Package 'OasisR'

Description

The absolute centralization index measures a group spatial distribution compared to the distribution of land area around the city center. The function can be used in two ways: to provide an area vector and a vector containing the distances between spatial units centroids and the central spatial unit or a external geographic information source (spatial object or shape file).

Usage

ACE(x, a = NULL, dc = NULL, center = 1, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Massey and Denton absolute centralisation index values for each group

References

Massey D. S. and Denton N. A. (1988) The dimensions of residential segregation. Social Forces 67(2), pp. 281-315.

See Also

ACEPoly,

RCE, RCEPoly, RCEPolyK,

ACEDuncan, ACEDuncanPoly,

ACEDuncanPolyK

Examples

x <- segdata@data[ ,1:2]
ar<-area(segdata)
distc<- distcenter(segdata, center = 28)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

ACE(x, a = ar, dc=distc) 

ACE(x, spatobj = segdata, center = 28) 

ACE(x, folder = foldername, shape = shapename, center = 28)

Description

Duncan's absolute centralization index measures the proportion of a group that should change its localization to achieve the same level of centralization as the rest of the population. The function can be used in two ways: to provide a vector containing the distances between spatial/organizational unit centroids or a external geographic information source (spatial object or shape file).

Usage

ACEDuncan(x, dc = NULL, center = 1, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Duncan's absolute centralisation index values for each group

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

See Also

ACEDuncanPoly, ACEDuncanPolyK,

RCE, RCEPoly, RCEPolyK

ACE, ACEPoly

Examples

x <- segdata@data[ ,1:2]
distc<- distcenter(segdata, center = 28)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

ACEDuncan(x, dc=distc) 

ACEDuncan(x, spatobj = segdata, center = 28) 

ACEDuncan(x, folder = foldername, shape = shapename, center = 28)

Description

Polycentric version of Duncan's absolute centralization index. The function can be used in two ways: to provide a vector containing the distances between spatial/organizational unit centroids or a external geographic information source (spatial object or shape file).

Usage

ACEDuncanPoly(x, dc = NULL, center = 1, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Duncan's absolute polycentric centralisation index value for each group

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

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

See Also

ACEDuncan, ACEDuncanPolyK,

RCE, RCEPoly, RCEPolyK

ACE, ACEPoly

Examples

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

ACEDuncanPoly(x, spatobj = segdata, center = c(28, 83) )

ACEDuncanPoly(x, folder = foldername, shape = shapename, center = c(28, 83))

center <- c(28, 83)
polydist <- matrix(data = NA, nrow = nrow(x), ncol = length(center))
for (i in 1:ncol(polydist))
  polydist[,i] <- distcenter(spatobj = segdata, center = center[i])
ACEDuncanPoly(x, dc = polydist)

distmin <- vector(length = nrow(x))
for (i in 1:nrow(polydist)) distmin[i] <- min(polydist[i,])
ACEDuncan(x, dc = distmin)

Description

Constrained (local) version of Duncan's centralization index. The function can be used in two ways: to provide a matrix containing the distances between spatial/organizational unit centroids or a external geographic information source (spatial object or shape file).

Usage

ACEDuncanPolyK(x, dc = NULL,  K = NULL, kdist = NULL, center = 1,
                spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Duncan's constrainted absolute centralisation index value for each group

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

Folch D.C and Rey S. J (2016) The centralization index: A measure of local spatial segregation. Papers in Regional Science 95 (3), pp. 555-576

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

See Also

ACEDuncan, ACEDuncanPoly,

RCE, RCEPoly, RCEPolyK

ACE, ACEPoly

Examples

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

ACEDuncanPolyK(x, spatobj = segdata, center = c(28, 83))

ACEDuncanPolyK(x, folder = foldername, shape = shapename, center = c(28, 83), K = 3)

center <- c(28, 83)
polydist <- matrix(data = NA, nrow = nrow(x), ncol = length(center))
for (i in 1:ncol(polydist))
  polydist[,i] <- distcenter(spatobj = segdata, center = center[i])
ACEDuncanPolyK(x, dc = polydist, kdist = 2)

Description

The absolute centralization index measures a group spatial distribution compared to the distribution of land area around the city center. The function can be used in two ways: to provide an area vector and a vector containing the distances between spatial units centroids and the central spatial unit or a external geographic information source (spatial object or shape file).

Usage

ACEPoly(x, a = NULL, dc = NULL, center = 1, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Massey and Denton absolute polycentric centralisation index values for each group

References

Massey D. S. and Denton N. A. (1988) The dimensions of residential segregation. Social Forces 67(2), pp. 281-315.

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

See Also

ACE, RCE,

RCEPoly, RCEPolyK,

ACEDuncan, ACEDuncanPoly,

ACEDuncanPolyK

Examples

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

ACEPoly(x, spatobj = segdata, center = c(28, 83) )

ACEPoly(x, folder = foldername, shape = shapename, center = c(28, 83))

center <- c(28, 83)
polydist <- matrix(data = NA, nrow = nrow(x), ncol = length(center))
for (i in 1:ncol(polydist))
  polydist[,i] <- distcenter(spatobj = segdata, center = center[i])
ACEPoly(x, a = ar, dc = polydist)

distmin <- vector(length = nrow(x))
for (i in 1:nrow(polydist)) distmin[i] <- min(polydist[i,])
ACE(x, a = ar, dc = distmin)

Description

The absolute clustering index, ACL, expresses the average number of a group's members in nearby spatial units, as a proportion of the total population in those spatial units. The spatial interactions can be expressed as a contiguity matrix (with diagonal equal to 1), as an inverse exponential function of the distance between spatial units centers (with diagonal equal to 0.6 of the square root of each spatial units area) or other user specified interaction matrix. The function can be used in two ways: to provide a spatial interactions matrix (a contiguity matrix or a distance matrix) or a external geographic information source (spatial object or shape file).

Usage

ACL(x, spatmat = 'c', c = NULL, queen = FALSE, d = NULL, distin = 'm',  
distout = 'm', diagval = '0', beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Absolute Clustering index values for each group

References

Massey D. S. and Denton N. A. (1988) The dimensions of residential segregation. Social Forces 67(2), pp. 281-315.

See Also

Proximity measures: Pxx, Pxy, Poo, SP

Relative Clustering Index: RCL

Examples

x <- segdata@data[ ,1:2]
contiguity <- contig(segdata)
diag(contiguity) <- 1
ar<-area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

ACL(x, c = contiguity) 

ACL(x, spatobj = segdata)

ACL(x, spatmat = 'd', folder = foldername, shape = shapename) 
 
ACL(x,  spatmat = 'd', diagval = 'a', spatobj = segdata)

ACL(x, d = dist, spatmat = 'd')

Description

The absolute concentration index, ACO, computes the total area inhabited by a group, and compares the result to the minimum and maximum possible areas that could be inhabited by that group in the study area. The function can be used in two ways: to provide an area vector or a external geographic information source (spatial object or shape file).

Usage

ACO(x, a = NULL, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Absolute Concentration index values for each group

References

Massey D. S. and Denton N. A. (1988) The dimensions of residential segregation. Social Forces 67(2), pp. 281-315.

See Also

Delta Index: Delta

Relative Concentration Index: RCO

Examples

x <- GreHSize@data[ ,3:5]
ar <- area(GreHSize)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'GreHSize'

ACO(x, a = ar) 

ACO(x, spatobj = GreHSize)

ACO(x, folder = foldername, shape = shapename)

Description

The function is based on sf package and can be used with a shape file or an R spatial object (class sf, sfc or sfg).

Usage

area(spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A vector containing the areas of spatial units

See Also

Other spatial functions used for segregation indices computation: contig, perimeter, distance, distcenter, boundaries

Examples

area(segdata) 
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
area(folder = foldername, shape = shapename)

Description

The spatial version of Atkinson inequality index is based on Lorenz curves. The user can decide wich part of the curve contributes more to the index, by choosing the value of the shape parameter, delta.

Usage

Atkinson (x, delta = 0.5)

Arguments

Value

A numeric vector containing Atkinson's segregation index values for each group

References

James, D. and K. E. Taeuber (1985) Measures of Segregation. Sociological Methodology 15, pp. 1-32

See Also

One-group evenness indices: ISDuncan, Gini, Gorard, HTheil, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

x <- segdata@data[ ,7:8]
Atkinson(x) 
Atkinson(x, 0.1)
Atkinson(x, delta = 0.9)

Description

The function is based on sf package and it can be used with a shape file or an R spatial object (class sf, sfc or sfg).

Usage

boundaries(spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A common boundaries matrix

See Also

Other spatial functions used for segregation indices computation: area, contig, perimeter, distance, distcenter

Examples

boundaries(segdata) 
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
boundaries(folder = foldername, shape = shapename)

Description

The index can be interpreted as a measure of the variance of the spatial representation of the groups accros spatial unite, or as a normalized chi-squared measure of association between groups and units.

Usage

CMulti(x)

Arguments

Value

The multigroup entropy segregation index value (numeric)

References

Reardon S. F. and Firebaugh G. (2002) Measures of multigroup segregation. Sociological Methodology, 32, pp. 33-67.

See Also

multigroup indices: PMulti, GiniMulti, DMulti, HMulti, RelDivers

Social diversity indices: HShannon, NShannon, ISimpson,

Examples

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

Description

The function is based on sf package and can be used with a shape file or an R spatial object (class sf, sfc or sfg).

Usage

contig(spatobj = NULL, folder = NULL, shape = NULL, queen = FALSE)

Arguments

Value

A first order contiguity (adjacency) matrix, where each element [i,j] equals 1 if i-th and j-th spatial units are adjacent, 0 otherwise (queen or rook criteria)

See Also

Other spatial functions used for segregation indices computation: area, perimeter, distance, distcenter, boundaries

Examples

contig(segdata) 
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
contig(folder = foldername, shape = shapename)

Description

The Delta index is a specific application of dissimilarity index DIDuncan which simply measures the dissimilarity between the spatial distribution of a group and the spatial distribution of available land. It can be interpreted as the share of group that would have to move to achieve uniform density over all spatial units. The function can be used in two ways: to provide an area vector or a external geographic information source (spatial object or shape file).

Usage

Delta(x, a = NULL, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Delta index values for each group

References

Duncan O. D., Cuzzoert and Duncan B. (1961) Problems in analyzing areal data. Statistical geography, Glencoe, Illinois: The free press of Glencoe

See Also

Absolute Concentration Index: ACO

Relative Concentration Index: RCO

Examples

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

Delta(x, a = ar) 

Delta(x, spatobj = segdata)

Delta(x, folder = foldername, shape = shapename)

Description

Duncan's dissimilarity index is the segregation index most commonly used in the literature. It is derived from Lorenz curves as the maximum difference between the segregation curve and the diagonal. The index measures the unevenness of a group's spatial distribution compared to another group. It can be interpreted as the share of the group that would have to move to achieve an even distribution compared to another group.

Usage

DIDuncan(x)

Arguments

Value

A matrix containing the dissimilarity index values for each pair of groups

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

See Also

Other one-group evenness indices: ISDuncan, Gini, Gorard, Atkinson, HTheil, ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIMorrill, DIMorrillK, DIWong

Examples

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

Description

Morrill's dissimilarity index is a development of DIDuncan's index which takes into account the interactions between spatial units(contiguity). The function can be used in two ways: to provide a contiguity matrix or a external geographic information source (spatial object or shape file).

Usage

DIMorrill(x, c = NULL, queen = FALSE, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the Morrill's dissimilarity index values for each pair of groups

References

Morrill B. (1991) On the measure of geographic segregation. Geography research forum, 11, pp. 25-36.

See Also

Other one-group evenness indices: ISDuncan, Gini, Gorard, Atkinson, HTheil, ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, DIMorrillK, DIWong

Examples

x <- segdata@data[ ,1:2]
contiguity <- contig(segdata)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

DIMorrill(x, c = contiguity) 

DIMorrill(x, spatobj = segdata, queen = FALSE)

DIMorrill(x, folder = foldername, shape = shapename)

Description

This function compute an adaptation of Morrill's dissimilarity index which takes into account the interactions between spatial units defined by K order contiguity matrix. The function can be used in two ways: to provide a contiguity matrix or a external geographic information source (spatial object or shape file).

Usage

DIMorrillK(x, ck = NULL, queen = FALSE, spatobj = NULL, 
folder = NULL, shape = NULL, K = 2, f = 'exp', beta = 1, prec = NULL)

Arguments

Value

A matrix containing the Generalized Morrill's dissimilarity index values for each pair of groups

References

Morrill B. (1991) On the measure of geographic segregation. Geography research forum, 11, pp. 25-36.

See Also

Other one-group evenness indices: ISDuncan, Gini, Gorard, Atkinson, HTheil, ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, DIMorrill, DIWong

Examples

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

DIMorrillK(x, spatobj = segdata, queen = FALSE, K = 3)

DIMorrillK(x, folder = foldername, shape = shapename, K = 4, f = 'rec')

Description

The function is based on sf package and can be used with a shape file or an R spatial object (class sf, sfc or sfg).

Usage

distance(spatobj = NULL, folder = NULL, shape = NULL,
distin = 'm',  distout = 'm', diagval = '0')

Arguments

Value

A matrix with the distance between spatial units centroids

See Also

Other spatial functions used for segregation indices computation: area, contig, perimeter, distcenter, boundaries

Examples

distance(segdata) 

foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
distance(folder = foldername, shape = shapename)

Description

The function is based on sf package and it can be used with a shape file or an R spatial object (class sf, sfc or sfg).

Usage

distcenter(spatobj = NULL, folder = NULL, shape = NULL, 
center = 1, distin = 'm',  distout = 'm')

Arguments

Value

A vector with the distance to the center's centroid

See Also

Other spatial functions used for segregation indices computation: area, contig, perimeter, distance, boundaries

Examples

distcenter(segdata, center = 46) 
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
distcenter(folder = foldername, shape = shapename, center = 19)

Description

Wong's dissimilarity index is a development of DIDuncan's which takes into account the interactions between spatial units(common boundaries and perimeter/area ratios). The function can be used in two ways: to provide spatial data ( boundaries matrix, a perimeter vector and an area vector) or a external geographic information source (spatial object or shape file).

Usage

DIWong(x, b = NULL,  a = NULL, p = NULL, ptype = 'int', variant = 's', 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the Wong's dissimilarity index values for each pair of groups

References

Wong D. W. S. (1993) Spatial Indices of Segregation. Urban Studies, 30 (3), pp. 559-572.

See Also

Other one-group evenness indices: ISDuncan, Gini, Gorard, Atkinson, HTheil, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, DIMorrill, DIMorrillK

Examples

x <- segdata@data[ ,1:2]
bound <- boundaries(segdata)
per <- perimeter(segdata)
ar <- area(segdata)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

DIWong(x, b = bound, p = per, a = ar) 

DIWong(x, spatobj = segdata, variant = 'w') 

DIWong(x, folder = foldername, shape = shapename, ptype ='all')

Description

multigroup dissimilarity index, is a multigroup version of Duncan's dissimilarity index (DIDuncan)

Usage

DMulti(x)

Arguments

Value

The multigroup dissimilarity index value (numeric)

References

Sakoda J. N. (1981) A generalized Index of dissimilarity. Demography,18, 245-250

See Also

multigroup indices: PMulti, GiniMulti, HMulti, CMulti, RelDivers

Social diversity indices: HShannon, NShannon, ISimpson,

Examples

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

Description

The distance decay isolation index, DPxx, is a spatial adaptation of isolation index xPx. The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file).

Usage

DPxx(x, d = NULL, distin = 'm',  distout = 'm', diagval = '0', beta = 1, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the distance-decay isolation index values for each group

References

Morgan, B. S. (1983) A Distance-Decay Based Interaction Index to Measure Residential Segregation. Area 15(3), pp. 211-217.

See Also

Isolation indices: xPx, Eta2

Interaction indices: xPy, DPxy

Examples

x <- segdata@data[ ,1:2]
ar <- area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

DPxx(x, d = dist)

DPxx(x, spatobj = segdata, diagval = 'a')

DPxx(x, folder = foldername, shape = shapename, diagval = '0')

Description

The distance decay interaction index, DPxy, is a spatial adaptation of interaction index xPy. The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file).

Usage

DPxy(x, d = NULL, distin = 'm',  distout = 'm', diagval = '0', 
beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the distance-decay interaction index values for each pair of groups

References

Morgan, B. S. (1983) An Alternate Approach to the Development of a Distance-Based Measure of Racial Segregation. American Journal of Sociology 88, pp. 1237-1249.

See Also

Isolation indices: xPx, Eta2, DPxx

Interaction index: xPy

Examples

x <- segdata@data[ ,1:2]
ar <- area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

DPxy(x, d = dist)

DPxy(x, spatobj = segdata, diagval = 'a')

DPxy(x, folder = foldername, shape = shapename, diagval = '0')

Description

The adjusted isolation index is the standardized version of the isolation index, xPx, which controls for the effect of total population structure. Using the approximate version of xPx, the adjusted index is equal to Eta2 (the square of the correlation ratio) which, in the case of the binomial variable, is identical to the square of the mean square contingency coefficient phi. It can be used as a segregation score and varies from 0 (minimum segregation) to 1 (maximum segregation).

Usage

Eta2(x)

Arguments

Value

A numeric vector containing the adjusted isolation index values for each group

References

Bell W. (1954) A probability model for the measurement of ecological segregation. Social Forces 32(4), pp. 357-364

Duncan O. D. and Duncan B. (1955) Residential Distribution and Occupational Stratification.. American Journal of Sociology 60 (5), pp. 493-503

See Also

Isolation indices: xPx, DPxx

Interaction indices: xPy, DPxy

Examples

x <- segdata@data[ ,1:2]
Eta2(x)

Description

The segregation version of the Gini index can be derived from the Lorenz curve as the area between the segregation curve and the diagonal.

Usage

Gini(x)

Arguments

Value

A numeric vector containing Gini's segregation index values for each group

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

See Also

Other one-group evenness indices: ISDuncan, Atkinson, Gorard, HTheil, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

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

Description

The between group version of Gini index is obtained by computing the index for a subpopulation formed by each pair of groups

Usage

Gini2(x)

Arguments

Value

A matrix containing the between-group Gini index values for each pair of groups

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

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

See Also

Other one-group evenness indices: ISDuncan, Gini, Gorard, Atkinson, HTheil, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, DIMorrill, DIMorrillK, DIWong

Examples

x <- segdata@data[ ,1:2]
Gini2(x)

Description

multigroup Gini is a multigroup version of the Gini index

Usage

GiniMulti(x)

Arguments

Value

The multigroup Gini index value (numeric)

References

Reardon S. F. (1998) Measures of racial diversity and segregation in multigroup and hierarchical structured Populations. Annual meeting of the Eastern Sociological Society, Philadelphia

See Also

multigroup indices: PMulti, GiniMulti, HMulti, CMulti, RelDivers

Social diversity indices: HShannon, NShannon, ISimpson,

Examples

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

Description

Gorard's index is an alternative to ISDuncan's index, which measures the dissimilarity between the distribution of a group and the total population.

Usage

Gorard(x)

Arguments

Value

A numeric vector containing Gorard's segregation index values for each group

References

Gorard S. (2000) Education and Social Justice. Cardiff, University of Wales Press

See Also

One-group evenness indices: ISDuncan, Gini, Atkinson, HTheil, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

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

Description

This data set gives the households distribution by size in Grenoble urban area in 2011, including the area vectorial map at municipality level.

Usage

data(GreHSize)

Format

A Spatial object including 52 polygons corresponding to each municipality of Grenoble Urban Area (Insee definition) and following data attributes:

Details

• code: Municipality code

• name: Municipality name

• small: (1-2 persons household)

• medium: (3-4 persons household)

• big: (more then 5 persons household)

Source

Insee: Resultats du recensement de la population 2011, Insee

Description

Local diversity index, HLoc, is a local adaptation of Pielou's normalized diversity index NShannon.

Usage

HLoc(x)

Arguments

Value

A numeric matrix containing the local diversity index values for each spatial unit

References

Theil H. (1972) Statistical Decomposition Analysis. North-Holland, Amsterdam

See Also

Other local indices LQ LShannon, LSimpson

Examples

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

Description

The multigroup version of Theil's entropy index HTheil

Usage

HMulti(x)

Arguments

Value

The multigroup entropy segregation index value (numeric)

References

Theil H. (1972) Statistical decomposition analysis: with applications in the social and administrative. Amsterdam, North-Holland, 337 p.

See Also

multigroup indices: PMulti, GiniMulti, DMulti, CMulti, RelDivers

Social diversity indices: HShannon, NShannon, ISimpson,

Examples

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

Description

The Shannon-Wiener diversity index is based on the notion of entropy and measures population heterogeneity.

Usage

HShannon(x)

Arguments

Value

The Shannon-Wiener diversity index value (numeric)

References

Shannon C. E. (1948) A mathematical theory of communication. Bell System Technical Journal (27)

See Also

Social diversity indices: NShannon, ISimpson,

multigroup indices: PMulti, GiniMulti, DMulti, HMulti, CMulti, RelDivers

Examples

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

Description

The entropy index (also called information index) measures departure from evenness by assessing each spatial unit deviation from the entropy in the area.

Usage

HTheil (x)

Arguments

Value

A numeric vector containing Theils's segregation index values for each group

References

Theil H. (1972) Statistical decomposition analysis: with applications in the social and administrative. Amsterdam, North-Holland, 337 p.

See Also

One-group evenness indices: ISDuncan, Gini, Gorard, Atkinson, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

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

Description

Duncan's segregation index is one-group form of dissimilarity index DIDuncan and measures the unevenness of a group distribution compared to the rest of the population. It can be interpreted as the share of the group that would have to move to achieve an even distribution compared to the rest of the population.

Usage

ISDuncan (x)

Arguments

Value

A numeric vector containing Duncan's segregation index values for each group

References

Duncan O. D. and Duncan B. (1955) Residential Distribution and Occupational Stratification. American Journal of Sociology 60 (5), pp. 493-503

See Also

One-group evenness indices: Gini, Atkinson, Gorard, HTheil, 'ISWong, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

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

Description

Simpson's interaction index measures the probability that randomly selected individuals are not in the same group.

Usage

ISimpson(x)

Arguments

Value

The Simpson's interaction index value (numeric)

References

Simpson E. H. (1949) Measurement of diversity. Nature 163:688

See Also

Social diversity indices: HShannon, NShannon,

multigroup indices: PMulti, GiniMulti, DMulti, HMulti, CMulti, RelDivers

Examples

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

Description

Morrill's segregation index is a development of ISDuncan's index which takes into account the interactions between spatial units(contiguity). The function can be used in two ways: to provide a contiguity matrix or a external geographic information source (spatial object or shape file).

Usage

ISMorrill(x, c = NULL, queen = FALSE, 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing Morrill's segregation index values for each group

References

Morrill B. (1991) On the measure of geographic segregation. Geography research forum, 11, pp. 25-36.

See Also

One-group evenness indices: ISDuncan, Gini, Gorard, HTheil, Atkinson, 'ISWong, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

x <- segdata@data[ ,1:2]
contiguity <- contig(segdata)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

ISMorrill(x, c = contiguity) 

ISMorrill(x, spatobj = segdata)

ISMorrill(x, folder = foldername, shape = shapename)

Description

This function computes an adaptation of Morrill's segregation index which takes into account the interactions between spatial units defined by K-th ordered contiguity matrix. The index can be used in two ways: to provide a contiguity units defined by K order contiguity matrix. The function can be used in two matrix or a external geographic information source (spatial object or shape file).

Usage

ISMorrillK(x, ck = NULL, queen = FALSE, spatobj = NULL, folder = NULL, 
shape = NULL, K = 2, f = 'exp', beta = 1, prec = NULL)

Arguments

Value

A numeric vector containing Generalized Morrill's segregation index values for each group

References

Morrill B. (1991) On the measure of geographic segregation. Geography research forum, 11, pp. 25-36.

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

See Also

One-group evenness indices: ISDuncan, Gini, Gorard, HTheil, Atkinson, 'ISWong, ISMorrill

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

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

ISMorrillK(x, spatobj = segdata, queen = FALSE, K = 3)

ISMorrillK(x, folder = foldername, shape = shapename, K = 4, f = 'rec')

Description

Wong's segregation index is a development of ISDuncan's which takes into account the interactions between spatial units (common boundaries and perimeter/area ratio). The function can be used in two ways: to provide spatial data ( boundaries matrix, a perimeter vector and an area vector) or a external geographic information source (spatial object or shape file).

Usage

ISWong(x, b = NULL,  a = NULL, p = NULL, ptype = 'int', variant = 's', 
spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing Wong's segregation index values for each group

References

Wong D. W. S. (1998) Measuring multiethnic spatial segregation. Urban Geography, 19 (1), pp. 77-87.

See Also

One-group evenness indices: ISDuncan, Gini, Gorard, HTheil, 'Atkinson, ISMorrill, ISMorrillK

Between groups dissimilarity indices: DIDuncan, Gini2, DIMorrill, DIMorrillK, DIWong

Examples

x <- segdata@data[ ,1:2]
bound <- boundaries(segdata)
per <- perimeter(segdata)
ar <- area(segdata)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

ISWong(x, b = bound, p = per, a = ar) 

ISWong(x, spatobj = segdata, variant = 's', ptype = 'int')

ISWong(x, folder = foldername, shape = shapename, variant = 'w')

Description

Location quotients compare the relative part of a group in a particular spatial unit, to the relative part of that same group in the area.

Usage

LQ(x)

Arguments

Value

A matrix containing the location quotients for each group in each spatial unit

References

Isard W. (1960) Methods of regional analysis: an introduction to regional science. The MIT Press, Cambridge

See Also

Other local indices LShannon HLoc, LSimpson

Examples

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

Description

The Shannon-Wiener diversity index is based on the notion of entropy and measures population heterogeneity.

Usage

LShannon(x)

Arguments

Value

A vector containing the local Shannon-Wiener diversity index values for each spatial unit

References

Shannon C. E. (1948) A mathematical theory of communication. Bell System Technical Journal (27)

See Also

Other local indices: LQ, HLoc, LSimpson

Examples

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

Description

Local Simpson's interaction index measures the probability that randomly selected individuals are not in the same group in each spatial unit.

Usage

LSimpson (x)

Arguments

Value

A vector containing the local Simpson's interaction index values for each spatial unit

References

Simpson E. H. (1949) Measurement of diversity. Nature 163:688

See Also

Other local indices: LQ, HLoc, LShannon

Examples

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

Description

The Shannon-Wiener diversity index is based on the notion of entropy and measures population heterogeneity.

Usage

NShannon(x)

Arguments

Value

The Shannon-Wiener normalized diversity index value (numeric)

References

Shannon C. E. (1948) A mathematical theory of communication. Bell System Technical Journal (27)

See Also

Other multigroup eveness indices: HShannon, ISimpson, GiniMulti, DMulti, HMulti, CMulti

Other multigroup indices: PMulti, RelDivers

Examples

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

Description

A function to compute Reardon (2009) ordinal indices

Usage

ordinalseg(x)

Arguments

Value

A vector containing Reardon's multigroup ordinal segregation indices: Lambda1 (the ordinal generalization of the information theory index), Lambda2 (the ordinal generalization of the variation ratio index), Lambda3 (the ordinal square root index), and Lambda4 (the ordinal absolute difference index)

References

Reardon S. F. (2009) Measures of ordinal segregation. Research on Economic Inequality, 17, pp. 129-155.

See Also

rankorderseg

Examples

x <- GreHSize@data[ ,3:5]
ordinalseg(x) 

x1 <- matrix(nrow = 4, ncol = 3)
x1[1,] <- c(0, 0, 30)
x1[2,] <- c(0, 20, 10)
x1[3,] <- c(10, 20 ,0)
x1[4,] <- c(30, 0 ,0)

x2 <- matrix(nrow = 4, ncol = 3)
x2[1,] <- c(0, 30, 0)
x2[2,] <- c(0, 10, 20)
x2[3,] <- c(10, 0, 20)
x2[4,] <- c(30, 0, 0)

ordinalseg(x1)
ordinalseg(x2)

Description

The function is based on on sf package and can be used with a shape file or an R spatial object (class sf, sfc or sfg).

Usage

perimeter(spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A vector containing the perimeter of spatial units

See Also

Other spatial functions used for segregation indices computation: area, contig, distance, distcenter, boundaries

Examples

perimeter(segdata)  
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'
perimeter(folder = foldername, shape = shapename)

Description

The multigroup normalised isolation index is a multigroup version of the isolation index (xPx)

Usage

PMulti(x)

Arguments

Value

The multigroup normalised isolation index value (numeric)

References

James, F. J. (1986) A New Generalized 'Exposure-Based' Segregation Index. Sociological Methods and Research, 14, pp. 301-316

Reardon S. F. and G. Firebaugh (2002) Measures of multigroup Segregation. Sociological Methodology, 32(1), pp 33-67

See Also

multigroup indices: GiniMulti, DMulti, HMulti, CMulti, RelDivers

Social diversity indices: HShannon, NShannon, ISimpson,

Examples

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

Description

Mean proximity, Poo, computes the mean distance between the individuals in the area with no regard for group. The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file)

Usage

Poo(x, d = NULL, fdist = 'e', distin = 'm',  distout = 'm', diagval = '0', 
itype = 'multi', beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

The Poo index value (numeric)

References

White M. J. (1983) The Measurement of Spatial Segregation. American Journal of Sociology, 88, p. 1008-1019

White, M. J. (1986) Segregation and Diversity Measures in Population DistributionE. Population Index 52(2): 198-221.

See Also

Proximity measures: Pxx, Pxy, SP

Clustering Indices: ACL, RCL

Examples

x <- segdata@data[ ,1:2]
ar<-area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

Poo(x, spatobj = segdata)

Poo(x, folder = foldername, shape = shapename, fdist = 'l') 

Poo(x, spatobj = segdata, diagval ='a')

Poo(x, d = dist, fdist = 'e')

Description

Mean proximity, Pxx, computes the mean distance between the members of a group. The distance matrix can be expressed as a linear or as an inverse exponential function of the distance between spatial unit centroids.The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file).

Usage

Pxx(x, d = NULL, fdist = 'e', distin = 'm',  distout = 'm', diagval = '0', 
beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A numeric vector containing the Pxx index values for each group

References

White M. J. (1983) The Measurement of Spatial Segregation. American Journal of Sociology, 88, p. 1008-1019

See Also

Proximity measures: Pxy, Poo, SP

Clustering Indices: ACL, RCL

Examples

x <- segdata@data[ ,1:2]
ar<-area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

Pxx(x, spatobj = segdata)

Pxx(x, folder = foldername, shape = shapename, fdist = 'l') 

Pxx(x, spatobj = segdata, diagval ='a')

Pxx(x, d = dist, fdist = 'e')

Description

Mean proximity, Pxy, computes the mean distance between the members of different groups.The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file).

Usage

Pxy(x, d = NULL, fdist = 'e', distin = 'm',  distout = 'm', diagval = '0', 
beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the Pxy index values for each pair of groups

References

White M. J. (1983) The Measurement of Spatial Segregation. American Journal of Sociology, 88, p. 1008-1019

See Also

Proximity measures: Pxx, Poo, SP

Clustering Indices: ACL, RCL

Examples

x <- segdata@data[ ,1:2]
ar<-area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

Pxy(x, spatobj = segdata)

Pxy(x, folder = foldername, shape = shapename, fdist = 'l') 

Pxy(x, spatobj = segdata, diagval ='a')

Pxy(x, d = dist, fdist = 'e')

Description

A function computing Reardon (2011) rank-ordered segregation indices

Usage

rankorderseg(x, polorder = 4, pred = NULL)

Arguments

Value

A list containing the results for three rank-ordered indices: rank-order information theory index (Hr), rank-order variation ratio index (Rr) and rank-order square root index (Sr). For each index, a sublist is provided, containing: Index (the rank-ordered index value), Hp/Rp/Sp (a vector containing the ordinal information theory/variance ratio/square root segregation index values at thresholds), Coefficients (the coefficients extracted from the polynomial estimation model, including basic statistics), Predict (a list containing predicted values of the corresponding ordinal index (fit); standard error of predicted means (se.fit); degrees of freedom for residual (df); and residual standard deviations (residuale.scale). If pred is NULL, the function will return the statistics at thresholds)

References

Reardon S. F. (2011) Measures of Income Segregation . The Stanford Center on Poverty and Inequality

See Also

ordinalseg

Examples

x1 <- matrix(nrow = 4, ncol = 7)
x1[1,] <- c( 10,  10, 10, 20, 30, 40, 50)
x1[2,] <- c( 0, 20, 10, 10, 10, 20, 20)
x1[3,] <- c(10, 20,  10, 10, 10, 0, 0 )
x1[4,] <- c(30, 30,  20, 10, 10, 0, 0 )
x2 <- x1
x2[,c(3,4,6,7)] <- x1[,c(6,7,3,4)]

rankorderseg(x1)
rankorderseg(x2, pred = seq(0, 1, 0.1))

Description

The relative centralisation index measures the proportion of a group that should change its localization to achieve the same level of centralization as another group. The function can be used in two ways: to provide a vector containing the distances between spatial unit centroids or a external geographic information source (spatial object or shape file).

Usage

RCE(x, dc = NULL, center = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the relative centralisation index values for each pair of groups

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

See Also

RCEPoly, RCEPolyK,

ACEDuncan, ACEDuncanPoly,

ACEDuncanPolyK, ACE, ACEPoly

Examples

x <- segdata@data[ ,1:2]
distc<- distcenter(segdata, center = 28)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

RCE(x, dc=distc) 

RCE(x, spatobj = segdata, center = 28) 

RCE(x, folder = foldername, shape = shapename, center = 28)

Description

The polycentric version of the relative centralisation index. The function can be used in two ways: to provide a matrix containing the distances between spatial/organizational unit centroids or a external geographic information source (spatial object or shape file).

Usage

RCEPoly(x, dc = NULL, center = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the polycentric relative centralisation index values for each pair of groups

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

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

See Also

RCE, RCEPolyK,

ACEDuncan, ACEDuncanPoly,

ACEDuncanPolyK, ACE, ACEPoly

Examples

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

RCEPoly(x, spatobj = segdata, center = c(28, 83) )

RCEPoly(x, folder = foldername, shape = shapename, center = c(28, 83))

center <- c(28, 83)
polydist <- matrix(data = NA, nrow = nrow(x), ncol = length(center))
for (i in 1:ncol(polydist))
  polydist[,i] <- distcenter(spatobj = segdata, center = center[i])
RCEPoly(x, dc = polydist)

distmin <- vector(length = nrow(x))
for (i in 1:nrow(polydist)) distmin[i] <- min(polydist[i,])
RCE(x, dc = distmin)

Description

The constrained (local) version of relative centralization index. The function can be used in two ways: to provide a matrix containing the distances between spatial unit centroids or a external geographic information source (spatial object or shape file).

Usage

RCEPolyK(x, dc = NULL,  K = NULL, kdist = NULL, center = 1,
                spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

a matrix containing the constrainted polycentric relative centralisation index values for each pair of groups

References

Duncan O. D. and Duncan B. (1955) A Methodological Analysis of Segregation Indexes. American Sociological Review 41, pp. 210-217

Folch D.C and Rey S. J (2016) The centralization index: A measure of local spatial segregation. Papers in Regional Science 95 (3), pp. 555-576

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

See Also

RCE, RCEPoly,

ACEDuncan, ACEDuncanPoly,

ACEDuncanPolyK, ACE, ACEPoly

Examples

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

RCEPolyK(x, spatobj = segdata, center = c(28, 83))

RCEPolyK(x, folder = foldername, shape = shapename, center = c(28, 83), K = 3)

center <- c(28, 83)
polydist <- matrix(data = NA, nrow = nrow(x), ncol = length(center))
for (i in 1:ncol(polydist))
  polydist[,i] <- distcenter(spatobj = segdata, center = center[i])
RCEPolyK(x, dc = polydist, kdist = 2)

Description

The relative clustering index, RCL, compares the mean proximity of a group to the mean proximity of another group. The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file).

Usage

RCL(x, d = NULL, fdist = 'e', distin = 'm',  distout = 'm', diagval = '0', 
beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the relative clustering index values for each pair of groups

References

Massey D. S. and Denton N. A. (1988) The dimensions of residential segregation. Social Forces 67(2), pp. 281-315.

See Also

Proximity measures: Pxx, Pxy, Poo, SP

Clustering Indices: ACL

Examples

x <- segdata@data[ ,1:2]
ar<-area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

RCL(x, spatobj = segdata)

RCL(x, folder = foldername, shape = shapename, fdist = 'l') 

RCL(x, spatobj = segdata, diagval ='a')

RCL(x, d = dist, fdist = 'e')

Description

The relative concentration index, measures the share of space occupied by a group compared to another group. The function can be used in two ways: to provide an area vector or a external geographic information source (spatial object or shape file).

Usage

RCO(x, a = NULL, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

A matrix containing the relative concentration index values for each pair of groups

References

Massey D. S. and Denton N. A. (1988) The dimensions of residential segregation. Social Forces 67(2), pp. 281-315.

See Also

one-group concentration indices: Delta, ACO

Examples

x <- GreHSize@data[ ,3:5]
ar <- area(GreHSize)
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'GreHSize'

RCO(x, a = ar) 

RCO(x, spatobj = GreHSize)

RCO(x, folder = foldername, shape = shapename)

Description

The relative diversity index is a multigroup index based on Simpson's interaction index ISimpson

Usage

RelDivers(x)

Arguments

Value

The multigroup relative diversity index value (numeric)

References

Carlson S. M. (1992) Trends in race/sex occupational inequality: conceptual and measurement issues. Social Problems, 39, p. 269-290

See Also

multigroup indices: PMulti, GiniMulti, DMulti, HMulti, CMulti

Social diversity indices: HShannon, NShannon, ISimpson,

Examples

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

Description

Plot of Monte Carlo simulations results. The function can be used in two ways: buy providing a ResampleTest object, using ResampleTest or a simulated distribution vector, a value and a name of the index

Usage

ResamplePlot(ResampleTest, var = 1, coldist = 'red', colind = 'blue', 
legend = TRUE, legendpos = 'top', cex.legend = 1, bty = 'o')

Arguments

Value

A plot with resampling theoretical distribution

References

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

See Also

ResampleTest

Examples

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

xtest <- ResampleTest (x, fun ='ISMorrill', simtype = 'MonteCarlo', 
                       sampleunit = 'unit', spatobj = segdata)
                       
ResamplePlot(xtest, var = 1)

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,
  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",
  ...
)

Arguments

Value

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

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

See Also

ResamplePlot

Examples

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

Description

The theoretical examples ( Morrill 1991, Wong 1993) adapted from Hong and O'Sullivan (2015). The space is represented by a 10x10 checkboard, with different distributions of two social groups in the area.

Usage

data(segdata)

Format

A 10x10 grid Spatial object and following data attributes:

Details

• : spatial ID;

• : municipality name;

• : pattern A: minority distribution;

• : pattern A: majority distribution;

• : pattern B: minority distribution;

• : pattern B: majority distribution;

• : pattern C: minority distribution;

• : pattern C: majority distribution;

• : pattern D: minority distribution;

• : pattern D: majority distribution;

• : pattern E: minority distribution;

• : pattern E: majority distribution;

• : pattern F: minority distribution;

• : pattern F: majority distribution;

• : pattern G: minority distribution;

• : pattern G: majority distribution;

• : pattern H: minority distribution;

• : pattern H: majority distribution;

• : pattern I: minority distribution;

• : pattern I: majority distribution;

Description

The function cleans and prepares the data for segregation analysis

Usage

segdataclean (x, c = NULL, b = NULL, a = NULL, p = NULL, 
ck = NULL, d = NULL, dc = NULL, spatobj = NULL, folder = NULL, shape = NULL, 
warnings = TRUE)

Arguments

Value

The objects (data matrix, geographical vectors/matrices, spatial objects) cleaned from null rows or columns

See Also

Other local indices: LQ, HLoc, LShannon

Examples

x <- segdata@data[ ,1:2]
x[ ,3] <- rep (0 ,100)
x[1:3, ] <- rep (c(0, 0, 0), 3)
x1 <- x
spatobj <- segdata
cldata <- segdataclean(x1, segdata)
x1 <- cldata$x
spatobj <- cldata$spatobj

c <- contig (segdata)
c <- segdataclean(x, c = c)$c

Description

The spatial proximity index, SP, compares the clustering level (mean proximity) of a group compared to another group. The function can be used in two ways: to provide a distance matrix or a external geographic information source (spatial object or shape file).

Usage

SP(x, d = NULL, fdist = 'e', distin = 'm',  distout = 'm', diagval = '0', 
itype = 'multi', beta = 1, spatobj = NULL, folder = NULL, shape = NULL)

Arguments

Value

If itype = 'multi' the function returns the multigroup spatial proximity index value (numeric). If itype = 'between', the function returns a matrix containing the between group values of the index. If itype = 'one', the function's output is a numeric vector containing the index values for each group

References

White M. J. (1983) The Measurement of Spatial Segregation. American Journal of Sociology, 88, p. 1008-1019.

White, M. J. (1986) Segregation and Diversity Measures in Population DistributionE. Population Index 52(2): 198-221.

Apparicio, P., V. Petkevitch and M. Charron (2008): Segregation Analyzer: A C#.Net application for calculating residential segregation indices, Cybergeo: European Journal of Geography, 414, 1-27.

See Also

Proximity measures: Pxx, Pxy, Poo

Clustering Indices: ACL, RCL

Examples

x <- segdata@data[ ,1:2]
ar<-area(segdata)
dist <- distance(segdata)
diag(dist)<-sqrt(ar) * 0.6
foldername <- system.file('extdata', package = 'OasisR')
shapename <- 'segdata'

SP(x, spatobj = segdata)

SP(x, folder = foldername, shape = shapename, fdist = 'l', itype = 'between') 

SP(x, spatobj = segdata, diagval ='a', itype = 'one')

SP(x, d = dist, fdist = 'e')

Description

The isolation index, xPx, is an exposure index that measures the probability that two members of a group share the same spatial unit. This index can be calculated using the approximate or the exact method (see Bell, 1954).

Usage

xPx(x, exact = FALSE)

Arguments

Value

A numeric vector containing the isolation index values for each group

References

Bell W. (1954) A probability model for the measurement of ecological segregation. Social Forces 32(4), pp. 357-364

See Also

Isolation indices: Eta2, DPxx

Interaction indices: xPy, DPxy

Examples

x <- segdata@data[ ,7:8]
xPx(x) 
xPx(x, exact = TRUE)

Description

The interaction index, xPy, is an exposure between groups index which measures the probability that a member of a group shares the same spatial unit with a member of another group. The index can be calculated with the approximate or exact method (see Bell, 1954).

Usage

xPy(x, exact = FALSE)

Arguments

Value

A matrix containing the interaction index values for each pair of groups

References

Bell W. (1954) A probability model for the measurement of ecological segregation. Social Forces 32(4), pp. 357-364

See Also

Isolation indices: xPx, Eta2, DPxx

Distance decay interaction index: DPxy

Examples

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