A function to test segregation indices using Monte Carlo simulations

Description

The Monte Carlo tests for one-group or multigroup segregation indexes.

Usage

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MCTest(x, fun, simtype = "rand", proba = NULL, delta = 0.5, ptype = "int", 
variant = "s", distin = "m", distout = "m", itype = "multi", exact = F, 
diagval = "0", spatmat = "c", c = NULL, queen = TRUE, b = NULL, p = NULL, 
a = NULL, d = NULL, dc = NULL, fdist = "e", center = 1, nsim = 99, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

x

- an object of class matrix (or which can be coerced to that class), where each column represents the distribution of a population group, within spatial units. The number of columns should be greater than 1 (at least 2 population groups are required). You should not include a column with total population in each unit, because this will be interpreted as a group.

fun

- a character vector with the segregation function to be tested (only one-group or multigroup indexes)

simtype

- a character vector with type of simulation. If simtype='perm', the function will use the permutation test. If simtype='rand', the population is realocated in the spatial units randomly. If simtype='area', the location probabilities are proportional to the spatial units' area. For the default value type='user', the function expects you to introduce a probability location vector.

proba

- a vector with location probabilities. By default proba = NULL being calculated depending on the simulation type. The parameter is necessary when a user method is specified.

delta

- a specific Atikinson inequality aversion parameter, by default equal to 0.5,varying from 0 to 1.

ptype

- a string variable giving two options for perimeter calculation, when needed: 'int' to use only interior boundaries of spatial units, and 'all' to use entire boundaries, including the boundaries to the exterior of the area

variant

- a character variable that allows to choose the Wong's index version: variant = 's' for the index adjusted for contiguous spatial units boundary lengths and perimeter/area ratio (by default) and variant = 'w' for the version based only on shared boundaries length

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.

itype

- a character string defining the type of some proximity indices: itype = 'multi' (by default) for the multigroup index (White, 1986) or itype = 'one' for the one-group version (Apparicio et al, 2008)

exact

- a logical variable to specifiy the version of interaction indices exact = FALSE (by default) for the approximate version of the index, and exact = TRUE for the exact version

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 units area) (White, 1983)

spatmat

- the method used for some 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.

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.

queen

- logical parameter difining criteria used for contiguity matrix computation, TRUE (by default) for queen , FALSE for rook

b

- a common boundaries matrix where each element Bij equals the shared boundary of i-th and j-th spatial units.

p

- a numeric vector containing the perimeters of spatial units

a

- a numeric vector containing the areas of spatial units

d

- a matrix of the distances between spatial unit centroids

dc

- a numeric vector containing the distances between spatial units centroids and the central spatial unit

fdist

- the method used for distance interaction matrix: e' for inverse exponential function (by default) and 'l' for linear.

center

- a numeric value giving the number of the spatial unit that represents the centre in the table

nsim

- the number of simulations

spatobj

- a spatial object (SpatialPolygonsDataFrame) containing geographic information

folder

- a character vector with the folder (directory) name indicating where the shapefile with the geographic information is located.

shape

- a character vector with the shape file name

Value

A list with thre elements: index's name, a Summary of the simulation and index simulated distribution

References

Tivadar M., Schaeffer Y, Torre A. and Bray F. (2014) OASIS - un Outil d'Analyse de la Segregation et des Inegalites Spatiales. Cybergeo : European Journal of Geography, GeOpenMod, document 699

See Also

MCPlot

Examples

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x <- segdata@data[ ,1:2]
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
ar <- area(segdata)
probavector<-ar/sum(ar)

MCTest (x, fun='ISMorrill', simtype = 'perm', spatobj = segdata)

MCTest (x, fun='ISMorrill', simtype = 'rand', spatobj = segdata)

MCTest (x, fun='ISMorrill', simtype = 'area', spatobj = segdata)

MCTest (x, fun='ISMorrill', simtype='user', proba = probavector, 
spatobj = segdata)

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