local.sp.runs.test: A function to calculate the local spatial runs tests.

In spqdep: Testing for Spatial Independence of Qualitative Data in Cross Section

A function to calculate the local spatial runs tests.

Description

This function calculates the local spatial runs tests for all localizations.

Usage

local.sp.runs.test(formula = NULL, data = NULL, fx = NULL,
distr = "asymptotic", listw = listw, alternative = "two.sided" , nsim = NULL,
control = list())

Arguments

formula	An (optional) formula with the factor included in data
data	An (optional) data frame or a sf object containing the variable to testing for.
fx	An (optional) factor of observations with the same length as the neighbors list in listw
distr	a character string specifying the distribution "asymptotic" (default) or "bootstrap"
listw	A neighbourhood list (an object type knn or nb) or a W matrix that indicates the order of the elements in each $m_i-environment$ (for example of inverse distance). To calculate the number of runs in each $m_i-environment$, an order must be established, for example from the nearest neighbour to the furthest one.
alternative	a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
nsim	Default value is NULL to obtain the asymptotic version of the local test. For the bootstrap version nsim is the number of permutations to obtain the pseudo-value.
control	Optional argument. See Control Argument section.

Details

The object listw can be the class:

• knn: Objects of the class knn that consider the neighbours in order of proximity.

• nb: If the neighbours are obtained from an sf object, the code internally will call the function nb2nb_order it will order them in order of proximity of the centroids.

• matrix: If a object of matrix class based in the inverse of the distance in introduced as argument, the function nb2nb_order will also be called internally to transform the object the class matrix to a matrix of the class nb with ordered neighbours.

Value

The output is an object of the class localsrq

local.SRQ A matrix with

runs.i	number of runs in the localization 'i'.
E.i	expectation of local runs statistic in the localization 'i'.
Sd.i	standard deviate of local runs statistic in the localization 'i'.
z.value	standard value of local runs statistic (only for asymptotic version).
p.value	p-value of local local runs statistic (only for asymptotic version).
zseudo.value	standard value of local runs statistic (only for boots version).
pseudo.value	p-value of local runs statistic (only for boots version).

MeanNeig Mean of run.i
MaxNeig Maximum of run.i
listw the object listw
alternative a character string describing the alternative hypothesis

Control arguments

seedinit	Numerical value for the seed in boot version. Default value seedinit = 123

Author(s)

Fernando López	[e-mail]
Román Mínguez	[e-mail]
Antonio Páez	[e-mail]
Manuel Ruiz	[e-mail]

@references

• Ruiz, M., López, F., and Páez, A. (2021). A test for global and local homogeneity of categorical data based on spatial runs. Working paper.

See Also

sp.runs.test, dgp.spq

Examples

# Case 1: Local spatial runs test based on knn
library(lwgeom)
N <- 100
cx <- runif(N)
cy <- runif(N)
x <- cbind(cx,cy)
listw <- spdep::knearneigh(cbind(cx,cy), k = 10)
p <- c(1/6,3/6,2/6)
rho <- 0.5
fx <- dgp.spq(p = p, listw = listw, rho = rho)

# Asymtotic version
lsrq <- local.sp.runs.test(fx = fx, listw = listw, alternative = "less")
print(lsrq)
plot(lsrq, sig = 0.05)
# Asymtotic version
lsrq <- local.sp.runs.test(fx = fx, listw = listw, alternative = "two.sided",
                           distr ="bootstrap", nsim = 399)
print(lsrq)
plot(lsrq, sig = 0.1)

# Case 2:Fastfood example. sf (points)
library(lwgeom)
data("FastFood.sf")
sf::sf_use_s2(FALSE)
x <- sf::st_coordinates(sf::st_centroid(FastFood.sf))
listw <- spdep::knearneigh(x, k = 10)
formula <- ~ Type
lsrq <- local.sp.runs.test(formula = formula, data = FastFood.sf, listw = listw)
print(lsrq)
plot(lsrq, sf = FastFood.sf, sig = 0.05)


# Case 3: With a sf object (poligons)
library(lwgeom)
fname <- system.file("shape/nc.shp", package="sf")
nc <- sf::st_read(fname)
listw <- spdep::poly2nb(as(nc,"Spatial"), queen = FALSE)
p <- c(1/6,3/6,2/6)
rho = 0.5
nc$fx <- dgp.spq(p = p, listw = listw, rho = rho)
plot(nc["fx"])
formula <- ~ fx
lsrq <- local.sp.runs.test(formula = formula, data = nc, listw = listw)
print(lsrq)
plot(lsrq, sf = nc)
# Version boot
lsrq <- local.sp.runs.test(formula = formula, data = nc, listw = listw,
                           distr ="bootstrap", nsim = 399)
print(lsrq)
plot(lsrq, sf = nc)

# Case 4: With isolated areas
library(lwgeom)
data(provinces_spain)
listw <- spdep::poly2nb(as(provinces_spain,"Spatial"), queen = FALSE)
provinces_spain$Male2Female <- factor(provinces_spain$Male2Female > 100)
levels(provinces_spain$Male2Female) = c("men","woman")
plot(provinces_spain["Male2Female"])
formula <- ~ Male2Female
lsrq <- local.sp.runs.test(formula = formula, data = provinces_spain, listw = listw)
print(lsrq)
plot(lsrq, sf = provinces_spain, sig = 0.1)

# Boots Version
lsrq <- local.sp.runs.test(formula = formula, data = provinces_spain, listw = listw,
                           distr ="bootstrap", nsim = 199)
print(lsrq)
plot(lsrq, sf = provinces_spain, sig = 0.10)

# Case 5: SRQ test based on a distance matrix (inverse distance)

library(lwgeom)
N <- 100
cx <- runif(N)
cy <- runif(N)
coor <- as.data.frame(cbind(cx,cy))
coor <- sf::st_as_sf(coor,coords = c("cx","cy"))
n = dim(coor)[1]
dis <- 1/matrix(as.numeric(sf::st_distance(coor,coor)), ncol = n, nrow = n)
diag(dis) <- 0
dis <- (dis < quantile(dis,.10))*dis
p <- c(1/6,3/6,2/6)
rho <- 0.5
fx <- dgp.spq(p = p, listw = dis, rho = rho)
lsrq <- local.sp.runs.test(fx = fx, listw = dis)
print(lsrq)
plot(lsrq, coor = cbind(cx,cy), sig = 0.05)
lsrq <- local.sp.runs.test(fx = fx, listw = dis, data = )
print(lsrq)
plot(lsrq, sf = coor)
# Version boots
lsrq <- local.sp.runs.test(fx = fx, listw = dis, data = coor,
                           distr ="bootstrap", nsim = 299)
print(lsrq)
plot(lsrq, sf = coor)

# SRQ test based on inverse distance
library(lwgeom)
data("FastFood.sf")
sf::sf_use_s2(FALSE)
n = dim(FastFood.sf)[1]
dis <- 1000000/matrix(as.numeric(
          sf::st_distance(FastFood.sf, FastFood.sf)),
          ncol = n, nrow = n)
diag(dis) <- 0
dis <- (dis < quantile(dis,.01))*dis
formula <- ~ Type
lsrq <- local.sp.runs.test(formula = formula, data = FastFood.sf, listw = dis)
print(lsrq)
plot(lsrq, sf = FastFood.sf)

spqdep documentation built on March 28, 2022, 5:06 p.m.