Author: Ian D. Buller (GitHub: @idblr)
Date: 2025-08-29

# 1. Neighborhood Deprivation Indices

#### Ian D. Buller (GitHub: @idblr)

#### 2025-08-29

Start with the necessary packages for the vignette.

    loadedPackages <- c('dplyr', 'ggplot2', 'ndi', 'sf', 'tidycensus', 'tigris')
    invisible(lapply(loadedPackages, library, character.only = TRUE))
    options(tigris_use_cache = TRUE)

Set your U.S. Census Bureau access key. Follow this link to obtain one. Specify your access key in the `messer()` or `powell_wiley()` functions using the `key` argument of the `get_acs()` function from the tidycensus package called within each or by using the `census_api_key()` function from the tidycensus package before running the `messer()` or `powell_wiley()` functions (see an example of the latter below).

    census_api_key('...') # INSERT YOUR OWN KEY FROM U.S. CENSUS API

## Compute NDI (Messer)

Compute the NDI (Messer) values (2006-2010 5-year ACS) for Georgia, U.S.A., census tracts. This metric is based on Messer et al. (2006) with the following socio-economic status (SES) variables:

Characteristic | SES dimension | ACS table source | Description
--- | --- | --- | ---
OCC | Occupation | C24030 | Percent males in management, science, and arts occupation
CWD | Housing | B25014 | Percent of crowded housing
POV | Poverty | B17017 | Percent of households in poverty
FHH | Poverty | B25115 | Percent of female headed households with dependents
PUB | Poverty | B19058 | Percent of households on public assistance
U30 | Poverty | B19001 | Percent households earning <$30,000 per year
EDU | Education | B06009 | Percent earning less than a high school education
EMP | Employment | B23001 (2010 only); B23025 (2011 onward) | Percent unemployed

    messer2010GA <- messer(state = 'GA', year = 2010, round_output = TRUE)

One output from the `messer()` function is a tibble containing the identification, geographic name, NDI (Messer) values, and raw census characteristics for each tract.

    messer2010GA$ndi

    ## # A tibble: 1,969 × 14
    ##    GEOID state county tract     NDI NDIQuart   OCC   CWD   POV   FHH   PUB   U30
    ##    <chr> <chr> <chr>  <chr>   <dbl> <fct>    <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
    ##  1 1300… Geor… Appli… 9501  -0.0075 2-Below…     0   0     0.1   0.1   0.1   0.3
    ##  2 1300… Geor… Appli… 9502   0.0458 4-Most …     0   0     0.3   0.1   0.2   0.5
    ##  3 1300… Geor… Appli… 9503   0.0269 3-Above…     0   0     0.2   0     0.2   0.4
    ##  4 1300… Geor… Appli… 9504  -0.0083 2-Below…     0   0     0.1   0     0.1   0.3
    ##  5 1300… Geor… Appli… 9505   0.0231 3-Above…     0   0     0.2   0     0.2   0.4
    ##  6 1300… Geor… Atkin… 9601   0.0619 4-Most …     0   0.1   0.2   0.2   0.2   0.5
    ##  7 1300… Geor… Atkin… 9602   0.0593 4-Most …     0   0.1   0.3   0.1   0.2   0.4
    ##  8 1300… Geor… Atkin… 9603   0.0252 3-Above…     0   0     0.3   0.1   0.2   0.4
    ##  9 1300… Geor… Bacon… 9701   0.0061 3-Above…     0   0     0.2   0     0.2   0.4
    ## 10 1300… Geor… Bacon… 9702…  0.0121 3-Above…     0   0     0.2   0.1   0.1   0.5
    ## # ℹ 1,959 more rows
    ## # ℹ 2 more variables: EDU <dbl>, EMP <dbl>

A second output from the `messer()` function is the results from the principal component analysis used to compute the NDI (Messer) values.

    messer2010GA$pca

    ## Principal Components Analysis
    ## Call: psych::principal(r = ndi_data_pca, nfactors = 1, n.obs = nrow(ndi_data_pca),
    ##     covar = FALSE, scores = TRUE, missing = imp)
    ## Standardized loadings (pattern matrix) based upon correlation matrix
    ##       PC1   h2   u2 com
    ## OCC -0.59 0.35 0.65   1
    ## CWD  0.47 0.22 0.78   1
    ## POV  0.87 0.76 0.24   1
    ## FHH  0.67 0.45 0.55   1
    ## PUB  0.89 0.79 0.21   1
    ## U30  0.90 0.81 0.19   1
    ## EDU  0.79 0.62 0.38   1
    ## EMP  0.46 0.21 0.79   1
    ##
    ##                 PC1
    ## SS loadings    4.21
    ## Proportion Var 0.53
    ##
    ## Mean item complexity =  1
    ## Test of the hypothesis that 1 component is sufficient.
    ##
    ## The root mean square of the residuals (RMSR) is  0.11
    ##  with the empirical chi square  1221.09  with prob <  2.3e-246
    ##
    ## Fit based upon off diagonal values = 0.95

A third output from the `messer()` function is a tibble containing a breakdown of the missingness of the census characteristics used to compute the NDI (Messer) values.

    messer2010GA$missing

    ## # A tibble: 8 × 4
    ##   variable total n_missing percent_missing
    ##   <chr>    <int>     <int> <chr>
    ## 1 CWD       1969        14 0.71 %
    ## 2 EDU       1969        13 0.66 %
    ## 3 EMP       1969        13 0.66 %
    ## 4 FHH       1969        14 0.71 %
    ## 5 OCC       1969        15 0.76 %
    ## 6 POV       1969        14 0.71 %
    ## 7 PUB       1969        14 0.71 %
    ## 8 U30       1969        14 0.71 %

We can visualize the NDI (Messer) values geographically by linking them to spatial information from the tigris package and plotting with the ggplot2 package suite.

    # Obtain the 2010 counties from the 'tigris' package
    county2010GA <- counties(state = 'GA', year = 2010, cb = TRUE)
    # Remove first 9 characters from GEOID for compatibility with tigris information
    county2010GA$GEOID <- substring(county2010GA$GEO_ID, 10)

    # Obtain the 2010 census tracts from the 'tigris' package
    tract2010GA <- tracts(state = 'GA', year = 2010, cb = TRUE)
    # Remove first 9 characters from GEOID for compatibility with tigris information
    tract2010GA$GEOID <- substring(tract2010GA$GEO_ID, 10)

    # Join the NDI (Messer) values to the census tract geometry
    GA2010messer <- tract2010GA %>%
      left_join(messer2010GA$ndi, by = 'GEOID')

    # Visualize the NDI (Messer) values (2006-2010 5-year ACS) for Georgia, U.S.A., census tracts
    ## Continuous Index
    ggplot() +
      geom_sf(
        data = GA2010messer,
        aes(fill = NDI),
        size = 0.05,
        color = 'transparent'
      ) +
      geom_sf(
        data = county2010GA,
        fill = 'transparent',
        color = 'white',
        size = 0.10
      ) +
      theme_minimal() +
      scale_fill_viridis_c() +
      labs(fill = 'Index (Continuous)', caption = 'Source: U.S. Census ACS 2006-2010 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Messer)',
        subtitle = 'GA census tracts as the referent'
      )

    ## Categorical Index
    ### Rename '9-NDI not avail' level as NA for plotting
    GA2010messer$NDIQuartNA <-
      factor(
        replace(
          as.character(GA2010messer$NDIQuart),
          GA2010messer$NDIQuart == '9-NDI not avail',
          NA
        ),
        c(levels(GA2010messer$NDIQuart)[-5], NA)
      )

    ggplot() +
      geom_sf(
        data = GA2010messer,
        aes(fill = NDIQuartNA),
        size = 0.05,
        color = 'transparent'
      ) +
      geom_sf(
        data = county2010GA,
        fill = 'transparent',
        color = 'white',
        size = 0.10
      ) +
      theme_minimal() +
      scale_fill_viridis_d(guide = guide_legend(reverse = TRUE), na.value = 'grey80') +
      labs(fill = 'Index (Categorical)', caption = 'Source: U.S. Census ACS 2006-2010 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Messer) Quartiles',
        subtitle = 'GA census tracts as the referent'
      )

The results above are at the tract level. The NDI (Messer) values can also be calculated at the county level.

    messer2010GA_county <- messer(geo = 'county', state = 'GA', year = 2010)

    # Join the NDI (Messer) values to the county geometry
    GA2010messer_county <- county2010GA %>%
      left_join(messer2010GA_county$ndi, by = 'GEOID')

    # Visualize the NDI (Messer) values (2006-2010 5-year ACS) for Georgia, U.S.A., counties
    ## Continuous Index
    ggplot() +
      geom_sf(
        data = GA2010messer_county,
        aes(fill = NDI),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_c() +
      labs(fill = 'Index (Continuous)', caption = 'Source: U.S. Census ACS 2006-2010 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Messer)',
        subtitle = 'GA counties as the referent'
      )

    ## Categorical Index
    ### Rename '9-NDI not avail' level as NA for plotting
    GA2010messer_county$NDIQuartNA <-
      factor(
        replace(
          as.character(GA2010messer_county$NDIQuart),
          GA2010messer_county$NDIQuart == '9-NDI not avail',
          NA
        ),
        c(levels(GA2010messer_county$NDIQuart)[-5], NA)
      )

    ggplot() +
      geom_sf(
        data = GA2010messer_county,
        aes(fill = NDIQuartNA),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_d(guide = guide_legend(reverse = TRUE), na.value = 'grey80') +
      labs(fill = 'Index (Categorical)', caption = 'Source: U.S. Census ACS 2006-2010 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Messer) Quartiles',
        subtitle = 'GA counties as the referent'
      )

## Compute NDI (Powell-Wiley)

Compute the NDI (Powell-Wiley) values (2016-2020 5-year ACS) for Maryland, Virginia, Washington, D.C., and West Virginia, U.S.A., census tracts. This metric is based on Andrews et al. (2020) and Slotman et al. (2022) with socio-economic status (SES) variables chosen by Roux and Mair (2010):

Characteristic | SES dimension | ACS table source | Description
--- | --- | --- | ---
MedHHInc | Wealth and income | B19013 | Median household income (dollars)
PctRecvIDR | Wealth and income | B19054 | Percent of households receiving dividends, interest, or rental income
PctPubAsst | Wealth and income | B19058 | Percent of households receiving public assistance
MedHomeVal | Wealth and income | B25077 | Median home value (dollars)
PctMgmtBusSciArt | Occupation | C24060 | Percent in a management, business, science, or arts occupation
PctFemHeadKids | Occupation | B11005 | Percent of households that are female headed with any children under 18 years
PctOwnerOcc | Housing conditions | DP04 | Percent of housing units that are owner occupied
PctNoPhone | Housing conditions | DP04 | Percent of households without a telephone
PctNComPlmb | Housing conditions | DP04 | Percent of households without complete plumbing facilities
PctEducHSPlus | Education | S1501 | Percent with a high school degree or higher (population 25 years and over)
PctEducBchPlus | Education | S1501 | Percent with a college degree or higher (population 25 years and over)
PctFamBelowPov | Wealth and income | S1702 | Percent of families with incomes below the poverty level
PctUnempl | Occupation | S2301 | Percent unemployed

More information about the codebook and computation of the NDI (Powell-Wiley) can be found on a GIS Portal for Cancer Research website.

    powell_wiley2020DMVW <- powell_wiley(
      state = c('DC', 'MD', 'VA', 'WV'),
      year = 2020,
      round_output = TRUE
    )

One output from the `powell_wiley()` function is a tibble containing the identification, geographic name, NDI (Powell-Wiley) values, and raw census characteristics for each tract.

    powell_wiley2020DMVW$ndi

    ## # A tibble: 4,425 × 20
    ##    GEOID       state  county tract   NDI NDIQuint MedHHInc PctRecvIDR PctPubAsst
    ##    <chr>       <chr>  <chr>  <chr> <dbl> <fct>       <dbl>      <dbl>      <dbl>
    ##  1 11001000101 Distr… Distr… 1.01  -2.13 1-Least…   187839       50.9        0.8
    ##  2 11001000102 Distr… Distr… 1.02  -2.46 1-Least…   184167       52.2        0.6
    ##  3 11001000201 Distr… Distr… 2.01  NA    9-NDI n…       NA      NaN        NaN
    ##  4 11001000202 Distr… Distr… 2.02  -2.30 1-Least…   164261       49.6        0.9
    ##  5 11001000300 Distr… Distr… 3     -2.06 1-Least…   156483       46          0.6
    ##  6 11001000400 Distr… Distr… 4     -2.09 1-Least…   153397       47.8        0
    ##  7 11001000501 Distr… Distr… 5.01  -2.11 1-Least…   119911       44.5        0.8
    ##  8 11001000502 Distr… Distr… 5.02  -2.21 1-Least…   153264       46.8        0.5
    ##  9 11001000600 Distr… Distr… 6     -2.16 1-Least…   154266       60.8        7.4
    ## 10 11001000702 Distr… Distr… 7.02  -1.20 1-Least…    71747       22.9        0
    ## # ℹ 4,415 more rows
    ## # ℹ 11 more variables: MedHomeVal <dbl>, PctMgmtBusScArti <dbl>,
    ## #   PctFemHeadKids <dbl>, PctOwnerOcc <dbl>, PctNoPhone <dbl>,
    ## #   PctNComPlmb <dbl>, PctEducHSPlus <dbl>, PctEducBchPlus <dbl>,
    ## #   PctFamBelowPov <dbl>, PctUnempl <dbl>, TotalPop <dbl>

A second output from the `powell_wiley()` function is the results from the principal component analysis used to compute the NDI (Powell-Wiley) values.

    powell_wiley2020DMVW$pca

    ## $loadings
    ##
    ## Loadings:
    ##                 PC1    PC2    PC3
    ## logMedHHInc     -0.638 -0.364
    ## PctNoIDRZ        0.612  0.319
    ## PctPubAsstZ      0.379  0.615
    ## logMedHomeVal   -0.893
    ## PctWorkClassZ    0.974
    ## PctFemHeadKidsZ  0.128  0.697 -0.233
    ## PctNotOwnerOccZ -0.375  0.923
    ## PctNoPhoneZ             0.329  0.524
    ## PctNComPlmbZ           -0.141  0.869
    ## PctEducLTHSZ     0.642  0.164
    ## PctEducLTBchZ    1.020 -0.121
    ## PctFamBelowPovZ  0.219  0.698
    ## PctUnemplZ              0.596
    ##
    ##                  PC1   PC2   PC3
    ## SS loadings    4.340 2.971 1.102
    ## Proportion Var 0.334 0.229 0.085
    ## Cumulative Var 0.334 0.562 0.647
    ##
    ## $rotmat
    ##             [,1]       [,2]       [,3]
    ## [1,]  0.68516447  0.4403017 0.04517229
    ## [2,] -0.95446519  1.0806634 0.03196818
    ## [3,] -0.09078904 -0.2028145 1.02053725
    ##
    ## $rotation
    ## [1] "promax"
    ##
    ## $Phi
    ##           [,1]      [,2]      [,3]
    ## [1,] 1.0000000 0.5250277 0.1649550
    ## [2,] 0.5250277 1.0000000 0.1923867
    ## [3,] 0.1649550 0.1923867 1.0000000
    ##
    ## $Structure
    ##             [,1]        [,2]        [,3]
    ##  [1,] -0.8432264 -0.71542812 -0.26037289
    ##  [2,]  0.7750210  0.63477178  0.13357439
    ##  [3,]  0.7001489  0.81237803  0.17181801
    ##  [4,] -0.8931597 -0.46211477 -0.19777858
    ##  [5,]  0.9253217  0.42037509  0.12424330
    ##  [6,]  0.4559503  0.71962940 -0.07780352
    ##  [7,]  0.1195748  0.73799969  0.17788881
    ##  [8,]  0.2552300  0.42753150  0.58693047
    ##  [9,]  0.1155170  0.05008712  0.84948765
    ## [10,]  0.7325510  0.50620197  0.16403994
    ## [11,]  0.9557341  0.41335682  0.13787215
    ## [12,]  0.5881663  0.81650181  0.18717861
    ## [13,]  0.3841044  0.63036827  0.09925687
    ##
    ## $communality
    ##  [1] 0.5468870 0.4774810 0.5220533 0.8012746 0.9576793 0.5566938 0.9968490
    ##  [8] 0.3829550 0.7774209 0.4398519 1.0560478 0.5359573 0.3616523
    ##
    ## $uniqueness
    ##     logMedHHInc       PctNoIDRZ     PctPubAsstZ   logMedHomeVal   PctWorkClassZ
    ##     0.453113047     0.522518997     0.477946655     0.198725386     0.042320711
    ## PctFemHeadKidsZ PctNotOwnerOccZ     PctNoPhoneZ    PctNComPlmbZ    PctEducLTHSZ
    ##     0.443306153     0.003150984     0.617045044     0.222579117     0.560148142
    ##   PctEducLTBchZ PctFamBelowPovZ      PctUnemplZ
    ##    -0.056047809     0.464042693     0.638347726
    ##
    ## $Vaccounted
    ##                            [,1]      [,2]       [,3]
    ## SS loadings           4.5987837 3.2131788 1.10386926
    ## Proportion Var        0.3537526 0.2471676 0.08491302
    ## Cumulative Var        0.3537526 0.6009202 0.68583321
    ## Proportion Explained  0.5157997 0.3603902 0.12381002
    ## Cumulative Proportion 0.5157997 0.8761900 1.00000000

A third output from the `powell_wiley()` function is a tibble containing a breakdown of the missingness of the census characteristics used to compute the NDI (Powell-Wiley) values.

    powell_wiley2020DMVW$missing

    ## # A tibble: 13 × 4
    ##    variable        total n_missing percent_missing
    ##    <chr>           <int>     <int> <chr>
    ##  1 PctEducLTBchZ    4425        47 1.06 %
    ##  2 PctEducLTHSZ     4425        47 1.06 %
    ##  3 PctFamBelowPovZ  4425        63 1.42 %
    ##  4 PctFemHeadKidsZ  4425        60 1.36 %
    ##  5 PctNComPlmbZ     4425        60 1.36 %
    ##  6 PctNoIDRZ        4425        60 1.36 %
    ##  7 PctNoPhoneZ      4425        60 1.36 %
    ##  8 PctNotOwnerOccZ  4425        60 1.36 %
    ##  9 PctPubAsstZ      4425        60 1.36 %
    ## 10 PctUnemplZ       4425        57 1.29 %
    ## 11 PctWorkClassZ    4425        57 1.29 %
    ## 12 logMedHHInc      4425        73 1.65 %
    ## 13 logMedHomeVal    4425       148 3.34 %

A fourth output from the `powell_wiley()` function is a character string or numeric value of a standardized Cronbach’s alpha. A value greater than 0.7 is desired.

    powell_wiley2020DMVW$cronbach

    ## [1] 0.9321693

We can visualize the NDI (Powell-Wiley) values geographically by linking them to spatial information from the tigris package and plotting with the ggplot2 package suite.

    # Obtain the 2020 counties from the 'tigris' package
    county2020 <- counties(cb = TRUE)
    county2020DMVW <- county2020[county2020$STUSPS %in% c('DC', 'MD', 'VA', 'WV'), ]

    # Obtain the 2020 census tracts from the 'tigris' package
    tract2020D <- tracts(state = 'DC', year = 2020, cb = TRUE)
    tract2020M <- tracts(state = 'MD', year = 2020, cb = TRUE)
    tract2020V <- tracts(state = 'VA', year = 2020, cb = TRUE)
    tract2020W <- tracts(state = 'WV', year = 2020, cb = TRUE)
    tracts2020DMVW <- rbind(tract2020D, tract2020M, tract2020V, tract2020W)

    # Join the NDI (Powell-Wiley) values to the census tract geometry
    DMVW2020pw <- tracts2020DMVW %>%
      left_join(powell_wiley2020DMVW$ndi, by = 'GEOID')

    # Visualize the NDI (Powell-Wiley) values (2016-2020 5-year ACS)
    ## Maryland, Virginia, Washington, D.C., and West Virginia, U.S.A., census tracts
    ## Continuous Index
    ggplot() +
      geom_sf(
        data = DMVW2020pw,
        aes(fill = NDI),
        color = NA
      ) +
      geom_sf(
        data = county2020DMVW,
        fill = 'transparent',
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_c(na.value = 'grey80') +
      labs(fill = 'Index (Continuous)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Powell-Wiley)',
        subtitle = 'DC, MD, VA, and WV tracts as the referent'
      )

    ## Categorical Index (Population-weighted quintiles)
    ### Rename '9-NDI not avail' level as NA for plotting
    DMVW2020pw$NDIQuintNA <-
      factor(replace(
        as.character(DMVW2020pw$NDIQuint),
        DMVW2020pw$NDIQuint == '9-NDI not avail',
        NA
      ),
      c(levels(DMVW2020pw$NDIQuint)[-6], NA))

    ggplot() +
      geom_sf(data = DMVW2020pw, aes(fill = NDIQuintNA), color = NA) +
      geom_sf(data = county2020DMVW, fill = 'transparent', color = 'white') +
      theme_minimal() +
      scale_fill_viridis_d(guide = guide_legend(reverse = TRUE), na.value = 'grey80') +
      labs(fill = 'Index (Categorical)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Powell-Wiley) Population-weighted Quintiles',
        subtitle = 'DC, MD, VA, and WV tracts as the referent'
      )

Like the NDI (Messer), we also compute county-level NDI (Powell-Wiley).

    # Obtain the 2020 counties from the 'tigris' package
    county2020DMVW <- counties(state = c('DC', 'MD', 'VA', 'WV'), year = 2020, cb = TRUE)

    # NDI (Powell-Wiley) at the county level (2016-2020)
    powell_wiley2020DMVW_county <- powell_wiley(
      geo = 'county',
      state = c('DC', 'MD', 'VA', 'WV'),
      year = 2020
    )

    # Join the NDI (Powell-Wiley) values to the county geometry
    DMVW2020pw_county <- county2020DMVW %>%
      left_join(powell_wiley2020DMVW_county$ndi, by = 'GEOID')

    # Visualize the NDI (Powell-Wiley) values (2016-2020 5-year ACS)
    ## Maryland, Virginia, Washington, D.C., and West Virginia, U.S.A., counties
    ## Continuous Index
    ggplot() +
      geom_sf(
        data = DMVW2020pw_county,
        aes(fill = NDI),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_c() +
      labs(fill = 'Index (Continuous)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Powell-Wiley)',
        subtitle = 'DC, MD, VA, and WV counties as the referent'
      )

    ## Categorical Index
    ### Rename '9-NDI not avail' level as NA for plotting
    DMVW2020pw_county$NDIQuintNA <-
      factor(
        replace(
          as.character(DMVW2020pw_county$NDIQuint),
          DMVW2020pw_county$NDIQuint == '9-NDI not avail',
          NA
        ),
        c(levels(DMVW2020pw_county$NDIQuint)[-6], NA)
      )

    ggplot() +
      geom_sf(
        data = DMVW2020pw_county,
        aes(fill = NDIQuint),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_d(guide = guide_legend(reverse = TRUE), na.value = 'grey80') +
      labs(fill = 'Index (Categorical)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Powell-Wiley) Population-weighted Quintiles',
        subtitle = 'DC, MD, VA, and WV counties as the referent'
      )

### Advanced Features

#### 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()` function in the psych package called within the `messer()` and `powell_wiley()` functions. 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 <- powell_wiley(state = 'DC', year = 2020) # without imputation
    powell_wiley2020DCi <- 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 <- tracts(state = 'DC', year = 2020, cb = TRUE)

    # Join the NDI (Powell-Wiley) values to the census tract geometry
    DC2020pw <- tract2020DC %>%
      left_join(powell_wiley2020DC$ndi, by = 'GEOID')
    DC2020pw <- DC2020pw %>%
      left_join(powell_wiley2020DCi$ndi, by = 'GEOID', suffix = c('_nonimp', '_imp'))

    # Visualize the NDI (Powell-Wiley) values (2016-2020 5-year ACS) for
    ## Washington, D.C., census tracts
    ## Continuous Index
    ggplot() +
      geom_sf(
        data = DC2020pw,
        aes(fill = NDI_nonimp),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_c() +
      labs(fill = 'Index (Continuous)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      ggtitle(
        'Neighborhood Deprivation Index (Powell-Wiley), Non-Imputed',
        subtitle = 'DC census tracts as the referent'
      )

    ggplot() +
      geom_sf(
        data = DC2020pw,
        aes(fill = NDI_imp),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_c() +
      labs(fill = 'Index (Continuous)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      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)
      )

    ggplot() +
      geom_sf(
        data = DC2020pw,
        aes(fill = NDIQuintNA_nonimp),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_d(guide = guide_legend(reverse = TRUE), na.value = 'grey80') +
      labs(fill = 'Index (Categorical)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      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)
      )

    ggplot() +
      geom_sf(
        data = DC2020pw,
        aes(fill = NDIQuintNA_imp),
        size = 0.10,
        color = 'white'
      ) +
      theme_minimal() +
      scale_fill_viridis_d(guide = guide_legend(reverse = TRUE), na.value = 'grey80') +
      labs(fill = 'Index (Categorical)', caption = 'Source: U.S. Census ACS 2016-2020 estimates') +
      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 <- 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 <- powell_wiley(state = y51, year = 2017)
    end_time <- Sys.time() # record end time
    time_srr <- end_time - start_time # Calculate run time

    ggplot(powell_wiley2017US$ndi, aes(x = NDI)) +
      geom_histogram(color = 'black', fill = 'white') +
      theme_minimal() +
      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 12.7 minutes to run on a machine with the features listed at the end of the vignette.

    sessionInfo()

    ## R version 4.5.1 (2025-06-13 ucrt)
    ## Platform: x86_64-w64-mingw32/x64
    ## Running under: Windows 11 x64 (build 26100)
    ##
    ## Matrix products: default
    ##   LAPACK version 3.12.1
    ##
    ## locale:
    ## [1] LC_COLLATE=English_United States.utf8
    ## [2] LC_CTYPE=English_United States.utf8
    ## [3] LC_MONETARY=English_United States.utf8
    ## [4] LC_NUMERIC=C
    ## [5] LC_TIME=English_United States.utf8
    ##
    ## time zone: America/New_York
    ## tzcode source: internal
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] tigris_2.2.1     tidycensus_1.7.3 sf_1.0-21        ndi_0.2.0
    ## [5] ggplot2_3.5.2    dplyr_1.1.4      knitr_1.50
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] tidyselect_1.2.1   psych_2.5.6        viridisLite_0.4.2  farver_2.1.2
    ##  [5] fastmap_1.2.0      digest_0.6.37      rpart_4.1.24       lifecycle_1.0.4
    ##  [9] cluster_2.1.8.1    Cairo_1.6-2        magrittr_2.0.3     compiler_4.5.1
    ## [13] rlang_1.1.6        Hmisc_5.2-3        sass_0.4.10        tools_4.5.1
    ## [17] utf8_1.2.6         yaml_2.3.10        data.table_1.17.8  labeling_0.4.3
    ## [21] htmlwidgets_1.6.4  classInt_0.4-11    mnormt_2.1.1       curl_6.4.0
    ## [25] xml2_1.3.8         RColorBrewer_1.1-3 abind_1.4-8        KernSmooth_2.23-26
    ## [29] withr_3.0.2        foreign_0.8-90     purrr_1.1.0        nnet_7.3-20
    ## [33] grid_4.5.1         e1071_1.7-16       colorspace_2.1-1   scales_1.4.0
    ## [37] MASS_7.3-65        cli_3.6.5          rmarkdown_2.29     crayon_1.5.3
    ## [41] generics_0.1.4     rstudioapi_0.17.1  httr_1.4.7         tzdb_0.5.0
    ## [45] DBI_1.2.3          cachem_1.1.0       proxy_0.4-27       stringr_1.5.1
    ## [49] rvest_1.0.4        parallel_4.5.1     base64enc_0.1-3    vctrs_0.6.5
    ## [53] Matrix_1.7-3       jsonlite_2.0.0     carData_3.0-5      car_3.1-3
    ## [57] hms_1.1.3          Formula_1.2-5      htmlTable_2.4.3    jquerylib_0.1.4
    ## [61] tidyr_1.3.1        units_0.8-7        glue_1.8.0         stringi_1.8.7
    ## [65] gtable_0.3.6       tibble_3.3.0       pillar_1.11.0      rappdirs_0.3.3
    ## [69] htmltools_0.5.8.1  R6_2.6.1           evaluate_1.0.5     lattice_0.22-7
    ## [73] readr_2.1.5        backports_1.5.0    bslib_0.9.0        class_7.3-23
    ## [77] Rcpp_1.1.0         uuid_1.2-1         gridExtra_2.3      nlme_3.1-168
    ## [81] checkmate_2.3.2    xfun_0.52          pkgconfig_2.0.3