R/relatedness_density_ext_avg.r

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

#' Compute the average relatedness density of regions to industries that are not part of the regional portfolio from regions - industries matrices and industries - industries matrices
#'
#' This function computes the average relatedness density of regions to industries that are not part of the regional portfolio from regions - industries (incidence) matrices and industries - industries (adjacency) matrices. This is the technological flexibility indicator proposed by Balland et al. (2015).
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @param relatedness An adjacency industry - industry matrix indicating the degree of relatedness between industries
#' @return A vector representing the average relatedness density of regions to industries that are not part of the regional portfolio. The values in the vector indicate the average relatedness density for each region, rounded to the nearest integer.
#' @keywords relatedness diversity
#' @export
#' @examples
#' ## generate a region - industry matrix in which cells represent the presence/absence
#' ## of a RCA
#' set.seed(31)
#' mat <- matrix(sample(0:1, 20, replace = TRUE), ncol = 4)
#' rownames(mat) <- c("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c("I1", "I2", "I3", "I4")
#'
#' ## generate an industry - industry matrix in which cells indicate if two industries are
#' ## related (1) or not (0)
#' relatedness <- matrix(sample(0:1, 16, replace = TRUE), ncol = 4)
#' relatedness[lower.tri(relatedness, diag = TRUE)] <- t(relatedness)[lower.tri(t(relatedness),
#'   diag = TRUE
#' )]
#' rownames(relatedness) <- c("I1", "I2", "I3", "I4")
#' colnames(relatedness) <- c("I1", "I2", "I3", "I4")
#'
#' ## run the function
#' relatedness_density_ext_avg(mat, relatedness)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{relatedness}}, \code{\link{relatedness_density}},  \code{\link{relatedness_density_ext}},  \code{\link{relatedness_density_int}},  \code{\link{relatedness_density_int_avg}}, \code{\link{relatedness_density_ext_avg}}
#' @references Boschma, R., Balland, P.A. and Kogler, D. (2015) Relatedness and Technological Change in Cities: The rise and fall of technological knowledge in U.S. metropolitan areas from 1981 to 2010, \emph{Industrial and Corporate Change} \strong{24} (1): 223-250 \cr
#' \cr
#' Balland P.A., Rigby, D., and Boschma, R. (2015) The Technological Resilience of U.S. Cities, \emph{Cambridge Journal of Regions, Economy and Society}, \strong{8} (2): 167-184

relatedness_density_ext_avg <- function(mat, relatedness) {
  # nb of tech related to i in each cities
  rel <- mat %*% relatedness

  # absolute nb of techs related to i (anywhere)
  reltot <- colSums(relatedness)

  # share of tech related to i in each cities
  reldens <- t(rel) / reltot

  # scale 0 to 100 - cities in rows / techs in columns
  reldens <- t(reldens) * 100

  # round
  reldens <- round(reldens, digits = 0)

  # set existing tech to NA
  mat[mat == 1] <- NA

  # set non existing tech to 1
  mat[mat == 0] <- 1

  reldensext <- round((rowSums(reldens * mat, na.rm = TRUE) /
    rowSums(mat, na.rm = TRUE)), digits = 0)

  return(reldensext)
}