R/Hoover.curve.r

In PABalland/EconGeo: Computing Key Indicators of the Spatial Distribution of Economic Activities

#' Plot a Hoover curve from regions - industries matrices
#'
#' This function plots a Hoover curve from regions - industries matrices.
#' @param mat An incidence matrix with regions in rows and industries in columns. The input can also be a vector of industrial regional count (a matrix with n regions in rows and a single column).
#' @param pop A vector of population regional count
#' @param plot Logical; shall the curve be automatically plotted? Defaults to TRUE. If set to TRUE, the function will return x y coordinates that you can latter use to plot and customize the curve.
#' @param pdf Logical; shall a pdf be saved to your current working directory? Defaults to FALSE. If set to TRUE, a pdf with all Hoover curves will be compiled and saved to your current working directory.
#' @keywords concentration inequality
#' @export
#' @examples
#' ## generate vectors of industrial and population count
#' ind <- c(0, 10, 10, 30, 50)
#' pop <- c(10, 15, 20, 25, 30)
#'
#' ## run the function (30% of the population produces 50% of the industrial output)
#' Hoover.curve (ind, pop)
#' Hoover.curve (ind, pop, pdf = TRUE)
#' Hoover.curve (ind, pop, plot = F)
#'
#' ## generate a region - industry matrix
#' mat = matrix (
#' c (0, 10, 0, 0,
#' 0, 15, 0, 0,
#' 0, 20, 0, 0,
#' 0, 25, 0, 1,
#' 0, 30, 1, 1), ncol = 4, byrow = T)
#' rownames(mat) <- c ("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c ("I1", "I2", "I3", "I4")
#'
#' ## run the function
#' Hoover.curve (mat, pop)
#' Hoover.curve (mat, pop, pdf = TRUE)
#' Hoover.curve (mat, pop, plot = FALSE)
#'
#' ## run the function by aggregating all industries
#' Hoover.curve (rowSums(mat), pop)
#' Hoover.curve (rowSums(mat), pop, pdf = TRUE)
#' Hoover.curve (rowSums(mat), pop, plot = FALSE)
#'
#' ## run the function for industry #1 only
#' Hoover.curve (mat[,1], pop)
#' Hoover.curve (mat[,1], pop, pdf = TRUE)
#' Hoover.curve (mat[,1], pop, plot = FALSE)
#'
#' ## run the function for industry #2 only (perfectly proportional to population)
#' Hoover.curve (mat[,2], pop)
#' Hoover.curve (mat[,2], pop, pdf = TRUE)
#' Hoover.curve (mat[,2], pop, plot = FALSE)
#'
#' ## run the function for industry #3 only (30% of the pop. produces 100% of the output)
#' Hoover.curve (mat[,3], pop)
#' Hoover.curve (mat[,3], pop, pdf = TRUE)
#' Hoover.curve (mat[,3], pop, plot = FALSE)
#'
#' ## run the function for industry #4 only (55% of the pop. produces 100% of the output)
#' Hoover.curve (mat[,4], pop)
#' Hoover.curve (mat[,4], pop, pdf = TRUE)
#' Hoover.curve (mat[,4], pop, plot = FALSE)
#'
#' Compare the distribution of the #industries
#' par(mfrow=c(2,2))
#' Hoover.curve (mat[,1], pop)
#' Hoover.curve (mat[,2], pop)
#' Hoover.curve (mat[,3], pop)
#' Hoover.curve (mat[,4], pop)
#'
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{Hoover.Gini}}, \code{\link{locational.Gini}}, \code{\link{locational.Gini.curve}}, \code{\link{Lorenz.curve}}, \code{\link{Gini}}
#' @references Hoover, E.M. (1936) The Measurement of Industrial Localization, \emph{The Review of Economics and Statistics} \strong{18} (1): 162-171

Hoover.curve <- function(mat, pop, plot = TRUE, pdf = FALSE) {

  if (!plot) {

    mat = as.matrix (mat)
    ind <- c(0, mat[,1])
    pop <- c(0, pop)
    c = data.frame (ind, pop)
    c = c[complete.cases(c),]
    ind = c$ind
    pop = c$pop
    o = ind/pop
    o[is.na(o)] = 0
    oind <- order(o)
    ind <- ind[oind]
    pop <- pop[oind]
    cind <- cumsum(ind)/max(cumsum(ind))
    cpop <- cumsum(pop)/max(cumsum(pop))
    return (list(cum.reg = cpop, cum.out = cind))

  }

  if (plot) {

  mat = as.matrix (mat)

  HC <- function(mat, pop, col = 1) {

      ind <- c(0, mat[,col])
      pop <- c(0, pop)
      c = data.frame (ind, pop)
      c = c[complete.cases(c),]
      ind = c$ind
      pop = c$pop
      o = ind/pop
      o[is.na(o)] = 0
      oind <- order(o)
      ind <- ind[oind]
      pop <- pop[oind]
      cind <- cumsum(ind)/max(cumsum(ind))
      cpop <- cumsum(pop)/max(cumsum(pop))
      plot (cpop, cind, type = "l", main = paste0("Hoover curve ", colnames(mat)[col]),
            xlab="Cumulative distribution of population shares", ylab="Cumulative distribution of industry shares",
            xlim=c(0, 1), ylim=c(0, 1))
      return(abline (0,1, col = "red"))

  }

  if (!pdf) {

    for (i in unique(1:ncol(mat)))
    {
      HC(mat, pop, i)
    }


  } else {

    pdf("Hoover.curve.pdf")
    for (i in unique(1:ncol(mat)))
    {
      HC(mat, pop, i)
    }
    dev.off()
    print ("Hoover.curve.pdf has been saved to your current working directory")

}

  }
}