ndi: Neighborhood Deprivation Indices

Imputing missing census variables

In the messer() and powell_wiley() functions, missing census characteristics can be imputed using the missing and impute arguments of the pca() and fa() functions in the psych package called within the messer() and powell_wiley() function, respectively. Impute values using the logical imp argument (currently only calls impute = "median" by default, which assigns the median values of each missing census variable for a geography).

powell_wiley2020DC <- ndi::powell_wiley(state = "DC", year = 2020) # without imputation
powell_wiley2020DCi <- ndi::powell_wiley(state = "DC", year = 2020, imp = TRUE) # with imputation

table(is.na(powell_wiley2020DC$ndi$NDI)) # n=13 tracts without NDI (Powell-Wiley) values
table(is.na(powell_wiley2020DCi$ndi$NDI)) # n=0 tracts without NDI (Powell-Wiley) values

# Obtain the 2020 census tracts from the "tigris" package
tract2020DC <- tigris::tracts(state = "DC", year = 2020, cb = TRUE)

# Join the NDI (Powell-Wiley) values to the census tract geometry
DC2020pw <- merge(tract2020DC, powell_wiley2020DC$ndi, by = "GEOID")
DC2020pw <- merge(DC2020pw, powell_wiley2020DCi$ndi, by = "GEOID", suffixes = c("_nonimp", "_imp"))

# Visualize the NDI (Powell-Wiley) values (2016-2020 5-year ACS) for Washington, D.C., census tracts
## Continuous Index
ggplot2::ggplot() + 
  ggplot2::geom_sf(data = DC2020pw, 
                   ggplot2::aes(fill = NDI_nonimp),
                   size = 0.2,
                   color = "white") +
  ggplot2::theme_minimal() + 
  ggplot2::scale_fill_viridis_c() +
  ggplot2::labs(fill = "Index (Continuous)",
                caption = "Source: U.S. Census ACS 2016-2020 estimates") +
  ggplot2::ggtitle("Neighborhood Deprivation Index (Powell-Wiley), Non-Imputed",
                   subtitle = "DC census tracts as the referent")

ggplot2::ggplot() + 
  ggplot2::geom_sf(data = DC2020pw, 
                   ggplot2::aes(fill = NDI_imp),
                   size = 0.2,
                   color = "white") +
  ggplot2::theme_minimal() + 
  ggplot2::scale_fill_viridis_c() +
  ggplot2::labs(fill = "Index (Continuous)",
                caption = "Source: U.S. Census ACS 2016-2020 estimates") +
  ggplot2::ggtitle("Neighborhood Deprivation Index (Powell-Wiley), Imputed",
                   subtitle = "DC census tracts as the referent")

## Categorical Index
### Rename "9-NDI not avail" level as NA for plotting
DC2020pw$NDIQuintNA_nonimp <- factor(replace(as.character(DC2020pw$NDIQuint_nonimp), 
                                            DC2020pw$NDIQuint_nonimp == "9-NDI not avail", NA),
                                         c(levels(DC2020pw$NDIQuint_nonimp)[-6], NA))

ggplot2::ggplot() + 
  ggplot2::geom_sf(data = DC2020pw, 
                   ggplot2::aes(fill = NDIQuintNA_nonimp),
                   size = 0.2,
                   color = "white") +
  ggplot2::theme_minimal() + 
  ggplot2::scale_fill_viridis_d(guide = ggplot2::guide_legend(reverse = TRUE),
                                na.value = "grey80") +
  ggplot2::labs(fill = "Index (Categorical)",
                caption = "Source: U.S. Census ACS 2016-2020 estimates") +
  ggplot2::ggtitle("Neighborhood Deprivation Index (Powell-Wiley) Quintiles, Non-Imputed",
                   subtitle = "DC census tracts as the referent")

### Rename "9-NDI not avail" level as NA for plotting
DC2020pw$NDIQuintNA_imp <- factor(replace(as.character(DC2020pw$NDIQuint_imp), 
                                            DC2020pw$NDIQuint_imp == "9-NDI not avail", NA),
                                      c(levels(DC2020pw$NDIQuint_imp)[-6], NA))

ggplot2::ggplot() + 
  ggplot2::geom_sf(data = DC2020pw, 
                   ggplot2::aes(fill = NDIQuintNA_imp),
                   size = 0.2,
                   color = "white") +
  ggplot2::theme_minimal() + 
  ggplot2::scale_fill_viridis_d(guide = ggplot2::guide_legend(reverse = TRUE),
                                na.value = "grey80") +
  ggplot2::labs(fill = "Index (Categorical)",
                caption = "Source: U.S. Census ACS 2016-2020 estimates") +
  ggplot2::ggtitle("Neighborhood Deprivation Index (Powell-Wiley) Quintiles, Imputed",
                   subtitle = "DC census tracts as the referent")

Assign the referent (U.S.-Standardized Metric)

To conduct a contiguous US-standardized index, compute an NDI for all states as in the example below that replicates the nationally standardized NDI (Powell-Wiley) values (2013-2017 ACS-5) found in Slotman et al. (2022) and available from a GIS Portal for Cancer Research website. To replicate the nationally standardized NDI (Powell-Wiley) values (2006-2010 ACS-5) found in Andrews et al. (2020) change the year argument to 2010 (i.e., year = 2010).

us <- tigris::states()
n51 <- c("Commonwealth of the Northern Mariana Islands", "Guam", "American Samoa",
         "Puerto Rico", "United States Virgin Islands")
y51 <- us$STUSPS[!(us$NAME %in% n51)]

start_time <- Sys.time() # record start time
powell_wiley2017US <- ndi::powell_wiley(state = y51, year = 2017)
end_time <- Sys.time() # record end time
time_srr <- end_time - start_time # Calculate run time
powell_wiley2017US

## $ndi
## # A tibble: 73,056 × 20
##    GEOID     state county tract      NDI NDIQu…¹ MedHH…² PctRe…³ PctPu…⁴ MedHo…⁵
##    <chr>     <chr> <chr>  <chr>    <dbl> <fct>     <dbl>   <dbl>   <dbl>   <dbl>
##  1 01001020… Alab… Autau… 201   -2.51e-1 2-Belo…   67826    26.9    12.1  152500
##  2 01001020… Alab… Autau… 202    8.27e-1 4-Abov…   41287    10.9    24.1   96100
##  3 01001020… Alab… Autau… 203    6.63e-1 4-Abov…   46806    12.3    12.9   98900
##  4 01001020… Alab… Autau… 204    1.90e-1 3-Aver…   55895    17.8     5.7  140800
##  5 01001020… Alab… Autau… 205   -5.44e-1 2-Belo…   68143    20.2     8.8  187900
##  6 01001020… Alab… Autau… 206    7.26e-1 4-Abov…   44549    17.8    16     93300
##  7 01001020… Alab… Autau… 207    1.03e+0 5-Most…   41250     8.4    23.2   90800
##  8 01001020… Alab… Autau… 208.… -7.12e-1 2-Belo…   80089    25.7    13.1  299100
##  9 01001020… Alab… Autau… 208.… -3.76e-4 3-Aver…   64439    22.2     9.4  163200
## 10 01001020… Alab… Autau… 209    5.07e-1 4-Abov…   49469    11.6    19    120200
## # … with 73,046 more rows, 10 more variables: PctMgmtBusScArti <dbl>,
## #   PctFemHeadKids <dbl>, PctOwnerOcc <dbl>, PctNoPhone <dbl>,
## #   PctNComPlmb <dbl>, PctEducHSPlus <dbl>, PctEducBchPlus <dbl>,
## #   PctFamBelowPov <dbl>, PctUnempl <dbl>, TotalPop <dbl>, and abbreviated
## #   variable names ¹​NDIQuint, ²​MedHHInc, ³​PctRecvIDR, ⁴​PctPubAsst, ⁵​MedHomeVal
## # ℹ Use `print(n = ...)` to see more rows, and `colnames()` to see all variable names
## 
## $pca
## $pca$loadings
## 
## Loadings:
##                 PC1    PC2    PC3   
## logMedHHInc     -0.508 -0.482 -0.106
## PctNoIDRZ        0.520  0.446       
## PctPubAsstZ      0.309  0.686       
## logMedHomeVal   -0.902  0.135       
## PctWorkClassZ    0.896              
## PctFemHeadKidsZ  0.194  0.701 -0.145
## PctNotOwnerOccZ -0.418  1.022       
## PctNoPhoneZ             0.208  0.654
## PctNComPlmbZ           -0.114  0.855
## PctEducLTHSZ     0.448  0.420       
## PctEducLTBchZ    0.989              
## PctFamBelowPovZ  0.183  0.772       
## PctUnemplZ       0.125  0.612       
## 
##                  PC1   PC2   PC3
## SS loadings    3.680 3.667 1.203
## Proportion Var 0.283 0.282 0.093
## Cumulative Var 0.283 0.565 0.658
## 
## $pca$rotmat
##             [,1]       [,2]       [,3]
## [1,]  0.55862784  0.5566946 0.05689447
## [2,] -1.07454532  1.0353417 0.11522338
## [3,] -0.02457479 -0.3181005 1.02299745
## 
## $pca$rotation
## [1] "promax"
## 
## $pca$Phi
##           [,1]      [,2]      [,3]
## [1,] 1.0000000 0.5589563 0.2019482
## [2,] 0.5589563 1.0000000 0.2257122
## [3,] 0.2019482 0.2257122 1.0000000
## 
## $pca$Structure
##             [,1]        [,2]       [,3]
##  [1,] -0.7983619 -0.78924511 -0.3169437
##  [2,]  0.7566491  0.72262792  0.1464839
##  [3,]  0.6945047  0.86105916  0.2250651
##  [4,] -0.8412442 -0.38554970 -0.2228492
##  [5,]  0.9209060  0.55006528  0.1613593
##  [6,]  0.5562044  0.77638871  0.0519852
##  [7,]  0.1563371  0.79221347  0.1626307
##  [8,]  0.2466075  0.35502655  0.7010271
##  [9,]  0.1201396  0.08519067  0.8311965
## [10,]  0.6827484  0.67044690  0.1843296
## [11,]  0.9475443  0.48138341  0.1669005
## [12,]  0.6232212  0.88362870  0.2527666
## [13,]  0.4705114  0.68557375  0.1788853
## 
## $pca$communality
##  [1] 0.5009586 0.4719001 0.5669373 0.8372646 0.8066373 0.5499017 1.2207095
##  [8] 0.4716959 0.7435617 0.3773519 0.9823819 0.6309002 0.3905570
## 
## $pca$uniqueness
##     logMedHHInc       PctNoIDRZ     PctPubAsstZ   logMedHomeVal   PctWorkClassZ 
##      0.49904136      0.52809991      0.43306269      0.16273538      0.19336271 
## PctFemHeadKidsZ PctNotOwnerOccZ     PctNoPhoneZ    PctNComPlmbZ    PctEducLTHSZ 
##      0.45009834     -0.22070951      0.52830412      0.25643832      0.62264809 
##   PctEducLTBchZ PctFamBelowPovZ      PctUnemplZ 
##      0.01761813      0.36909983      0.60944297 
## 
## $pca$Vaccounted
##                            [,1]      [,2]       [,3]
## SS loadings           4.0565234 4.0415662 1.21158031
## Proportion Var        0.3120403 0.3108897 0.09319849
## Cumulative Var        0.3120403 0.6229300 0.71612846
## Proportion Explained  0.4357322 0.4341256 0.13014213
## Cumulative Proportion 0.4357322 0.8698579 1.00000000
## 
## 
## $missing
## # A tibble: 13 × 5
## # Groups:   variable, total, missing [13]
##    variable         total missing     n percent
##    <chr>            <int> <lgl>   <int> <chr>  
##  1 MedHHInc         73056 TRUE      995 1.36 % 
##  2 MedHomeVal       73056 TRUE     1948 2.67 % 
##  3 PctEducBchPlus   73056 TRUE      646 0.88 % 
##  4 PctEducHSPlus    73056 TRUE      646 0.88 % 
##  5 PctFamBelowPov   73056 TRUE      867 1.19 % 
##  6 PctFemHeadKids   73056 TRUE      816 1.12 % 
##  7 PctMgmtBusScArti 73056 TRUE      752 1.03 % 
##  8 PctNComPlmb      73056 TRUE      816 1.12 % 
##  9 PctNoPhone       73056 TRUE     1377 1.88 % 
## 10 PctOwnerOcc      73056 TRUE      816 1.12 % 
## 11 PctPubAsst       73056 TRUE      816 1.12 % 
## 12 PctRecvIDR       73056 TRUE      816 1.12 % 
## 13 PctUnempl        73056 TRUE      751 1.03 % 
## 
## $cronbach
## [1] 0.9372104

ggplot2::ggplot(powell_wiley2017US$ndi, ggplot2::aes(x = NDI)) +
  ggplot2::geom_histogram(color = "black", fill = "white") + 
  ggplot2::theme_minimal() +
  ggplot2::ggtitle("Histogram of US-standardized NDI (Powell-Wiley) values (2013-2017)",
                   subtitle = "U.S. census tracts as the referent (including AK, HI, and DC)")

The process to compute a US-standardized NDI (Powell-Wiley) took about 3.1 minutes to run on a machine with the features listed at the end of the vignette.

Compute Racial Isolation Index (RI)

Compute the RI (Anthopolos) values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts. This metric is based on Anthopolos et al. (2011) that assessed the racial isolation of the population that identifies as non-Hispanic or Latino, Black or African American alone. Multiple racial/ethnic subgroups are available in the anthopolos() function, including:

A census geography (and its neighbors) that has nearly all of its population who identify with the specified race/ethnicity subgroup(s) (e.g., Not Hispanic or Latino, Black or African American alone) will have an RI value that is close to 1. In contrast, a census geography (and its neighbors) that is nearly none of its population who identify with the specified race/ethnicity subgroup(s) (e.g., not Not Hispanic or Latino, Black or African American alone) will have an RI value that is close to 0.

anthopolos2010NC <- ndi::anthopolos(state = "NC", year = 2010, subgroup = "NHoLB")

# Obtain the 2010 census tracts from the "tigris" package
tract2010NC <- tigris::tracts(state = "NC", year = 2010, cb = TRUE)
# Remove first 9 characters from GEOID for compatibility with tigris information
tract2010NC$GEOID <- substring(tract2010NC$GEO_ID, 10) 

# Obtain the 2010 counties from the "tigris" package
county2010NC <- tigris::counties(state = "NC", year = 2010, cb = TRUE)

# Join the RI (Anthopolos) values to the census tract geometry
NC2010anthopolos <- merge(tract2010NC, anthopolos2010NC$ri, by = "GEOID")

# Visualize the RI (Anthopolos) values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts 
ggplot2::ggplot() + 
  ggplot2::geom_sf(data = NC2010anthopolos, 
                   ggplot2::aes(fill = RI),
                   size = 0.05,
                   color = "white") +
   ggplot2::geom_sf(data = county2010NC,
                   fill = "transparent", 
                   color = "white",
                   size = 0.2) +
  ggplot2::theme_minimal() +
  ggplot2::scale_fill_viridis_c() +
  ggplot2::labs(fill = "Index (Continuous)",
                caption = "Source: U.S. Census ACS 2006-2010 estimates") +
  ggplot2::ggtitle("Racial Isolation Index (Anthopolos), non-Hispanic Black",
                   subtitle = "NC census tracts (not corrected for edge effects)")

Current version of ndi package does not correct for edge effects (e.g., census geographies along the specified spatial extent border, coastline, or U.S.-Mexico / U.S.-Canada border) may have few neighboring census geographies and RI values in these census geographies may be unstable. A stop-gap solution for the former source of edge effect is to compute the RI for neighboring census geographies (i.e., the states bordering a study area of interest) and then use the estimates of the study area of interest.

# Compute RI for all census tracts in neighboring states
anthopolos2010GNSTV <- ndi::anthopolos(state = c("GA", "NC", "SC", "TN", "VA"),
                                     year = 2010, subgroup = "NHoLB")

# Crop to only North Carolina, U.S.A. census tracts
anthopolos2010NCe <- anthopolos2010GNSTV$ri[anthopolos2010GNSTV$ri$GEOID %in% anthopolos2010NC$ri$GEOID, ]

# Obtain the 2010 census tracts from the "tigris" package
tract2010NC <- tigris::tracts(state = "NC", year = 2010, cb = TRUE)
# Remove first 9 characters from GEOID for compatibility with tigris information
tract2010NC$GEOID <- substring(tract2010NC$GEO_ID, 10) 

# Obtain the 2010 counties from the "tigris" package
county2010NC <- tigris::counties(state = "NC", year = 2010, cb = TRUE)

# Join the RI (Anthopolos) values to the census tract geometry
edgeNC2010anthopolos <- merge(tract2010NC, anthopolos2010NCe, by = "GEOID")

# Visualize the RI (Anthopolos) values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts 
ggplot2::ggplot() + 
  ggplot2::geom_sf(data = edgeNC2010anthopolos, 
                   ggplot2::aes(fill = RI),
                   size = 0.05,
                   color = "white") +
   ggplot2::geom_sf(data = county2010NC,
                   fill = "transparent", 
                   color = "white",
                   size = 0.2) +
  ggplot2::theme_minimal() +
  ggplot2::scale_fill_viridis_c() +
  ggplot2::labs(fill = "Index (Continuous)",
                caption = "Source: U.S. Census ACS 2006-2010 estimates") +
  ggplot2::ggtitle("Racial Isolation Index (Anthopolos), non-Hispanic Black",
                   subtitle = "NC census tracts (corrected for interstate edge effects)")

Compute Educational Isolation Index (EI)

Compute the EI (Bravo) values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts. This metric is based on Bravo et al. (2021) that assessed the educational isolation of the population without a four-year college degree. Multiple educational attainment categories are available in the bravo() function, including:

A census geography (and its neighbors) that has nearly all of its population with the specified educational attainment category (e.g., a four-year college degree or more) will have an EI value that is close to 1. In contrast, a census geography (and its neighbors) that is nearly none of its population with the specified educational attainment category (e.g., with a four-year college degree) will have an EI value that is close to 0.

bravo2010NC <- ndi::bravo(state = "NC", year = 2010, subgroup = c("LtHS", "HSGiE", "SCoAD"))

# Obtain the 2010 census tracts from the "tigris" package
tract2010NC <- tigris::tracts(state = "NC", year = 2010, cb = TRUE)
# Remove first 9 characters from GEOID for compatibility with tigris information
tract2010NC$GEOID <- substring(tract2010NC$GEO_ID, 10) 

# Obtain the 2010 counties from the "tigris" package
county2010NC <- tigris::counties(state = "NC", year = 2010, cb = TRUE)

# Join the RI (Bravo) values to the census tract geometry
NC2010bravo <- merge(tract2010NC, bravo2010NC$ei, by = "GEOID")

# Visualize the RI (Bravo) values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts 
ggplot2::ggplot() + 
  ggplot2::geom_sf(data = NC2010bravo, 
                   ggplot2::aes(fill = EI),
                   size = 0.05,
                   color = "white") +
   ggplot2::geom_sf(data = county2010NC,
                   fill = "transparent", 
                   color = "white",
                   size = 0.2) +
  ggplot2::theme_minimal() +
  ggplot2::scale_fill_viridis_c() +
  ggplot2::labs(fill = "Index (Continuous)",
                caption = "Source: U.S. Census ACS 2006-2010 estimates") +
  ggplot2::ggtitle("Educational Isolation Index (Bravo), without a four-year college degree",
                   subtitle = "NC census tracts (not corrected for edge effects)")

Can correct for one source of edge effect in the same manner as shown for the RI (Anthopolos) metric.

Retrieve the Educational Isolation Index (EI)

Retrieve the Gini Index values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts. This metric is based on Gini (1921) and the gini() function retrieve the estimate from the ACS-5.

According to the U.S. Census Bureau: “The Gini Index is a summary measure of income inequality. The Gini coefficient incorporates the detailed shares data into a single statistic, which summarizes the dispersion of income across the entire income distribution. The Gini coefficient ranges from 0, indicating perfect equality (where everyone receives an equal share), to 1, perfect inequality (where only one recipient or group of recipients receives all the income). The Gini is based on the difference between the Lorenz curve (the observed cumulative income distribution) and the notion of a perfectly equal income distribution.”

gini2010NC <- ndi::gini(state = "NC", year = 2010)

# Obtain the 2010 census tracts from the "tigris" package
tract2010NC <- tigris::tracts(state = "NC", year = 2010, cb = TRUE)
# Remove first 9 characters from GEOID for compatibility with tigris information
tract2010NC$GEOID <- substring(tract2010NC$GEO_ID, 10) 

# Obtain the 2010 counties from the "tigris" package
county2010NC <- tigris::counties(state = "NC", year = 2010, cb = TRUE)

# Join the Gini Index values to the census tract geometry
NC2010gini <- merge(tract2010NC, gini2010NC$gini, by = "GEOID")

# Visualize the Gini Index values (2006-2010 5-year ACS) for North Carolina, U.S.A., census tracts 
ggplot2::ggplot() + 
  ggplot2::geom_sf(data = NC2010gini, 
                   ggplot2::aes(fill = gini),
                   size = 0.05,
                   color = "white") +
   ggplot2::geom_sf(data = county2010NC,
                   fill = "transparent", 
                   color = "white",
                   size = 0.2) +
  ggplot2::theme_minimal() +
  ggplot2::scale_fill_viridis_c() +
  ggplot2::labs(fill = "Index (Continuous)",
                caption = "Source: U.S. Census ACS 2006-2010 estimates") +
  ggplot2::ggtitle("Gini Index",
                   subtitle = "NC census tracts")

sessionInfo()

## R version 4.2.1 (2022-06-23)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.7
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] tigris_1.6.1     tidycensus_1.2.2 sf_1.0-7         ndi_0.1.1       
## [5] ggplot2_3.3.6    knitr_1.39      
## 
## loaded via a namespace (and not attached):
##  [1] httr_1.4.3         sass_0.4.2         tidyr_1.2.0        jsonlite_1.8.0    
##  [5] viridisLite_0.4.0  bslib_0.4.0        highr_0.9          sp_1.5-0          
##  [9] yaml_2.3.5         pillar_1.8.0       lattice_0.20-45    glue_1.6.2        
## [13] uuid_1.1-0         digest_0.6.29      rvest_1.0.2        colorspace_2.0-3  
## [17] htmltools_0.5.3    Matrix_1.4-1       psych_2.2.5        pkgconfig_2.0.3   
## [21] s2_1.1.0           purrr_0.3.4        scales_1.2.0       tzdb_0.3.0        
## [25] tibble_3.1.8       proxy_0.4-27       generics_0.1.3     farver_2.1.1      
## [29] ellipsis_0.3.2     cachem_1.0.6       withr_2.5.0        cli_3.3.0         
## [33] mnormt_2.1.0       magrittr_2.0.3     crayon_1.5.1       maptools_1.1-4    
## [37] evaluate_0.15      fansi_1.0.3        nlme_3.1-158       MASS_7.3-57       
## [41] xml2_1.3.3         foreign_0.8-82     class_7.3-20       tools_4.2.1       
## [45] hms_1.1.1          lifecycle_1.0.1    stringr_1.4.0      munsell_0.5.0     
## [49] compiler_4.2.1     jquerylib_0.1.4    e1071_1.7-11       rlang_1.0.4       
## [53] classInt_0.4-7     units_0.8-0        grid_4.2.1         rstudioapi_0.13   
## [57] rappdirs_0.3.3     labeling_0.4.2     rmarkdown_2.14     wk_0.6.0          
## [61] gtable_0.3.0       DBI_1.1.3          curl_4.3.2         R6_2.5.1          
## [65] dplyr_1.0.9        rgdal_1.5-30       fastmap_1.1.0      utf8_1.2.2        
## [69] KernSmooth_2.23-20 readr_2.1.2        stringi_1.7.8      parallel_4.2.1    
## [73] Rcpp_1.0.9         vctrs_0.4.1        tidyselect_1.1.2   xfun_0.31