ResampleTest: A function to test segregation indices by resampling

Description

Resampling tests for segregation indexes.

Usage

ResampleTest(
  x,
  fun,
  var = NULL,
  simtype = "MonteCarlo",
  sampleunit = "unit",
  samplesize = NULL,
  perc = c(0.05, 0.95),
  outl = FALSE,
  outmeth = "bp",
  sdtimes = 2,
  IQRrange = 1.5,
  proba = NULL,
  nsim = NULL,
  setseed = FALSE,
  spatobj = NULL,
  folder = NULL,
  shape = NULL,
  delta = 0.5,
  exact = FALSE,
  d = NULL,
  c = NULL,
  a = NULL,
  ck = NULL,
  f = "exp",
  b = NULL,
  p = NULL,
  spatmat = "c",
  queen = FALSE,
  distin = "m",
  distout = "m",
  diagval = "0",
  fdist = "e",
  itype = "multi",
  dc = NULL,
  center = 1,
  polorder = 4,
  pred = NULL,
  K = 2,
  ptype = "int",
  variant = "s",
  ...
)

Value

A list with: - index's name - simulation type - statistics summary of the simulations - simulated index distribution - simulated population distribution - matrix with outliers (jackknife) - list with outliers values (jackknife)

Arguments

x: - an object of class matrix (or which can be coerced to that class), where each column represents the distribution of a group within spatial units. The number of columns should be greater than 1 (at least 2 groups are required). You should not include a column with total population, because this will be interpreted as a group.
fun: - a character vector with the segregation function to be tested
var: - vector with the variables to be tested
simtype: - a character vector with the type of simulation. If simtype = 'Boot', the function generates bootstrap replications If simtype = 'Jack', the function generates jackknife replications If simtype = 'MonteCarlo', the function produces a randomization test using Monte Carlo simulations
sampleunit: = 'unit' (by default) when the sampling unit is the spatial/organisational unit and sampleunit = 'ind' for individual sampling
samplesize: - the size of the sample used for bootstraping. If null, the samplesize equals the number of spatial/organizational units(sampleunit = 'unit') or the total total population (sampleunit = 'ind')
perc: - the percentiles for the bootstrap replications
outl: - logical parameter for jackknife simulations, if TRUE the function provides the outliers obtained by jackknife iterations
outmeth: - a character vector designing the outliers detection method: outmeth = 'bp' (by default) for boxplot method outmeth = 'sd' for standard deviation method outmeth = 'z' for normal scores method outmeth = 't' for t Student scores method outmeth = 'chisq' for chi-squared scores method outmeth = 'mad' for median absolute deviation method The estimations based on scoring methods are obtained using outliers package
sdtimes: - multiplication factor of the standard deviation used for outliers detection with jackknife simulations (2 by default)
IQRrange: - determines the boxplot thresholds (1.5 by default) as multiplication of IQR (Inter Quartile Range)
proba: - for Monte Carlo simulations, proba is a vector with location probabilities. If proba = NULL, the vector is equiprobable. If outliers are determined with jackknife technique, proba indicates the probability (confidence interval) for scoring tests.
nsim: - the number of simulations
setseed: - if TRUE, specify zero seed for repetead simulation
spatobj: - a spatial object (SpatialPolygonsDataFrame) with geographic information
folder: - a character vector with the folder (directory) name indicating where the shapefile is located on the drive
shape: - a character vector with the name of the shapefile (without the .shp extension).
delta: - an inequality aversion parameter
exact: - a logical variable to specifiy the index version: exact = FALSE (by default) for the approximate version of the index, and exact = TRUE for the exact version
d: - a matrix of the distances between spatial unit centroids
c: - a standard binary contiguity (adjacency) symmetric matrix where each element Cij equals 1 if i-th and j-th spatial units are adjacent, and 0 otherwise.
a: - a numeric vector containing spatial unit areas
ck: - a list containing contiguity matrices coresponding to each order (from 1 to K)
f: - the distance function, f = 'exp' (by default) for negative exponential function and f = 'rec' for reciprocal function
b: - a common boundaries matrix where each element Bij
p: - a numeric vector containing spatial units perimeters.
spatmat: - the method used for spatial calculations: 'c' for the contiguity matrix (by default) or any other user spatial interaction matrix and 'd' for the inverse exponential function of the distance.
queen: - logical parameter defining criteria used for contiguity matrix computation, TRUE for queen, FALSE (by default) for rook
distin: - input metric conversion, based on bink package and includes conversions from 'm', 'km', 'inch', 'ft', 'yd', 'mi', 'naut_mi', etc.
distout: - output metric conversion, based on bink package and includes conversions to 'm', 'km', 'inch', 'ft', 'yd', 'mi', 'naut_mi', etc.
diagval: - when providing a spatial object or a shape file, the user has the choice of the spatial matrix diagonal definition: diagval = '0' (by default) for an null diagonal and diagval = 'a' to compute the diagonal as 0.6 * square root (spatial/organizational unitsarea) (White, 1983)
fdist: - the method used for distance interaction matrix: e' for inverse exponential function (by default) and 'l' for linear.
itype: - a character string defining the index type: itype = 'multi' (by default) for the multi-group index (White, 1986) or itype = 'between' for the between groups version (White, 1983)
dc: - a numeric vector containing the distances between spatial units centroids and the central spatial unit
center: - a numeric value giving the number of the spatial unit that represents the center in the table
polorder: - order of the polynomial approximation (4 by default)
pred: - a numerical vector with percentiles to be predicted.
K: - the order of the contiguity matrix
ptype: - a string variable giving two options for perimeter calculation when a spatial object or shapefile is provided: 'int' to use only interior boundaries of spatial units, and 'all' to use entire boundaries, including the boundaries to the exterior
variant: - a character variable that allows to choose the index version: variant = 's' for the dissimilarity index adjusted for contiguous spatial units boundary lengths and perimeter/area ratio (by default) and variant = 'w' for the version without perimeter/area ratio
...: - other specific parameters

References

Efron, B., and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. New York, Chapman and Hall

Tivadar M. (2019) OasisR: An R Package to Bring Some Order to the World of Segregation Measurement. Journal of Statistical Software, 89 (7), pp 1-39

Examples

Run this code

x <- segdata@data[ ,1:2]

xtest <- ResampleTest (x, fun ='ISMorrill', simtype = 'MonteCarlo', 
                       sampleunit = 'ind', spatobj = segdata)
xtest$Summary

xtest <- ResampleTest (x, fun ='ISMorrill', simtype = 'Boot', 
                       sampleunit = 'unit', spatobj = segdata)
xtest$Summary

xtest <- ResampleTest (GreHSize@data[,3:5], fun='ISDuncan', simtype = 'Jack', 
                       sampleunit = 'unit',  spatobj = GreHSize, 
                       outl = TRUE, outmeth = 'sd', sdtimes = 3)
xtest$Summary
xtest$OutliersVal