Nothing
R/gini.R
In migration.indices: Migration Indices
Defines functions
print.migration.gini
migration.gini
migration.weighted.gini.mean
migration.weighted.gini.in
migration.gini.in
migration.weighted.gini.out
migration.gini.out
migration.gini.exchange.standardized
migration.gini.exchange
migration.gini.col.standardized
migration.gini.col
migration.gini.row.standardized
migration.gini.row
migration.gini.total
check.migration.matrix
Documented in
check.migration.matrix
migration.gini
migration.gini.col
migration.gini.col.standardized
migration.gini.exchange
migration.gini.exchange.standardized
migration.gini.in
migration.gini.out
migration.gini.row
migration.gini.row.standardized
migration.gini.total
migration.weighted.gini.in
migration.weighted.gini.mean
migration.weighted.gini.out
#' Check Migration Matrix
#'
#' Checks if provided R object looks like a migration matrix.
#'
#' A migration matrix is a symmetric matrix with the exact same row and column names. The diagonal equals to zero. The upper triangle shows the in- and the lower triangle shows the out-migration.
#' @param m R object to check
#' @return (invisibly) TRUE
#' @keywords internal
check.migration.matrix <- function(m) {
## dummy checks on provided matrix
if (missing(m))
stop('No data provided!')
if (!is.matrix(m))
stop('Wrong data type (!matrix) provided!')
if (nrow(m) != ncol(m))
stop('Wrong data tpye (!symmetrical matrix) provided!')
if (!is.numeric(m))
stop('Wrong data tpye (!numeric) provided!')
if (length(which(is.na(m[xor(upper.tri(m), lower.tri(m))]))) > 0)
stop('Missing values (outside of diagonal) found in provided matrix!')
if (!any(all(is.na(diag(m))), all(diag(m) == 0)))
stop('Diagonal should be zero or missing.')
return(invisible(TRUE))
}
#' Total Flows Gini Index
#'
#' The Total Gini Index shows the overall concentration of migration with a simple number computed by comparing each cell of the migration matrix with every other cell except for the diagonal:
#' \deqn{G^T = \frac{\sum_i \sum_{j \neq i} \sum_k \sum_{l \neq k} | M_{ij} - M_{kl} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by a simple loop for performance issues to compare all values to the others at one go, although smaller migration matrices could also be addressed by a much faster \code{dist} method. Please see the sources for more details.
#' @param m migration matrix
#' @param corrected Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to have \eqn{2{n(n-1)-1}} instead of \eqn{2n(n-1)} in the denominator to "ensure that the index can assume the upper limit of 1".
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows that all migrants are found in one single flow.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.total(migration.hyp) # 0.2666667
#' migration.gini.total(migration.hyp2) # 0.225
#' migration.gini.total(migration.hyp, FALSE) # 0.2222222
#' migration.gini.total(migration.hyp2, FALSE) # 0.1875
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row}} \code{\link{migration.gini.exchange}} \code{\link{migration.gini.in}} \code{\link{migration.gini.out}}
migration.gini.total <- function(m, corrected = TRUE) {
check.migration.matrix(m)
n <- nrow(m)
m.val <- m[xor(upper.tri(m), lower.tri(m))]
if (corrected)
denominator <- 2*(n*(n-1)-1)
else
denominator <- 2*n*(n-1)
return(sum(apply(as.data.frame(m.val), 1, function(x) sum(abs(m.val-x))), na.rm = TRUE)/(denominator * sum(m, na.rm = TRUE)))
## faster method (fails with "low memory")
diag(m) <- NA
sum(dist(as.vector(m)), na.rm = TRUE)*2/(denominator * sum(m, na.rm = TRUE))
}
#' Rows Gini Index
#'
#' The Rows Gini index concentrates on the "relative extent to which the destination selections of out-migrations are spatially focused":
#' \deqn{G^T_R = \frac{\sum_i \sum_{j \neq i} \sum_{h \neq i,j} | M_{ij} - M_{ih} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by computing the \code{dist} matrix for each row.
#' @param m migration matrix
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.row(migration.hyp) # 0
#' migration.gini.row(migration.hyp2) # 0.02083333
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row.standardized}}
migration.gini.row <- function(m) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
sum(apply(m, 1, function(m.row) sum(dist(m.row), na.rm = TRUE)*2))/(2*n*(n-1)*sum(m, na.rm = TRUE))
}
#' Standardized Rows Gini Index
#'
#' The standardized version of the Rows Gini Index (\code{\link{migration.gini.row}}) by dividing that with the Total Flows Gini Index (\code{\link{migration.gini.total}}):
#' \deqn{G^{T*}_R = 100\frac{G^T_R}{G^T}}
#' As this index is standardized, it "facilitate comparisons from one period to the next of the rows" indices.
#' @param m migration matrix
#' @param gini.total optionally pass the pre-computed Total Flows Gini Index to save computational resources
#' @return A percentage range from 0\% to 100\% where 0\% means that the migration flows are uniform, while a higher value indicates spatial focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.row.standardized(migration.hyp) # 0
#' migration.gini.row.standardized(migration.hyp2) # 11.11111
#' @export
#' @seealso \code{\link{migration.gini.row}} \code{\link{migration.gini.col.standardized}}
migration.gini.row.standardized <- function(m, gini.total = migration.gini.total(m, FALSE)) {
100 * migration.gini.row(m) / gini.total
}
#' Columns Gini Index
#'
#' The Columns Gini index concentrates on the "relative extent to which the destination selections of in-migrations are spatially focused":
#' \deqn{G^T_R = \frac{\sum_j \sum_{i \neq j} \sum_{g \neq i,j} | M_{ij} - M_{gj} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by computing the \code{dist} matrix for each columns.
#' @param m migration matrix
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.col(migration.hyp) # 0.05555556
#' migration.gini.col(migration.hyp2) # 0.04166667
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini.row}} \code{\link{migration.gini.col.standardized}}
migration.gini.col <- function(m) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
sum(apply(m, 2, function(m.row) sum(dist(m.row), na.rm = TRUE)*2))/(2*n*(n-1)*sum(m, na.rm = TRUE))
}
#' Standardized Columns Gini Index
#'
#' The standardized version of the Columns Gini Index (\code{\link{migration.gini.col}}) by dividing that with the Total Flows Gini Index (\code{\link{migration.gini.total}}):
#' \deqn{G^{T*}_C = 100\frac{G^T_C}{G^T}}
#' As this index is standardized, it "facilitate comparisons from one period to the next" of the columns indices.
#' @param m migration matrix
#' @param gini.total optionally pass the pre-computed Total Flows Gini Index to save computational resources
#' @return A percentage range from 0\% to 100\% where 0\% means that the migration flows are uniform, while a higher value indicates spatial focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.col.standardized(migration.hyp) # 25
#' migration.gini.col.standardized(migration.hyp2) # 22.22222
#' @export
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row.standardized}}
migration.gini.col.standardized <- function(m, gini.total = migration.gini.total(m, FALSE)) {
100 * migration.gini.col(m) / gini.total
}
#' Exchange Gini Index
#'
#' The Exchange Gini Index "indicates the contribution to spatial focusing represented by the \eqn{n(n-q)} net interchanges in the system":
#' \deqn{G^T_{RC, CR} = \frac{\sum_i \sum_{j \neq i} | M_{ij} - M_{ji} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by simply substracting the transposed matrix's values from the original one at one go.
#' @param m migration matrix
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @export
#' @examples
#' data(migration.hyp)
#' migration.gini.exchange(migration.hyp) # 0.05555556
#' migration.gini.exchange(migration.hyp2) # 0.04166667
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.exchange.standardized}}
migration.gini.exchange <- function(m) {
check.migration.matrix(m)
n <- nrow(m)
m.t <- t(m)
m.val <- m[xor(upper.tri(m), lower.tri(m))]
m.t.val <- m.t[xor(upper.tri(m.t), lower.tri(m.t))]
sum(abs(m.val - m.t.val))/(2*n*(n-1)*sum(m))
}
#' Standardized Exchange Gini Index
#'
#' The standardized version of the Exchange Gini Index (\code{\link{migration.gini.exchange}}) by dividing that with the Total Flows Gini Index (\code{\link{migration.gini.total}}):
#' \deqn{G^{T*}_{RC, CR} = 100\frac{G^T_{RC, CR}}{G^T}}
#' As this index is standardized, it "facilitate comparisons from one period to the next" of the exchange indices.
#' @param m migration matrix
#' @param gini.total optionally pass the pre-computed Total Flows Gini Index to save resources
#' @return A percentage range from 0\% to 100\% where 0\% means that the migration flows are uniform, while a higher value indicates spatial focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.exchange.standardized(migration.hyp) # 25
#' migration.gini.exchange.standardized(migration.hyp2) # 22.22222
#' @export
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.exchange}}
migration.gini.exchange.standardized <- function(m, gini.total = migration.gini.total(m, FALSE)) {
100 * migration.gini.exchange(m) / gini.total
}
#' Out-migration Field Gini Index
#'
#' The Out-migration Field Gini Index is a decomposed version of the Rows Gini Index (\code{\link{migration.gini.row}}) representing "the contribution of each region's row to the total index" () (\code{\link{migration.gini.total}}):
#' \deqn{G^O_i = \frac{\sum_{j \neq i} \sum_{l \neq i,j} | M_{ij} - M_{il} | }{ 2(n-2) \sum_{j \neq k} M_{ij}}}
#' These Gini indices facilitates the direct comparison of different territories without further standardization.
#' @param m migration matrix
#' @param corrected Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to be \eqn{2(n-2)} instead of \eqn{2(n-1)} because "the number of comparisons should exclude the diagonal cell in each row and column, and the comparison of each cell with itself".
#' @return A numeric vector with the range of 0 to 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.out(migration.hyp) # 0 0 0
#' migration.gini.out(migration.hyp2) # 0.000 0.25 0.000
#' migration.gini.out(migration.hyp, FALSE) # 0 0 0
#' migration.gini.out(migration.hyp2, FALSE) # 0.000 0.125 0.000
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.in}} \code{\link{migration.weighted.gini.out}}
migration.gini.out <- function(m, corrected = TRUE) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
if (corrected)
denominator <- 2 * (n - 2)
else
denominator <- 2 * (n - 1)
apply(m, 1, function(m.row) sum(dist(m.row), na.rm = TRUE) * 2) / (denominator * rowSums(m, na.rm = TRUE))
}
#' Migration-weighted Out-migration Gini Index
#'
#' The Migration-weighted Out-migration Gini Index is a weighted version of the Out-migration Field Gini Index (\code{\link{migration.gini.out}}) "according to the zone of destination's share of total migration and the mean of the weighted values is computed as":
#' \deqn{MWG^O = \frac{ \sum_i G^O_i \frac{\sum_j M_{ij}}{\sum_{ij} M_{ij}}}{n}}
#' @param m migration matrix
#' @param mgo optionally passed (precomputed) Migration In-migration Gini Index
#' @references \itemize{
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.weighted.gini.out(migration.hyp) # 0
#' migration.weighted.gini.out(migration.hyp2) # 0.02083333
#' @seealso \code{\link{migration.weighted.gini.in}} \code{\link{migration.weighted.gini.mean}}
#' @export
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.out}} \code{\link{migration.weighted.gini.in}} \code{\link{migration.weighted.gini.mean}}
migration.weighted.gini.out <- function(m, mgo = migration.gini.out(m)) {
diag(m) <- NA
n <- nrow(m)
m.sum <- sum(m, na.rm = TRUE)
sum(mgo * colSums(m, na.rm = TRUE) / m.sum) / n
}
#' In-migration Field Gini Index
#'
#' The In-migration Field Gini Index is a decomposed version of the Columns Gini Index (\code{\link{migration.gini.col}}) representing "the contribution of each region's columns to the total index" () (\code{\link{migration.gini.total}}):
#' \deqn{G^I_j = \frac{\sum_{i \neq j} \sum_{k \neq j,i} | M_{ij} - M_{kj} | }{ 2(n-2) \sum_{i \neq j} M_{ij}}}
#' These Gini indices facilitates the direct comparison of different territories without further standardization.
#' @param m migration matrix
#' @param corrected Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to be \eqn{2(n-2)} instead of \eqn{2(n-1)} because "the number of comparisons should exclude the diagonal cell in each row and column, and the comparison of each cell with itself".
#' @return A numeric vector with the range of 0 to 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.in(migration.hyp) # 0.2000000 0.5000000 0.3333333
#' migration.gini.in(migration.hyp2) # 0.2000000 0.0000000 0.4285714
#' migration.gini.in(migration.hyp, FALSE) # 0.1000000 0.2500000 0.1666667
#' migration.gini.in(migration.hyp2, FALSE) # 0.1000000 0.0000000 0.2142857
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.out}} \code{\link{migration.weighted.gini.in}}
migration.gini.in <- function(m, corrected = TRUE) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
if (corrected)
denominator <- 2 * (n - 2)
else
denominator <- 2 * (n - 1)
apply(m, 2, function(m.row) sum(dist(m.row), na.rm = TRUE) * 2) / (denominator * colSums(m, na.rm = TRUE))
}
#' Migration-weighted In-migration Gini Index
#'
#' The Migration-weighted In-migration Gini Index is a weighted version of the In-migration Field Gini Index (\code{\link{migration.gini.in}}) "according to the zone of destination's share of total migration and the mean of the weighted values is computed as":
#' \deqn{MWG^I = \frac{ \sum_j G^I_j \frac{\sum_j M_{ij}}{\sum_{ij} M_{ij}}}{n}}
#' @param m migration matrix
#' @param mgi optionally passed (precomputed) Migration In-migration Gini Index
#' @references \itemize{
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.weighted.gini.in(migration.hyp) # 0.1222222
#' migration.weighted.gini.in(migration.hyp2) # 0.05238095
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.in}} \code{\link{migration.weighted.gini.out}} \code{\link{migration.weighted.gini.mean}}
#' @export
migration.weighted.gini.in <- function(m, mgi = migration.gini.in(m)) {
diag(m) <- NA
n <- nrow(m)
m.sum <- sum(m, na.rm = TRUE)
sum(mgi * rowSums(m, na.rm = TRUE) / m.sum) / n
}
#' Migration-weighted Mean Gini Index
#'
#' The Migration-weighted Mean Gini Index is simply the average of the Migration-weighted In-migration (\code{\link{migration.weighted.gini.in}}) and the Migration-weighted Out-migration (\code{\link{migration.weighted.gini.out}}) Gini Indices:
#' \deqn{MWG^A = \frac{MWG^O + MWG^I}{2}}
#' @param m migration matrix
#' @param mwgi optionally passed (precomputed) Migration-weighted In-migration Gini Index
#' @param mwgo optionally passed (precomputed) Migration-weighted Out-migration Gini Index
#' @return This combined index results in a number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.weighted.gini.mean(migration.hyp) # 0.06111111
#' migration.weighted.gini.mean(migration.hyp2) # 0.03660714
#' @seealso \code{\link{migration.weighted.gini.in}} \code{\link{migration.weighted.gini.out}}
#' @export
migration.weighted.gini.mean <- function(m, mwgi, mwgo) {
if (missing(mwgi))
mwgi <- migration.weighted.gini.in(m)
if (missing(mwgo))
mwgo <- migration.weighted.gini.out(m)
(mwgi + mwgo) / 2
}
#' Spatial Gini Indexes
#'
#' This is a wrapper function computing all the following Gini indices:
#' \itemize{
#' \item Total Flows Gini Index (\code{\link{migration.gini.total}})
#' \item Rows Gini Index (\code{\link{migration.gini.row}})
#' \item Standardized Rows Gini Index (\code{\link{migration.gini.row.standardized}})
#' \item Columns Gini Index (\code{\link{migration.gini.col}})
#' \item Standardized Columns Gini Index (\code{\link{migration.gini.col.standardized}})
#' \item Exchange Gini Index (\code{\link{migration.gini.exchange}})
#' \item Standardized Exchange Gini Index (\code{\link{migration.gini.exchange.standardized}})
#' \item Out-migration Field Gini Index (\code{\link{migration.gini.out}})
#' \item Migration-weighted Out-migration Gini Index (\code{\link{migration.weighted.gini.out}})
#' \item In-migration Field Gini Index (\code{\link{migration.gini.in}})
#' \item Migration-weighted In-migration Gini Index (\code{\link{migration.weighted.gini.in}})
#' \item Migration-weighted Mean Gini Index (\code{\link{migration.weighted.gini.mean}})
#' }
#' @return List of all Gini indices.
#' @param m migration matrix
#' @param corrected to use Bell et al. (2002) updated formulas instead of Plane and Mulligan (1997)
#' @examples
#' data(migration.hyp)
#' migration.gini(migration.hyp)
#' migration.gini(migration.hyp2)
#' @export
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row}} \code{\link{migration.gini.exchange}} \code{\link{migration.gini.in}} \code{\link{migration.gini.out}}
migration.gini <- function(m, corrected = TRUE) {
res <- list(
migration.gini.total = migration.gini.total(m, corrected),
migration.gini.exchange = migration.gini.exchange(m),
migration.gini.row = migration.gini.row(m),
migration.gini.col = migration.gini.col(m),
migration.gini.in = migration.gini.in(m, corrected),
migration.gini.out = migration.gini.out(m, corrected)
)
res$migration.gini.row.standardized <- migration.gini.row.standardized(m, res$migration.gini.total)
res$migration.gini.col.standardized <- migration.gini.col.standardized(m, res$migration.gini.total)
res$migration.gini.exchange.standardized <- migration.gini.exchange.standardized(m, res$migration.gini.total)
res$migration.gini.in.weighted <- migration.weighted.gini.in(m, res$migration.gini.in)
res$migration.gini.out.weighted <- migration.weighted.gini.out(m, res$migration.gini.out)
res$migration.gini.mean.weighted <- migration.weighted.gini.mean(m, res$migration.gini.in.weighted, res$migration.gini.out.weighted)
class(res) <- 'migration.gini'
return(res)
}
#' @export
print.migration.gini <- function(x, ...) {
cat('\n')
cat('Total Flows Gini Index: ', x$migration.gini.total, '\n')
cat('Rows Gini Index: ', x$migration.gini.row, '\n')
cat('Standardized Rows Gini Index: ', x$migration.gini.row.standardized, '\n')
cat('Columns Gini Index: ', x$migration.gini.col, '\n')
cat('Standardized Columns Gini Index: ', x$migration.gini.col.standardized, '\n')
cat('Exchange Gini Index: ', x$migration.gini.exchange, '\n')
cat('Standardized Exchange Gini Index: ', x$migration.gini.exchange.standardized, '\n')
cat('In-migration Field Gini Index: ', 'vector', '\n')
cat('Weighted In-migration Gini Index: ', x$migration.gini.in.weighted, '\n')
cat('Out-migration Field Gini Index: ', 'vector', '\n')
cat('Weighted Out-migration Gini Index: ', x$migration.gini.out.weighted, '\n')
cat('Migration-weighted Mean Gini Index: ', x$migration.gini.mean.weighted, '\n')
cat('\n')
}
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Defines functions print.migration.gini migration.gini migration.weighted.gini.mean migration.weighted.gini.in migration.gini.in migration.weighted.gini.out migration.gini.out migration.gini.exchange.standardized migration.gini.exchange migration.gini.col.standardized migration.gini.col migration.gini.row.standardized migration.gini.row migration.gini.total check.migration.matrix
Documented in check.migration.matrix migration.gini migration.gini.col migration.gini.col.standardized migration.gini.exchange migration.gini.exchange.standardized migration.gini.in migration.gini.out migration.gini.row migration.gini.row.standardized migration.gini.total migration.weighted.gini.in migration.weighted.gini.mean migration.weighted.gini.out
#' Check Migration Matrix
#'
#' Checks if provided R object looks like a migration matrix.
#'
#' A migration matrix is a symmetric matrix with the exact same row and column names. The diagonal equals to zero. The upper triangle shows the in- and the lower triangle shows the out-migration.
#' @param m R object to check
#' @return (invisibly) TRUE
#' @keywords internal
check.migration.matrix <- function(m) {
## dummy checks on provided matrix
if (missing(m))
stop('No data provided!')
if (!is.matrix(m))
stop('Wrong data type (!matrix) provided!')
if (nrow(m) != ncol(m))
stop('Wrong data tpye (!symmetrical matrix) provided!')
if (!is.numeric(m))
stop('Wrong data tpye (!numeric) provided!')
if (length(which(is.na(m[xor(upper.tri(m), lower.tri(m))]))) > 0)
stop('Missing values (outside of diagonal) found in provided matrix!')
if (!any(all(is.na(diag(m))), all(diag(m) == 0)))
stop('Diagonal should be zero or missing.')
return(invisible(TRUE))
}
#' Total Flows Gini Index
#'
#' The Total Gini Index shows the overall concentration of migration with a simple number computed by comparing each cell of the migration matrix with every other cell except for the diagonal:
#' \deqn{G^T = \frac{\sum_i \sum_{j \neq i} \sum_k \sum_{l \neq k} | M_{ij} - M_{kl} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by a simple loop for performance issues to compare all values to the others at one go, although smaller migration matrices could also be addressed by a much faster \code{dist} method. Please see the sources for more details.
#' @param m migration matrix
#' @param corrected Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to have \eqn{2{n(n-1)-1}} instead of \eqn{2n(n-1)} in the denominator to "ensure that the index can assume the upper limit of 1".
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows that all migrants are found in one single flow.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.total(migration.hyp) # 0.2666667
#' migration.gini.total(migration.hyp2) # 0.225
#' migration.gini.total(migration.hyp, FALSE) # 0.2222222
#' migration.gini.total(migration.hyp2, FALSE) # 0.1875
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row}} \code{\link{migration.gini.exchange}} \code{\link{migration.gini.in}} \code{\link{migration.gini.out}}
migration.gini.total <- function(m, corrected = TRUE) {
check.migration.matrix(m)
n <- nrow(m)
m.val <- m[xor(upper.tri(m), lower.tri(m))]
if (corrected)
denominator <- 2*(n*(n-1)-1)
else
denominator <- 2*n*(n-1)
return(sum(apply(as.data.frame(m.val), 1, function(x) sum(abs(m.val-x))), na.rm = TRUE)/(denominator * sum(m, na.rm = TRUE)))
## faster method (fails with "low memory")
diag(m) <- NA
sum(dist(as.vector(m)), na.rm = TRUE)*2/(denominator * sum(m, na.rm = TRUE))
}
#' Rows Gini Index
#'
#' The Rows Gini index concentrates on the "relative extent to which the destination selections of out-migrations are spatially focused":
#' \deqn{G^T_R = \frac{\sum_i \sum_{j \neq i} \sum_{h \neq i,j} | M_{ij} - M_{ih} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by computing the \code{dist} matrix for each row.
#' @param m migration matrix
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.row(migration.hyp) # 0
#' migration.gini.row(migration.hyp2) # 0.02083333
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row.standardized}}
migration.gini.row <- function(m) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
sum(apply(m, 1, function(m.row) sum(dist(m.row), na.rm = TRUE)*2))/(2*n*(n-1)*sum(m, na.rm = TRUE))
}
#' Standardized Rows Gini Index
#'
#' The standardized version of the Rows Gini Index (\code{\link{migration.gini.row}}) by dividing that with the Total Flows Gini Index (\code{\link{migration.gini.total}}):
#' \deqn{G^{T*}_R = 100\frac{G^T_R}{G^T}}
#' As this index is standardized, it "facilitate comparisons from one period to the next of the rows" indices.
#' @param m migration matrix
#' @param gini.total optionally pass the pre-computed Total Flows Gini Index to save computational resources
#' @return A percentage range from 0\% to 100\% where 0\% means that the migration flows are uniform, while a higher value indicates spatial focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.row.standardized(migration.hyp) # 0
#' migration.gini.row.standardized(migration.hyp2) # 11.11111
#' @export
#' @seealso \code{\link{migration.gini.row}} \code{\link{migration.gini.col.standardized}}
migration.gini.row.standardized <- function(m, gini.total = migration.gini.total(m, FALSE)) {
100 * migration.gini.row(m) / gini.total
}
#' Columns Gini Index
#'
#' The Columns Gini index concentrates on the "relative extent to which the destination selections of in-migrations are spatially focused":
#' \deqn{G^T_R = \frac{\sum_j \sum_{i \neq j} \sum_{g \neq i,j} | M_{ij} - M_{gj} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by computing the \code{dist} matrix for each columns.
#' @param m migration matrix
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.col(migration.hyp) # 0.05555556
#' migration.gini.col(migration.hyp2) # 0.04166667
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini.row}} \code{\link{migration.gini.col.standardized}}
migration.gini.col <- function(m) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
sum(apply(m, 2, function(m.row) sum(dist(m.row), na.rm = TRUE)*2))/(2*n*(n-1)*sum(m, na.rm = TRUE))
}
#' Standardized Columns Gini Index
#'
#' The standardized version of the Columns Gini Index (\code{\link{migration.gini.col}}) by dividing that with the Total Flows Gini Index (\code{\link{migration.gini.total}}):
#' \deqn{G^{T*}_C = 100\frac{G^T_C}{G^T}}
#' As this index is standardized, it "facilitate comparisons from one period to the next" of the columns indices.
#' @param m migration matrix
#' @param gini.total optionally pass the pre-computed Total Flows Gini Index to save computational resources
#' @return A percentage range from 0\% to 100\% where 0\% means that the migration flows are uniform, while a higher value indicates spatial focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.col.standardized(migration.hyp) # 25
#' migration.gini.col.standardized(migration.hyp2) # 22.22222
#' @export
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row.standardized}}
migration.gini.col.standardized <- function(m, gini.total = migration.gini.total(m, FALSE)) {
100 * migration.gini.col(m) / gini.total
}
#' Exchange Gini Index
#'
#' The Exchange Gini Index "indicates the contribution to spatial focusing represented by the \eqn{n(n-q)} net interchanges in the system":
#' \deqn{G^T_{RC, CR} = \frac{\sum_i \sum_{j \neq i} | M_{ij} - M_{ji} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}}
#' This implementation solves the above formula by simply substracting the transposed matrix's values from the original one at one go.
#' @param m migration matrix
#' @return A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @export
#' @examples
#' data(migration.hyp)
#' migration.gini.exchange(migration.hyp) # 0.05555556
#' migration.gini.exchange(migration.hyp2) # 0.04166667
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.exchange.standardized}}
migration.gini.exchange <- function(m) {
check.migration.matrix(m)
n <- nrow(m)
m.t <- t(m)
m.val <- m[xor(upper.tri(m), lower.tri(m))]
m.t.val <- m.t[xor(upper.tri(m.t), lower.tri(m.t))]
sum(abs(m.val - m.t.val))/(2*n*(n-1)*sum(m))
}
#' Standardized Exchange Gini Index
#'
#' The standardized version of the Exchange Gini Index (\code{\link{migration.gini.exchange}}) by dividing that with the Total Flows Gini Index (\code{\link{migration.gini.total}}):
#' \deqn{G^{T*}_{RC, CR} = 100\frac{G^T_{RC, CR}}{G^T}}
#' As this index is standardized, it "facilitate comparisons from one period to the next" of the exchange indices.
#' @param m migration matrix
#' @param gini.total optionally pass the pre-computed Total Flows Gini Index to save resources
#' @return A percentage range from 0\% to 100\% where 0\% means that the migration flows are uniform, while a higher value indicates spatial focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.exchange.standardized(migration.hyp) # 25
#' migration.gini.exchange.standardized(migration.hyp2) # 22.22222
#' @export
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.exchange}}
migration.gini.exchange.standardized <- function(m, gini.total = migration.gini.total(m, FALSE)) {
100 * migration.gini.exchange(m) / gini.total
}
#' Out-migration Field Gini Index
#'
#' The Out-migration Field Gini Index is a decomposed version of the Rows Gini Index (\code{\link{migration.gini.row}}) representing "the contribution of each region's row to the total index" () (\code{\link{migration.gini.total}}):
#' \deqn{G^O_i = \frac{\sum_{j \neq i} \sum_{l \neq i,j} | M_{ij} - M_{il} | }{ 2(n-2) \sum_{j \neq k} M_{ij}}}
#' These Gini indices facilitates the direct comparison of different territories without further standardization.
#' @param m migration matrix
#' @param corrected Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to be \eqn{2(n-2)} instead of \eqn{2(n-1)} because "the number of comparisons should exclude the diagonal cell in each row and column, and the comparison of each cell with itself".
#' @return A numeric vector with the range of 0 to 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.out(migration.hyp) # 0 0 0
#' migration.gini.out(migration.hyp2) # 0.000 0.25 0.000
#' migration.gini.out(migration.hyp, FALSE) # 0 0 0
#' migration.gini.out(migration.hyp2, FALSE) # 0.000 0.125 0.000
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.in}} \code{\link{migration.weighted.gini.out}}
migration.gini.out <- function(m, corrected = TRUE) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
if (corrected)
denominator <- 2 * (n - 2)
else
denominator <- 2 * (n - 1)
apply(m, 1, function(m.row) sum(dist(m.row), na.rm = TRUE) * 2) / (denominator * rowSums(m, na.rm = TRUE))
}
#' Migration-weighted Out-migration Gini Index
#'
#' The Migration-weighted Out-migration Gini Index is a weighted version of the Out-migration Field Gini Index (\code{\link{migration.gini.out}}) "according to the zone of destination's share of total migration and the mean of the weighted values is computed as":
#' \deqn{MWG^O = \frac{ \sum_i G^O_i \frac{\sum_j M_{ij}}{\sum_{ij} M_{ij}}}{n}}
#' @param m migration matrix
#' @param mgo optionally passed (precomputed) Migration In-migration Gini Index
#' @references \itemize{
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.weighted.gini.out(migration.hyp) # 0
#' migration.weighted.gini.out(migration.hyp2) # 0.02083333
#' @seealso \code{\link{migration.weighted.gini.in}} \code{\link{migration.weighted.gini.mean}}
#' @export
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.out}} \code{\link{migration.weighted.gini.in}} \code{\link{migration.weighted.gini.mean}}
migration.weighted.gini.out <- function(m, mgo = migration.gini.out(m)) {
diag(m) <- NA
n <- nrow(m)
m.sum <- sum(m, na.rm = TRUE)
sum(mgo * colSums(m, na.rm = TRUE) / m.sum) / n
}
#' In-migration Field Gini Index
#'
#' The In-migration Field Gini Index is a decomposed version of the Columns Gini Index (\code{\link{migration.gini.col}}) representing "the contribution of each region's columns to the total index" () (\code{\link{migration.gini.total}}):
#' \deqn{G^I_j = \frac{\sum_{i \neq j} \sum_{k \neq j,i} | M_{ij} - M_{kj} | }{ 2(n-2) \sum_{i \neq j} M_{ij}}}
#' These Gini indices facilitates the direct comparison of different territories without further standardization.
#' @param m migration matrix
#' @param corrected Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to be \eqn{2(n-2)} instead of \eqn{2(n-1)} because "the number of comparisons should exclude the diagonal cell in each row and column, and the comparison of each cell with itself".
#' @return A numeric vector with the range of 0 to 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.gini.in(migration.hyp) # 0.2000000 0.5000000 0.3333333
#' migration.gini.in(migration.hyp2) # 0.2000000 0.0000000 0.4285714
#' migration.gini.in(migration.hyp, FALSE) # 0.1000000 0.2500000 0.1666667
#' migration.gini.in(migration.hyp2, FALSE) # 0.1000000 0.0000000 0.2142857
#' @export
#' @importFrom stats dist
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.out}} \code{\link{migration.weighted.gini.in}}
migration.gini.in <- function(m, corrected = TRUE) {
check.migration.matrix(m)
diag(m) <- NA
n <- nrow(m)
if (corrected)
denominator <- 2 * (n - 2)
else
denominator <- 2 * (n - 1)
apply(m, 2, function(m.row) sum(dist(m.row), na.rm = TRUE) * 2) / (denominator * colSums(m, na.rm = TRUE))
}
#' Migration-weighted In-migration Gini Index
#'
#' The Migration-weighted In-migration Gini Index is a weighted version of the In-migration Field Gini Index (\code{\link{migration.gini.in}}) "according to the zone of destination's share of total migration and the mean of the weighted values is computed as":
#' \deqn{MWG^I = \frac{ \sum_j G^I_j \frac{\sum_j M_{ij}}{\sum_{ij} M_{ij}}}{n}}
#' @param m migration matrix
#' @param mgi optionally passed (precomputed) Migration In-migration Gini Index
#' @references \itemize{
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.weighted.gini.in(migration.hyp) # 0.1222222
#' migration.weighted.gini.in(migration.hyp2) # 0.05238095
#' @seealso \code{\link{migration.gini}} \code{\link{migration.gini.in}} \code{\link{migration.weighted.gini.out}} \code{\link{migration.weighted.gini.mean}}
#' @export
migration.weighted.gini.in <- function(m, mgi = migration.gini.in(m)) {
diag(m) <- NA
n <- nrow(m)
m.sum <- sum(m, na.rm = TRUE)
sum(mgi * rowSums(m, na.rm = TRUE) / m.sum) / n
}
#' Migration-weighted Mean Gini Index
#'
#' The Migration-weighted Mean Gini Index is simply the average of the Migration-weighted In-migration (\code{\link{migration.weighted.gini.in}}) and the Migration-weighted Out-migration (\code{\link{migration.weighted.gini.out}}) Gini Indices:
#' \deqn{MWG^A = \frac{MWG^O + MWG^I}{2}}
#' @param m migration matrix
#' @param mwgi optionally passed (precomputed) Migration-weighted In-migration Gini Index
#' @param mwgo optionally passed (precomputed) Migration-weighted Out-migration Gini Index
#' @return This combined index results in a number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
#' @references \itemize{
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @examples
#' data(migration.hyp)
#' migration.weighted.gini.mean(migration.hyp) # 0.06111111
#' migration.weighted.gini.mean(migration.hyp2) # 0.03660714
#' @seealso \code{\link{migration.weighted.gini.in}} \code{\link{migration.weighted.gini.out}}
#' @export
migration.weighted.gini.mean <- function(m, mwgi, mwgo) {
if (missing(mwgi))
mwgi <- migration.weighted.gini.in(m)
if (missing(mwgo))
mwgo <- migration.weighted.gini.out(m)
(mwgi + mwgo) / 2
}
#' Spatial Gini Indexes
#'
#' This is a wrapper function computing all the following Gini indices:
#' \itemize{
#' \item Total Flows Gini Index (\code{\link{migration.gini.total}})
#' \item Rows Gini Index (\code{\link{migration.gini.row}})
#' \item Standardized Rows Gini Index (\code{\link{migration.gini.row.standardized}})
#' \item Columns Gini Index (\code{\link{migration.gini.col}})
#' \item Standardized Columns Gini Index (\code{\link{migration.gini.col.standardized}})
#' \item Exchange Gini Index (\code{\link{migration.gini.exchange}})
#' \item Standardized Exchange Gini Index (\code{\link{migration.gini.exchange.standardized}})
#' \item Out-migration Field Gini Index (\code{\link{migration.gini.out}})
#' \item Migration-weighted Out-migration Gini Index (\code{\link{migration.weighted.gini.out}})
#' \item In-migration Field Gini Index (\code{\link{migration.gini.in}})
#' \item Migration-weighted In-migration Gini Index (\code{\link{migration.weighted.gini.in}})
#' \item Migration-weighted Mean Gini Index (\code{\link{migration.weighted.gini.mean}})
#' }
#' @return List of all Gini indices.
#' @param m migration matrix
#' @param corrected to use Bell et al. (2002) updated formulas instead of Plane and Mulligan (1997)
#' @examples
#' data(migration.hyp)
#' migration.gini(migration.hyp)
#' migration.gini(migration.hyp2)
#' @export
#' @references \itemize{
#' \item David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. \emph{Demography} \bold{34}, 251--262
#' \item M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. \emph{Journal of the Royal Statistical Society. Series A (Statistics in Society)} \bold{165}, 435--464
#' }
#' @seealso \code{\link{migration.gini.col}} \code{\link{migration.gini.row}} \code{\link{migration.gini.exchange}} \code{\link{migration.gini.in}} \code{\link{migration.gini.out}}
migration.gini <- function(m, corrected = TRUE) {
res <- list(
migration.gini.total = migration.gini.total(m, corrected),
migration.gini.exchange = migration.gini.exchange(m),
migration.gini.row = migration.gini.row(m),
migration.gini.col = migration.gini.col(m),
migration.gini.in = migration.gini.in(m, corrected),
migration.gini.out = migration.gini.out(m, corrected)
)
res$migration.gini.row.standardized <- migration.gini.row.standardized(m, res$migration.gini.total)
res$migration.gini.col.standardized <- migration.gini.col.standardized(m, res$migration.gini.total)
res$migration.gini.exchange.standardized <- migration.gini.exchange.standardized(m, res$migration.gini.total)
res$migration.gini.in.weighted <- migration.weighted.gini.in(m, res$migration.gini.in)
res$migration.gini.out.weighted <- migration.weighted.gini.out(m, res$migration.gini.out)
res$migration.gini.mean.weighted <- migration.weighted.gini.mean(m, res$migration.gini.in.weighted, res$migration.gini.out.weighted)
class(res) <- 'migration.gini'
return(res)
}
#' @export
print.migration.gini <- function(x, ...) {
cat('\n')
cat('Total Flows Gini Index: ', x$migration.gini.total, '\n')
cat('Rows Gini Index: ', x$migration.gini.row, '\n')
cat('Standardized Rows Gini Index: ', x$migration.gini.row.standardized, '\n')
cat('Columns Gini Index: ', x$migration.gini.col, '\n')
cat('Standardized Columns Gini Index: ', x$migration.gini.col.standardized, '\n')
cat('Exchange Gini Index: ', x$migration.gini.exchange, '\n')
cat('Standardized Exchange Gini Index: ', x$migration.gini.exchange.standardized, '\n')
cat('In-migration Field Gini Index: ', 'vector', '\n')
cat('Weighted In-migration Gini Index: ', x$migration.gini.in.weighted, '\n')
cat('Out-migration Field Gini Index: ', 'vector', '\n')
cat('Weighted Out-migration Gini Index: ', x$migration.gini.out.weighted, '\n')
cat('Migration-weighted Mean Gini Index: ', x$migration.gini.mean.weighted, '\n')
cat('\n')
}
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