R/relatedness_density_ext.r

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

#' Compute the relatedness density between regions and industries that are not part of the regional portfolio from regions - industries matrices and industries - industries matrices
#'
#' This function computes the relatedness density between regions and industries that are not part of the regional portfolio from regions - industries (incidence) matrices and industries - industries (adjacency) matrices
#' @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 matrix representing the relatedness density between regions and industries that are not part of the regional portfolio. The values in the matrix indicate the share of industries related to each industry in each region, scaled from 0 to 100. Rows represent regions and columns represent industries. Industries that are part of the regional portfolio are assigned NA.
#' @keywords relatedness
#' @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(mat, relatedness)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{relatedness}}, \code{\link{co_occurrence}}
#' @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
#' Boschma, R., Heimeriks, G. and Balland, P.A. (2014) Scientific Knowledge Dynamics and Relatedness in Bio-Tech Cities, \emph{Research Policy} \strong{43} (1): 107-114

relatedness_density_ext <- 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 <- reldens * mat

  return(reldensext)
}