R/kci.r

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

#' Compute an index of knowledge complexity of regions using the eigenvector method
#'
#' This function computes an index of knowledge complexity of regions using the eigenvector method from regions - industries (incidence) matrices. Technically, the function returns the eigenvector associated with the second largest eigenvalue of the projected region - region matrix.
#' @param mat An incidence matrix with regions in rows and industries in columns
#' @param rca Logical; should the index of relative comparative advantage (RCA - also refered to as location quotient) first be computed? Defaults to FALSE (a binary matrix - 0/1 - is expected as an input), but can be set to TRUE if the index of relative comparative advantage first needs to be computed
#' @return A vector representing the index of knowledge complexity of regions computed using the eigenvector method.
#' @keywords complexity
#' @export
#' @examples
#' ## generate a region - industry matrix with full count
#' set.seed(31)
#' mat <- matrix(sample(0:10, 20, replace = TRUE), ncol = 4)
#' rownames(mat) <- c("R1", "R2", "R3", "R4", "R5")
#' colnames(mat) <- c("I1", "I2", "I3", "I4")
#'
#' ## run the function
#' kci(mat, rca = TRUE)
#'
#' ## 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")
#'
#' ## run the function
#' kci(mat)
#'
#' ## generate the simple network of Hidalgo and Hausmann (2009) presented p.11 (Fig. S4)
#' countries <- c("C1", "C1", "C1", "C1", "C2", "C3", "C3", "C4")
#' products <- c("P1", "P2", "P3", "P4", "P2", "P3", "P4", "P4")
#' my_data <- data.frame(countries, products)
#' my_data$freq <- 1
#' mat <- get_matrix(my_data)
#'
#' ## run the function
#' kci(mat)
#' @author Pierre-Alexandre Balland \email{p.balland@uu.nl}
#' @seealso \code{\link{location_quotient}}, \code{\link{ubiquity}}, \code{\link{diversity}}, \code{\link{morc}}, \code{\link{tci}}, \code{\link{mort}}
#' @references Hidalgo, C. and Hausmann, R. (2009) The building blocks of economic complexity, \emph{Proceedings of the National Academy of Sciences} \strong{106}: 10570 - 10575. \cr
#' \cr
#' Balland, P.A. and Rigby, D. (2017) The Geography of Complex Knowledge, \emph{Economic Geography} \strong{93} (1): 1-23.


kci <- function(mat, rca = FALSE) {
  mat <- mat[rowSums(mat) > 0, ]
  mat <- mat[, colSums(mat) > 0]

  if (rca) {
    mat <- rca(mat, binary = TRUE)
  }

  rs_mat <- mat / rowSums(mat)
  cs_mat <- t(mat) / colSums(mat)
  CC <- round(rs_mat %*% cs_mat, 4)
  e <- eigen(CC)
  v <- as.numeric(e$vec[, 2])

  kci <- v / sum(v)

  if (isTRUE(cor(kci, morc(mat, steps = 20), use = "pairwise.complete.obs") < 0)) {
    kci <- -kci
  }

  return(kci)
}