R/relatedness_density_int_avg.r

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

#' Compute the average relatedness density within the regional portfolio from regions - industries matrices and industries - industries matrices
#'
#' This function computes the average relatedness density within the regional portfolio from regions - industries (incidence) matrices and industries - industries (adjacency) matrices. This is a measure of the technological coherence of the regional industrial structure.
#' @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 within the regional portfolio. The values in the vector indicate the average relatedness density for each region, scaled from 0 to 100.
#' @keywords relatedness specialization
#' @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_int_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_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_int_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 non existing tech to NA
  mat[mat == 0] <- NA

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

  return(reldensint)
}