R/hachman.r

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

#' Compute the Hachman index from regions - industries matrices
#'
#' This function computes the Hachman index from regions - industries matrices. The Hachman index indicates how closely the industrial distribution of a region resembles the one of a more global economy (nation, world). The index varies between 0 (extreme dissimilarity between the region and the more global economy) and 1 (extreme similarity between the region and the more global economy)
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @return A vector of Hachman index values indicating the similarity between the industrial distribution of a region and a more global economy
#' @keywords specialization
#' @export
#' @examples
#' ## generate a region - industry matrix
#' set.seed(31)
#' mat <- matrix(sample(0:100, 20, replace = TRUE), ncol = 4)
#' rownames(mat) <- c("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c("I1", "I2", "I3", "I4")
#'
#' ## run the function
#' hachman(mat)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{location_quotient_avg}}


hachman <- function(mat) {
  share_tech_city <- mat / rowSums(mat)
  share_tech_total <- colSums(mat) / sum(mat)
  lq <- t(t(share_tech_city) / share_tech_total)
  lq[is.na(lq)] <- 0
  meanlq <- rowSums(lq * share_tech_city)
  hachman_v <- 1 / meanlq
  return(hachman_v)
}