va_income = get_acs(
geography = "tract",
variables = "B19013_001",
state = "VA",
year = 2020,
geometry = TRUE
)## Getting data from the 2016-2020 5-year ACS
## Downloading feature geometry from the Census website. To cache shapefiles for use in future sessions, set `options(tigris_use_cache = TRUE)`.##
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|======================================================================| 100%hoi_county = hoi %>%
rename(
GEOID = `Census Tract`)
hoi_county$GEOID = as.character(hoi_county$GEOID)
va_income$GEOID = as.character(va_income$GEOID)
hoi_county = va_income %>%
left_join(hoi_county, by = "GEOID")
hoi_county = select(hoi_county, -c("variable", "moe", "estimate"))
colnames(hoi_county) = gsub(" ", "_", colnames(hoi_county))
hoi_county$LOCATION = hoi_county$NAME
hoi_county$LOCATION2 = str_extract_all(hoi_county$NAME,"(?<=, ).+(?=,)")
hoi_county = select(as.data.frame(hoi_county), -c("GEOID", "NAME", "LOCATION", "geometry", `Rural~Urban`))
hoi_county = hoi_county %>%
group_by(LOCATION2) %>%
summarize_all("median", na.rm=T)
# hoi_county = na.omit(hoi_county)
hoi_county = as.data.frame(hoi_county)
hoi_county = hoi_county %>%
left_join(va_county, by = "LOCATION2")
hoi_county = as.data.frame(hoi_county)
hoi_county = select(hoi_county, -c("variable", "moe", "estimate", "NAME", "GEOID", "geometry"))
svi_county_pc_median = hoi_county %>%
left_join(svi_county_pc_median, by = "LOCATION2")
# remove all other columns from HOI dataset besides median HOI
svi_county_pc_median = select(svi_county_pc_median, -c("Access_to_Care", "Affordability", "Employment_Accessibility", "Air_Quality", "Population_Churning", "Education", "Food_Accessibility",
"Income_Inequality", "Job_Participation", "Population_Density", "Segregation", "Material_Deprivation", "Walkability", "Community_Environment_Profile", "Consumer_Opportunity_Profile", "Economic_Opportunity_Profile",
"Wellness_Disparity_Profile"))
svi_county_pc_128 = na.omit(svi_county_pc_median)
svi_county_pc_numeric = na.omit(svi_county_pc_median)
svi_county_pc_numeric = select(svi_county_pc_numeric, -c("LOCATION2"))
# divide all columns (except HOI) by 100 so they're all on the same scale
svi_county_pc_numeric = svi_county_pc_numeric %>% mutate(svi_county_pc_numeric[,2:16] / 100)PCA
# first, conduct principal component analysis
pca_res = prcomp(svi_county_pc_numeric)
pca_res$rotation## PC1 PC2 PC3 PC4
## Health_Opportunity_Index -0.084098991 0.28571097 -0.361615876 0.011521564
## EP_POV 0.041903254 -0.40847464 0.452592375 -0.264020974
## EP_NOHSDP 0.009998088 -0.40945180 -0.036410996 -0.127373003
## EP_AGE65 -0.121117306 -0.19653380 -0.135950362 -0.004092889
## EP_AGE17 0.044770473 0.07585217 -0.139973365 -0.172500966
## EP_DISABL -0.077404604 -0.31314136 0.007410657 -0.188925287
## EP_SNGPNT 0.084529203 -0.07698988 0.031291969 -0.251818933
## EP_MINRTY 0.939755415 -0.14220393 -0.241221019 0.136844530
## EP_LIMENG 0.023866472 0.03041623 0.013409972 0.017728105
## EP_MUNIT 0.150437484 0.22531333 0.695852297 0.448782295
## EP_MOBILE -0.213671211 -0.55957297 -0.194637791 0.673065421
## EP_CROWD 0.008542874 0.00244183 0.016855845 0.016345873
## EP_NOVEH 0.074536597 -0.14247742 0.193080154 -0.193226379
## EP_GROUPQ 0.018296289 -0.04162013 0.050037543 0.110340171
## EP_UNINSUR 0.029853581 -0.13786514 0.029140125 -0.198270528
## EP_UNEMP 0.049088829 -0.09707200 0.050798887 -0.150014420
## PC5 PC6 PC7 PC8
## Health_Opportunity_Index -0.302227349 0.05518448 -0.56747235 0.2187314356
## EP_POV -0.023727434 -0.43704271 -0.23324151 -0.1893570741
## EP_NOHSDP -0.278981168 0.43573932 0.33605499 0.0706027328
## EP_AGE65 0.721707351 0.45117465 -0.19377808 0.0429136600
## EP_AGE17 -0.394806365 0.17492042 0.05746962 0.0925027736
## EP_DISABL -0.061418738 0.15283591 -0.42690612 0.1633666998
## EP_SNGPNT -0.123065042 0.02468668 0.04827142 0.2399148659
## EP_MINRTY 0.070670899 -0.02048722 -0.09265913 -0.0414606244
## EP_LIMENG -0.088421604 0.10654178 0.09333488 0.0050705284
## EP_MUNIT -0.124851747 0.39362845 -0.15246310 0.0957415060
## EP_MOBILE -0.229250995 -0.10085439 -0.07816388 -0.0115200182
## EP_CROWD -0.041195668 0.08136020 0.05183996 -0.0008072342
## EP_NOVEH -0.006871349 0.12117682 -0.28037595 0.2611076614
## EP_GROUPQ 0.175378536 -0.25819536 0.30767753 0.8214103630
## EP_UNINSUR -0.116638692 0.29956312 0.22565114 -0.1314924623
## EP_UNEMP -0.086896872 -0.05799628 -0.10805206 0.2131726763
## PC9 PC10 PC11 PC12
## Health_Opportunity_Index -0.500774196 -0.11454303 0.145602703 -0.112897782
## EP_POV -0.330569879 -0.12175059 0.296487360 -0.070132163
## EP_NOHSDP -0.234217689 0.31178737 0.361327023 -0.183135221
## EP_AGE65 -0.026140345 -0.24332679 0.249944158 -0.085340400
## EP_AGE17 0.309333513 -0.14901221 0.208294901 0.001804473
## EP_DISABL 0.171270092 0.42784589 -0.130025488 0.603943010
## EP_SNGPNT 0.326955655 -0.23816423 0.118355260 -0.246531067
## EP_MINRTY -0.034696311 0.02420696 0.003377656 0.041703544
## EP_LIMENG -0.157996144 -0.04329142 0.038878029 0.044987739
## EP_MUNIT -0.008253917 -0.05039382 0.119916471 0.069439917
## EP_MOBILE 0.111014025 -0.19299703 -0.114909933 -0.096646932
## EP_CROWD -0.005802071 -0.06302912 -0.015684092 0.131640780
## EP_NOVEH 0.106564107 0.10030712 -0.539809116 -0.575331038
## EP_GROUPQ -0.252389883 0.03590189 -0.012275708 0.132752195
## EP_UNINSUR -0.410649467 -0.43645994 -0.532054967 0.250059892
## EP_UNEMP 0.264961852 -0.55280243 0.139943637 0.263765592
## PC13 PC14 PC15 PC16
## Health_Opportunity_Index 0.05369174 -0.1017549460 0.066889168 0.0243066893
## EP_POV -0.22945158 0.0673289953 0.013130056 0.0272411645
## EP_NOHSDP 0.32122281 0.0501273493 0.082464334 0.0205046545
## EP_AGE65 -0.17580574 0.0610244908 -0.005964000 -0.0089827929
## EP_AGE17 -0.59990937 0.4586301232 0.081005971 -0.0805450008
## EP_DISABL -0.08499917 -0.1333307565 -0.043515123 -0.0565675742
## EP_SNGPNT -0.12345814 -0.7694256878 0.003735493 -0.0348168294
## EP_MINRTY -0.01935502 0.0003816526 0.008961285 -0.0030862976
## EP_LIMENG -0.11315465 -0.0293843044 -0.962322519 0.0003483533
## EP_MUNIT -0.02584089 -0.0556347583 0.086010228 -0.0712284707
## EP_MOBILE -0.08614106 -0.0362388180 -0.018515860 -0.0125928221
## EP_CROWD -0.10516198 -0.0463856563 0.042085080 0.9756032520
## EP_NOVEH 0.06496694 0.2622558426 -0.101616539 0.1042464364
## EP_GROUPQ -0.15732878 0.0749230025 0.053074192 -0.0224783041
## EP_UNINSUR -0.11771139 -0.0910281083 0.152034533 -0.1356133384
## EP_UNEMP 0.59402417 0.2619924389 -0.090188925 0.0214330540summary(pca_res)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 0.1964 0.1231 0.09332 0.05709 0.04687 0.03577 0.03188
## Proportion of Variance 0.5235 0.2056 0.11816 0.04423 0.02981 0.01736 0.01379
## Cumulative Proportion 0.5235 0.7291 0.84725 0.89148 0.92128 0.93864 0.95243
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.03096 0.02952 0.02240 0.01898 0.01612 0.01542 0.01404
## Proportion of Variance 0.01300 0.01182 0.00681 0.00489 0.00353 0.00323 0.00267
## Cumulative Proportion 0.96544 0.97726 0.98407 0.98896 0.99249 0.99571 0.99839
## PC15 PC16
## Standard deviation 0.00848 0.006843
## Proportion of Variance 0.00098 0.000640
## Cumulative Proportion 0.99936 1.000000get_eig(pca_res) # Dim 1 and 2 - highest variance.percent## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 3.857919e-02 52.35029375 52.35029
## Dim.2 1.515043e-02 20.55847838 72.90877
## Dim.3 8.707779e-03 11.81607998 84.72485
## Dim.4 3.259323e-03 4.42276082 89.14761
## Dim.5 2.196596e-03 2.98068517 92.12830
## Dim.6 1.279183e-03 1.73579587 93.86409
## Dim.7 1.016338e-03 1.37912682 95.24322
## Dim.8 9.583723e-04 1.30046974 96.54369
## Dim.9 8.712809e-04 1.18229047 97.72598
## Dim.10 5.018349e-04 0.68096832 98.40695
## Dim.11 3.603315e-04 0.48895433 98.89590
## Dim.12 2.599320e-04 0.35271654 99.24862
## Dim.13 2.378604e-04 0.32276634 99.57139
## Dim.14 1.971301e-04 0.26749702 99.83888
## Dim.15 7.190936e-05 0.09757790 99.93646
## Dim.16 4.682432e-05 0.06353857 100.00000# pc1 accounts for 52.35% of the direction of max variance, and within PC1, percent minority accounts for 94% of the max direction of variance
# Visualize how correlated variables are with PC1 and PC2
fviz_pca_var(pca_res, col.var="steelblue")+
theme_minimal() # we see that median percent minority and median per capita income are loosely correlated with nearly all other variables, with EP_AGE17, EP_LIMENG, EP_CROWD, EP_GROUPQ, EP_SNGPNT, EP_UNINSUR and all others highly correlated with one another
# Visualize Dim2 vs. Dim1 for individual points
fviz_pca_ind(pca_res, title = "Individuals Factor Map (PCA)", geom="point") +
geom_point(show.legend = FALSE) +
geom_text_repel(aes(label = (svi_county_pc_128$LOCATION2), show.legend = FALSE))## Warning in geom_text_repel(aes(label = (svi_county_pc_128$LOCATION2),
## show.legend = FALSE)): Ignoring unknown aesthetics: show.legend## Warning: ggrepel: 70 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
Cluster Analysis
#############################################################
# find optimal number of clusters with a scree (elbow) plot #
#############################################################
# Decide how many clusters to look at
n_clusters <- 10
# Initialize total within sum of squares error: wss
wss <- numeric(n_clusters)
set.seed(123)
# Look over 1 to n possible clusters
for (i in 1:n_clusters) {
# Fit the model: km.out
km_svi_pc_county <- kmeans(svi_county_pc_numeric, centers = i, nstart = 20)
# Save the within cluster sum of squares
wss[i] <- km_svi_pc_county$tot.withinss
}
# Produce a scree plot
wss_df <- tibble(clusters = 1:n_clusters, wss = wss)
scree_plot <- ggplot(wss_df, aes(x = clusters, y = wss, group = 1)) +
geom_point(size = 4)+
geom_line() +
scale_x_continuous(breaks = c(2, 4, 6, 8, 10)) +
xlab('Number of clusters') + theme_economist()
scree_plot +
geom_hline(
yintercept = wss,
linetype = 'dashed') # we see that within cluster sum of squares sharply reduces up to 6 clusters but the variability doesn't change much past that point. For this reason, we will do cluster analysis with 6 clusters.
# fitting and evaluating the model
set.seed(134)
km_svi_pc_county <- kmeans(svi_county_pc_numeric, centers = 6, nstart = 20)
km_svi_pc_county## K-means clustering with 6 clusters of sizes 36, 16, 22, 30, 11, 13
##
## Cluster means:
## Health_Opportunity_Index EP_POV EP_NOHSDP EP_AGE65 EP_AGE17 EP_DISABL
## 1 0.4431281 0.08562500 0.10705556 0.1907917 0.2044444 0.13198611
## 2 0.3569403 0.18525000 0.17568750 0.1565000 0.2130625 0.16118750
## 3 0.3890466 0.18297727 0.17350000 0.2211818 0.1869773 0.21500000
## 4 0.3895936 0.15175000 0.16840000 0.2123667 0.1944667 0.16168333
## 5 0.3495323 0.17227273 0.07727273 0.1172273 0.1769545 0.09336364
## 6 0.4627851 0.05815385 0.07865385 0.1203846 0.2418462 0.10161538
## EP_SNGPNT EP_MINRTY EP_LIMENG EP_MUNIT EP_MOBILE EP_CROWD
## 1 0.06316667 0.15733333 0.005138889 0.02368056 0.056013889 0.01058333
## 2 0.11859375 0.62518750 0.010406250 0.07306250 0.050625000 0.01303125
## 3 0.06790909 0.05290909 0.001636364 0.02000000 0.202886364 0.01038636
## 4 0.07458333 0.33540000 0.006916667 0.01495000 0.145650000 0.01241667
## 5 0.06936364 0.32559091 0.018272727 0.26531818 0.003272727 0.01768182
## 6 0.07600000 0.39203846 0.018230769 0.04257692 0.006423077 0.01065385
## EP_NOVEH EP_GROUPQ EP_UNINSUR EP_UNEMP
## 1 0.04016667 0.0049583333 0.08444444 0.04256944
## 2 0.10937500 0.0140312500 0.11534375 0.08775000
## 3 0.06940909 0.0105909091 0.09943182 0.06006818
## 4 0.05848333 0.0214666667 0.10746667 0.04930000
## 5 0.08431818 0.0236818182 0.07572727 0.04809091
## 6 0.02669231 0.0002307692 0.07488462 0.04776923
##
## Clustering vector:
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
## 6 2 1 6 4 4 3 5 5 1 2 5 5 6 3 1 6 6 6 6
## 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
## 5 5 2 2 2 2 5 1 3 1 1 1 1 3 1 4 2 1 4 6
## 41 42 43 44 45 46 47 48 49 50 51 53 54 55 56 57 58 59 60 61
## 1 1 2 6 5 3 6 4 4 6 5 2 4 4 4 1 4 5 4 5
## 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 81 82
## 2 2 3 6 1 1 1 4 4 4 3 1 3 3 4 1 4 4 4 3
## 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102
## 1 3 2 3 1 4 4 3 3 4 3 4 1 1 6 3 4 4 3 2
## 103 104 105 106 107 108 109 110 111 112 114 115 116 117 118 119 120 121 122 123
## 3 1 3 1 1 1 1 1 1 4 1 4 1 4 4 2 3 1 1 1
## 124 125 127 128 129 130 131 133
## 2 4 1 1 4 3 2 3
##
## Within cluster sum of squares by cluster:
## [1] 0.6326554 0.5939735 0.4994669 0.6559988 0.5329950 0.1551270
## (between_SS / total_SS = 67.2 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"#####################################
# initial visualization of clusters #
#####################################
fviz_cluster(km_svi_pc_county, svi_county_pc_numeric) 
# Add cluster column to main data frame
svi_county_pc_median = na.omit(svi_county_pc_median)
svi_county_pc_median$cluster = km_svi_pc_county$cluster
# map of counties and clusters
svi_county_pc_median = svi_county_pc_median %>%
left_join(va_county, by = "LOCATION2")
svi_county_pc_median = select(svi_county_pc_median, -c("variable", "estimate", "moe", "GEOID"))
svi_county_pc_median$cluster = as.factor(svi_county_pc_median$cluster)
svi_county_pc_median$LOCATION2 = as.character(svi_county_pc_median$LOCATION2)
svi_county_pc_median_sf = st_as_sf(svi_county_pc_median)
mylabel1 = glue::glue("<strong>{svi_county_pc_median$LOCATION2}</strong><br />
Cluster: {svi_county_pc_median$cluster}<br />") %>%
lapply(htmltools::HTML)
cluster_map = mapview(st_as_sf(svi_county_pc_median), zcol = "cluster",
col.regions = RColorBrewer::brewer.pal(6, "Accent"),
alpha.regions = 1,
label = mylabel1,
legend = F)
cluster_mapVisualize by Variables
# according to pca, percent below poverty is very influential
pov_plot = ggplot(svi_county_pc_median, aes(y = EP_POV, x = cluster, colour = factor(cluster))) +
geom_violin(show.legend = TRUE) +
geom_text_repel(aes(label = LOCATION2), show.legend = FALSE, colour = "black") +
labs(title = "Scatterplot for Poverty & Cluster",
x = "Cluster",
y = "Median % Living Below Poverty Line") + theme_economist_white()
pov_plot## Warning: ggrepel: 110 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
More Visualizations by Variables with High Influence
# percent minority by cluster
minrty_plot = ggplot(svi_county_pc_median, aes(y = EP_MINRTY, x = cluster, colour = factor(cluster))) +
geom_violin(show.legend = TRUE) +
geom_text_repel(aes(label = LOCATION2), show.legend = FALSE, colour = "black") +
labs(title = "Scatterplot for Percent Minority & Cluster",
x = "Cluster",
y = "Median % Minority") + theme_economist_white()
minrty_plot## Warning: ggrepel: 114 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
# percent minority map
mylabel2 = glue::glue("<strong>{svi_county_pc_median$LOCATION2}</strong><br />
Median % Minority: {svi_county_pc_median$EP_MINRTY}<br />") %>%
lapply(htmltools::HTML)
minrty_map = mapview(st_as_sf(svi_county_pc_median), zcol = "EP_MINRTY",
col.regions = RColorBrewer::brewer.pal(5, "YlGnBu"),
alpha.regions = 1,
label = mylabel2,
legend = F,
layer.name = "Median % Minority of VA Localities")## Warning: Found less unique colors (5) than unique zcol values (126)!
## Interpolating color vector to match number of zcol values.minrty_map# percent living in mobile homes
mobile_plot = ggplot(svi_county_pc_median, aes(y = EP_MOBILE, x = cluster, colour = factor(cluster))) +
geom_violin(show.legend = TRUE) +
geom_text_repel(aes(label = LOCATION2), show.legend = FALSE, colour = "black") +
labs(title = "Scatterplot for Percent Living in Mobile Homes & Cluster",
x = "Cluster",
y = "Median % Living in Mobile Homes") + theme_economist_white()
mobile_plot## Warning: ggrepel: 90 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
# percent mobile home map
mylabel3 = glue::glue("<strong>{svi_county_pc_median$LOCATION2}</strong><br />
Median % Minority: {svi_county_pc_median$EP_MOBILE}<br />") %>%
lapply(htmltools::HTML)
mobile_map = mapview(st_as_sf(svi_county_pc_median), zcol = "EP_MOBILE",
col.regions = RColorBrewer::brewer.pal(5, "RdPu"),
alpha.regions = 1,
label = mylabel3,
legend = F,
layer.name = "Median % Living in Mobile Homes per VA Locality")## Warning: Found less unique colors (5) than unique zcol values (91)!
## Interpolating color vector to match number of zcol values.mobile_map# median HOI
HOI_plot = ggplot(svi_county_pc_median, aes(y = Health_Opportunity_Index, x = cluster, colour = factor(cluster))) +
geom_violin(show.legend = TRUE) +
geom_text_repel(aes(label = LOCATION2), show.legend = FALSE, colour = "black") +
labs(title = "Scatterplot for Health Opportunity Index & Cluster",
x = "Cluster",
y = "Median HOI") + theme_economist_white()
HOI_plot## Warning: ggrepel: 100 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
# HOI map
mylabel4 = glue::glue("<strong>{svi_county_pc_median$LOCATION2}</strong><br />
Median Health Opportunity Index (HOI): {svi_county_pc_median$Health_Opportunity_Index}<br />") %>%
lapply(htmltools::HTML)
HOI_map = mapview(st_as_sf(svi_county_pc_median), zcol = "Health_Opportunity_Index",
col.regions = RColorBrewer::brewer.pal(4, "YlOrRd"),
alpha.regions = 1,
label = mylabel4,
legend = F,
layer.name = "Median HOI per VA Locality")## Warning: Found less unique colors (4) than unique zcol values (128)!
## Interpolating color vector to match number of zcol values.HOI_map# HSDP
HSD_plot = ggplot(svi_county_pc_median, aes(y = EP_NOHSDP, x = cluster, colour = factor(cluster))) +
geom_violin(show.legend = TRUE) +
geom_text_repel(aes(label = LOCATION2), show.legend = FALSE, colour = "black") +
labs(title = "Scatterplot for High School Diploma & Cluster",
x = "Cluster",
y = "Median % Without High School Diploma") + theme_economist_white()
HSD_plot## Warning: ggrepel: 86 unlabeled data points (too many overlaps). Consider
## increasing max.overlaps
# HOI map
mylabel5 = glue::glue("<strong>{svi_county_pc_median$LOCATION2}</strong><br />
Median % Without High School Diploma: {svi_county_pc_median$EP_NOHSDP}<br />") %>%
lapply(htmltools::HTML)
HSD_map = mapview(st_as_sf(svi_county_pc_median), zcol = "EP_NOHSDP",
col.regions = RColorBrewer::brewer.pal(4, "PuRd"),
alpha.regions = 1,
label = mylabel5,
legend = F,
layer.name = "Median % without HS Diploma per VA Locality")## Warning: Found less unique colors (4) than unique zcol values (108)!
## Interpolating color vector to match number of zcol values.HSD_map