morgan_denton.R

#' Distance-Decay Interaction Index based on Morgan (1983) and Massey & Denton (1988)
#' 
#' Compute the aspatial Distance-Decay Interaction Index (Morgan) of a selected racial or ethnic subgroup(s) and U.S. geographies.
#'
#' @param geo_large Character string specifying the larger geographical unit of the data. The default is counties \code{geo_large = 'county'}.
#' @param geo_small Character string specifying the smaller geographical unit of the data. The default is census tracts \code{geo_small = 'tract'}.
#' @param year Numeric. The year to compute the estimate. The default is 2020, and the years 2009 onward are currently available.
#' @param subgroup Character string specifying the racial or ethnic subgroup(s) as the comparison population. See Details for available choices.
#' @param subgroup_ixn Character string specifying the racial or ethnic subgroup(s) as the interaction population. If the same as \code{subgroup}, will compute the simple isolation of the group. See Details for available choices.
#' @param crs Numeric or character string specifying the coordinate reference system to compute the distance-based metric. The default is Albers North America \code{crs = 'ESRI:102008'}.
#' @param omit_NAs Logical. If FALSE, will compute index for a larger geographical unit only if all of its smaller geographical units have values. The default is TRUE.
#' @param quiet Logical. If TRUE, will display messages about potential missing census information. The default is FALSE.
#' @param ... Arguments passed to \code{\link[tidycensus]{get_acs}} to select state, county, and other arguments for census characteristics
#'
#' @details This function will compute the aspatial Distance-Decay Interaction Index (_DPxy\*_) of selected racial or ethnic subgroups and U.S. geographies for a specified geographical extent (e.g., the entire U.S. or a single state) based on Morgan (1986) \url{https://www.jstor.org/stable/20001935} and Massey & Denton (1988) \doi{10.1093/sf/67.2.281}. This function provides the computation of _DPxy\*_ for any of the U.S. Census Bureau race or ethnicity subgroups (including Hispanic and non-Hispanic individuals).
#' 
#' The function uses the \code{\link[tidycensus]{get_acs}} function to obtain U.S. Census Bureau 5-year American Community Survey characteristics used for the computation. The yearly estimates are available for 2009 onward when ACS-5 data are available (2010 onward for \code{geo_large = 'cbsa'} and 2011 onward for \code{geo_large = 'place'}, \code{geo_large = 'csa'}, or \code{geo_large = 'metro'}) but may be available from other U.S. Census Bureau surveys. The twenty racial or ethnic subgroups (U.S. Census Bureau definitions) are:
#' \itemize{
#'  \item \strong{B03002_002}: not Hispanic or Latino \code{'NHoL'}
#'  \item \strong{B03002_003}: not Hispanic or Latino, white alone \code{'NHoLW'}
#'  \item \strong{B03002_004}: not Hispanic or Latino, Black or African American alone \code{'NHoLB'}
#'  \item \strong{B03002_005}: not Hispanic or Latino, American Indian and Alaska Native alone \code{'NHoLAIAN'}
#'  \item \strong{B03002_006}: not Hispanic or Latino, Asian alone \code{'NHoLA'}
#'  \item \strong{B03002_007}: not Hispanic or Latino, Native Hawaiian and Other Pacific Islander alone \code{'NHoLNHOPI'}
#'  \item \strong{B03002_008}: not Hispanic or Latino, Some other race alone \code{'NHoLSOR'}
#'  \item \strong{B03002_009}: not Hispanic or Latino, Two or more races \code{'NHoLTOMR'}
#'  \item \strong{B03002_010}: not Hispanic or Latino, Two races including Some other race \code{'NHoLTRiSOR'}
#'  \item \strong{B03002_011}: not Hispanic or Latino, Two races excluding Some other race, and three or more races \code{'NHoLTReSOR'}
#'  \item \strong{B03002_012}: Hispanic or Latino \code{'HoL'}
#'  \item \strong{B03002_013}: Hispanic or Latino, white alone \code{'HoLW'}
#'  \item \strong{B03002_014}: Hispanic or Latino, Black or African American alone \code{'HoLB'}
#'  \item \strong{B03002_015}: Hispanic or Latino, American Indian and Alaska Native alone \code{'HoLAIAN'}
#'  \item \strong{B03002_016}: Hispanic or Latino, Asian alone \code{'HoLA'}
#'  \item \strong{B03002_017}: Hispanic or Latino, Native Hawaiian and Other Pacific Islander alone \code{'HoLNHOPI'}
#'  \item \strong{B03002_018}: Hispanic or Latino, Some other race alone \code{'HoLSOR'}
#'  \item \strong{B03002_019}: Hispanic or Latino, Two or more races \code{'HoLTOMR'}
#'  \item \strong{B03002_020}: Hispanic or Latino, Two races including Some other race \code{'HoLTRiSOR'}
#'  \item \strong{B03002_021}: Hispanic or Latino, Two races excluding Some other race, and three or more races \code{'HoLTReSOR'}
#' }
#'
#' Use the internal \code{state} and \code{county} arguments within the \code{\link[tidycensus]{get_acs}} function to specify geographic extent of the data output.
#'
#' _DPxy\*_ is a measure of clustering of racial or ethnic populations within smaller geographical units that are located within larger geographical units. _DPxy\*_ is some measure of the probability that a member of a racial or ethnic subgroup will meet or interact with a member of another racial or ethnic subgroup(s). _DPxy\*_ can range in value from 0 to 1 with higher values signifying higher probability of interaction.
#' 
#' The metric uses the exponential transform of a distance matrix (kilometers) between smaller geographical area centroids, with a diagonal defined as \code{(0.6*a_{i})^{0.5}} where \code{a_{i}} is the area (square kilometers) of smaller geographical unit \code{i} as defined by White (1983) \doi{10.1086/227768}.
#'
#' Larger geographical units available include states \code{geo_large = 'state'}, counties \code{geo_large = 'county'}, census tracts \code{geo_large = 'tract'}, census-designated places \code{geo_large = 'place'}, core-based statistical areas \code{geo_large = 'cbsa'}, combined statistical areas \code{geo_large = 'csa'}, and metropolitan divisions \code{geo_large = 'metro'}. Smaller geographical units available include, counties \code{geo_small = 'county'}, census tracts \code{geo_small = 'tract'}, and census block groups \code{geo_small = 'cbg'}. If a larger geographical unit is comprised of only one smaller geographical unit (e.g., a U.S county contains only one census tract), then the _DPxy\*_ value returned is NA. If the larger geographical unit is census-designated places \code{geo_large = 'place'}, core-based statistical areas \code{geo_large = 'cbsa'}, combined statistical areas \code{geo_large = 'csa'}, or metropolitan divisions \code{geo_large = 'metro'}, only the smaller geographical units completely within a larger geographical unit are considered in the \emph{V} computation (see internal \code{\link[sf]{st_within}} function for more information) and recommend specifying all states within which the interested larger geographical unit are located using the internal \code{state} argument to ensure all appropriate smaller geographical units are included in the _DPxy\*_ computation.
#' 
#' @return An object of class 'list'. This is a named list with the following components:
#'
#' \describe{
#' \item{\code{dpxy_star}}{An object of class 'tbl' for the GEOID, name, and _DPxy\*_ at specified larger census geographies.}
#' \item{\code{dpxy_star_data}}{An object of class 'tbl' for the raw census values at specified smaller census geographies.}
#' \item{\code{missing}}{An object of class 'tbl' of the count and proportion of missingness for each census variable used to compute _DPxy\*_.}
#' }
#'
#' @import dplyr
#' @importFrom sf st_centroid st_distance st_drop_geometry st_transform st_within
#' @importFrom stats complete.cases
#' @importFrom stringr str_trim
#' @importFrom tidycensus get_acs
#' @importFrom tidyr pivot_longer separate
#' @importFrom tigris combined_statistical_areas core_based_statistical_areas metro_divisions places
#' @importFrom units drop_units set_units
#' @importFrom utils stack
#' @export
#'
#' @seealso \code{\link[tidycensus]{get_acs}} for additional arguments for geographic extent selection (i.e., \code{state} and \code{county}).
#'
#' @examples
#' \dontrun{
#' # Wrapped in \dontrun{} because these examples require a Census API key.
#'
#'   # Distance-Decay Interaction Index (a measure of clustering)
#'   ## of non-Hispanic Black vs. non-Hispanic white populations
#'   ## in census tracts within counties of Georgia, U.S.A. (2020)
#'   morgan_denton(
#'     geo_large = 'county',
#'     geo_small = 'tract',
#'     state = 'GA',
#'     year = 2020,
#'     subgroup = 'NHoLB',
#'     subgroup_ixn = 'NHoLW'
#'    )
#'
#' }
#'
morgan_denton <- function(geo_large = 'county',
                          geo_small = 'tract',
                          year = 2020,
                          subgroup,
                          subgroup_ixn,
                          crs = 'ESRI:102008',
                          omit_NAs = TRUE,
                          quiet = FALSE,
                          ...) {
  
  # Check arguments
  match.arg(geo_large, choices = c('state', 'county', 'tract', 'place', 'cbsa', 'csa', 'metro'))
  match.arg(geo_small, choices = c('county', 'tract', 'cbg', 'block group'))
  stopifnot(is.numeric(year), year >= 2009) # all variables available 2009 onward
  match.arg(
    subgroup,
    several.ok = TRUE,
    choices = c(
      'NHoL',
      'NHoLW',
      'NHoLB',
      'NHoLAIAN',
      'NHoLA',
      'NHoLNHOPI',
      'NHoLSOR',
      'NHoLTOMR',
      'NHoLTRiSOR',
      'NHoLTReSOR',
      'HoL',
      'HoLW',
      'HoLB',
      'HoLAIAN',
      'HoLA',
      'HoLNHOPI',
      'HoLSOR',
      'HoLTOMR',
      'HoLTRiSOR',
      'HoLTReSOR'
    )
  )
  match.arg(
    subgroup_ixn,
    several.ok = TRUE,
    choices = c(
      'NHoL',
      'NHoLW',
      'NHoLB',
      'NHoLAIAN',
      'NHoLA',
      'NHoLNHOPI',
      'NHoLSOR',
      'NHoLTOMR',
      'NHoLTRiSOR',
      'NHoLTReSOR',
      'HoL',
      'HoLW',
      'HoLB',
      'HoLAIAN',
      'HoLA',
      'HoLNHOPI',
      'HoLSOR',
      'HoLTOMR',
      'HoLTRiSOR',
      'HoLTReSOR'
    )
  )
  
  # Select census variables
  vars <- c(
    TotalPop = 'B03002_001',
    NHoL = 'B03002_002',
    NHoLW = 'B03002_003',
    NHoLB = 'B03002_004',
    NHoLAIAN = 'B03002_005',
    NHoLA = 'B03002_006',
    NHoLNHOPI = 'B03002_007',
    NHoLSOR = 'B03002_008',
    NHoLTOMR = 'B03002_009',
    NHoLTRiSOR = 'B03002_010',
    NHoLTReSOR = 'B03002_011',
    HoL = 'B03002_012',
    HoLW = 'B03002_013',
    HoLB = 'B03002_014',
    HoLAIAN = 'B03002_015',
    HoLA = 'B03002_016',
    HoLNHOPI = 'B03002_017',
    HoLSOR = 'B03002_018',
    HoLTOMR = 'B03002_019',
    HoLTRiSOR = 'B03002_020',
    HoLTReSOR = 'B03002_021'
  )
  
  selected_vars <- vars[c('TotalPop', subgroup, subgroup_ixn)]
  out_names <- c(names(selected_vars), 'ALAND') # save for output
  in_subgroup <- paste0(subgroup, 'E')
  in_subgroup_ixn <- paste0(subgroup_ixn, 'E')
  
  # Acquire DPxy_star variables and sf geometries
  out_dat <- suppressMessages(suppressWarnings(
    tidycensus::get_acs(
      geography = geo_small,
      year = year,
      output = 'wide',
      variables = selected_vars,
      geometry = TRUE,
      keep_geo_vars = TRUE,
      ...
    )
  ))
  
  # Format output
  if (geo_small == 'county') {
    out_dat <- out_dat %>%
      tidyr::separate(NAME.y, into = c('county', 'state'), sep = ',')
  }
  if (geo_small == 'tract') {
    out_dat <- out_dat %>%
      tidyr::separate(NAME.y, into = c('tract', 'county', 'state'), sep = ',') %>%
      dplyr::mutate(tract = gsub('[^0-9\\.]', '', tract))
  }
  if (geo_small == 'cbg' | geo_small == 'block group') {
    out_dat <- out_dat %>%
      tidyr::separate(NAME.y, into = c('cbg', 'tract', 'county', 'state'), sep = ',') %>%
      dplyr::mutate(
        tract = gsub('[^0-9\\.]', '', tract),
        cbg = gsub('[^0-9\\.]', '', cbg)
      )
  }
  
  # Grouping IDs for DPxy_star computation
  if (geo_large == 'state') {
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = STATEFP,
        state = stringr::str_trim(state)
      )
  }
  if (geo_large == 'tract') {
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = paste0(STATEFP, COUNTYFP, TRACTCE),
        state = stringr::str_trim(state),
        county = stringr::str_trim(county)
      )
  }
  if (geo_large == 'county') {
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = paste0(STATEFP, COUNTYFP),
        state = stringr::str_trim(state),
        county = stringr::str_trim(county)
      )
  }
  if (geo_large == 'place') {
    stopifnot(is.numeric(year), year >= 2011) # Places only available 2011 onward
    lgeom <- suppressMessages(suppressWarnings(tigris::places(
      year = year, state = unique(out_dat$state))
    ))
    wlgeom <- sf::st_within(out_dat, lgeom)
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 4] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist(),
        place = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 5] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist()
      )
  }
  if (geo_large == 'cbsa') {
    stopifnot(is.numeric(year), year >= 2010) # CBSAs only available 2010 onward
    lgeom <- suppressMessages(suppressWarnings(tigris::core_based_statistical_areas(year = year)))
    wlgeom <- sf::st_within(out_dat, lgeom)
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 3] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist(),
        cbsa = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 4] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist()
      )
  }
  if (geo_large == 'csa') {
    stopifnot(is.numeric(year), year >= 2011) # CSAs only available 2011 onward
    lgeom <- suppressMessages(suppressWarnings(tigris::combined_statistical_areas(year = year)))
    wlgeom <- sf::st_within(out_dat, lgeom)
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 2] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist(),
        csa = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 3] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist()
      )
  }
  if (geo_large == 'metro') {
    stopifnot(is.numeric(year), year >= 2011) # Metropolitan Divisions only available 2011 onward
    lgeom <- suppressMessages(suppressWarnings(tigris::metro_divisions(year = year)))
    wlgeom <- sf::st_within(out_dat, lgeom)
    out_dat <- out_dat %>%
      dplyr::mutate(
        oid = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 4] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist(),
        metro = lapply(wlgeom, function(x) { 
          tmp <- lgeom[x, 5] %>% sf::st_drop_geometry()
          lapply(tmp, function(x) { if (length(x) == 0) NA else x })
        }) %>% 
          unlist()
      )
  }
  
  # Count of racial or ethnic subgroup populations
  ## Count of racial or ethnic comparison subgroup population
  if (length(in_subgroup) == 1) {
    out_dat <- out_dat %>%
      dplyr::mutate(subgroup = as.data.frame(.)[, in_subgroup])
  } else {
    out_dat <- out_dat %>%
      dplyr::mutate(subgroup = rowSums(as.data.frame(.)[, in_subgroup]))
  }
  ## Count of racial or ethnic interaction subgroup population
  if (length(in_subgroup_ixn) == 1) {
    out_dat <- out_dat %>%
      dplyr::mutate(subgroup_ixn = as.data.frame(.)[, in_subgroup_ixn])
  } else {
    out_dat <- out_dat %>%
      dplyr::mutate(subgroup_ixn = rowSums(as.data.frame(.)[, in_subgroup_ixn]))
  }
  
  # Compute DPxy*
  ## From Massey & Denton (1988) https://doi.org/10.1093/sf/67.2.281
  ## DP_{xy}^{*}=\sum_{i=1}^{n}\frac{x_{i}}{X}\sum_{j=1}^{n}\frac{K_{ij}y_{j}}{t_{j}}
  ## Where for i & j smaller geographical units:
  ## x_{i} denotes the racial or ethnic subgroup population of smaller geographical unit i
  ## X denotes the racial or ethnic subgroup population of a larger geographical unit
  ## y_{j} denotes the interaction racial or ethnic subgroup population of smaller geographical unit i
  ## t_{j} denotes the total population of smaller geographical unit j
  ## and
  ## K_{ij} = \frac{exp(-d_{ij})t_{j}}{\sum_{i=1}^{n}exp(-d_{ij})t_{j}}
  
  ## Compute
  out_tmp <- out_dat %>%
    .[.$oid != 'NANA', ] %>%
    split(., f = list(.$oid)) %>%
    lapply(., FUN = dpxy_star_fun, crs = crs, omit_NAs = omit_NAs) %>%
    utils::stack(.) %>%
    dplyr::mutate(
      DPxy_star = values,
      oid = ind
    ) %>%
    dplyr::select(DPxy_star, oid) %>%
    sf::st_drop_geometry()
  
  # Warning for missingness of census characteristics
  missingYN <- out_dat[, c('TotalPopE', in_subgroup, in_subgroup_ixn, 'ALAND')] %>% 
    sf::st_drop_geometry()
  names(missingYN) <- out_names
  missingYN <- missingYN %>%
    tidyr::pivot_longer(
      cols = dplyr::everything(),
      names_to = 'variable',
      values_to = 'val'
    ) %>%
    dplyr::group_by(variable) %>%
    dplyr::summarise(
      total = dplyr::n(),
      n_missing = sum(is.na(val)),
      percent_missing = paste0(round(mean(is.na(val)) * 100, 2), ' %')
    )
  
  if (quiet == FALSE) {
    # Warning for missing census data
    if (sum(missingYN$n_missing) > 0) {
      message('Warning: Missing census data')
    }
  }
  
  # Format output
  out <- out_dat %>%
    sf::st_drop_geometry() %>%
    dplyr::left_join(out_tmp, by = dplyr::join_by(oid))
  if (geo_large == 'state') {
    out <- out %>%
      dplyr::select(oid, state, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, state, DPxy_star)
  }
  if (geo_large == 'county') {
    out <- out %>%
      dplyr::select(oid, state, county, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, state, county, DPxy_star)
  }
  if (geo_large == 'tract') {
    out <- out %>%
      dplyr::select(oid, state, county, tract, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, state, county, tract, DPxy_star)
  }
  if (geo_large == 'place') {
    out <- out %>%
      dplyr::select(oid, place, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, place, DPxy_star)
  }
  if (geo_large == 'cbsa') {
    out <- out %>%
      dplyr::select(oid, cbsa, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, cbsa, DPxy_star)
  }
  if (geo_large == 'csa') {
    out <- out %>%
      dplyr::select(oid, csa, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, csa, DPxy_star)
  }
  if (geo_large == 'metro') {
    out <- out %>%
      dplyr::select(oid, metro, DPxy_star) %>%
      unique(.) %>%
      dplyr::mutate(GEOID = oid) %>%
      dplyr::select(GEOID, metro, DPxy_star)
  }
  
  out <- out %>%
    .[.$GEOID != 'NANA', ] %>%
    dplyr::filter(!is.na(GEOID)) %>%
    dplyr::distinct(GEOID, .keep_all = TRUE) %>%
    dplyr::arrange(GEOID) %>%
    dplyr::as_tibble()
  
  out_dat <- out_dat %>%
    dplyr::arrange(GEOID) %>%
    dplyr::as_tibble()
  
  out <- list(dpxy_star = out, dpxy_star_data = out_dat, missing = missingYN)
  
  return(out)
}