# crossCorrelation

0th

Percentile

##### Spatial cross correlation

Calculates univariate or bivariate spatial cross-correlation using local Moran's-I (LISA), following Chen (2015)

##### Usage
crossCorrelation(
x,
y = NULL,
coords = NULL,
w = NULL,
type = c("LSCI", "GSCI"),
k = 1000,
dist.function = "inv.power",
scale.xy = TRUE,
scale.partial = FALSE,
scale.matrix = FALSE,
alpha = 0.05,
clust = TRUE,
return.sims = FALSE
)
##### Arguments
x

Vector of x response variables

y

Vector of y response variables, if not specified the univariate statistic is returned

coords

A matrix of coordinates corresponding to [x,y], only used if k = NULL. Can also be an sp object with relevant x,y coordinate slot (ie., points or polygons)

w

Spatial neighbors/weights in matrix format. Dimensions must match [n(x),n(y)] and be symmetrical. If w is not defined then a default method is used.

type

c("LSCI","GSCI") Return Local Spatial Cross-correlation Index (LSCI) or Global Spatial cross-correlation Index (GSCI)

k

Number of simulations for calculating permutation distribution under the null hypothesis of no spatial autocorrelation

dist.function

("inv.power", "neg.exponent") If w = NULL, the default method for deriving spatial weights matrix, options are: inverse power or negative exponent

scale.xy

(TRUE/FALSE) scale the x,y vectors, if FALSE it is assumed that they are already scaled following Chen (2015)

scale.partial

(FALSE/TRUE) rescale partial spatial autocorrelation statistics [-1 - 1]

scale.matrix

(FALSE/TRUE) If a neighbor/distance matrix is passed, should it be scaled using [w/sum(w)]

alpha

= 0.05 confidence interval (default is 95 pct)

clust

(FALSE/TRUE) Return approximated lisa clusters

return.sims

(FALSE/TRUE) Return randomizations vector n = k

##### Value

When not simulated k=0, a list containing:

• I Global autocorrelation statistic

• SCI A data.frame with two columns representing the xy and yx autocorrelation

• nsim value of NULL to represent p values were derived from observed data (k=0)

• p Probability based observations above/below confidence interval

• t.test Probability based on t-test

• clusters If "clust" argument TRUE, vector representing LISA clusters

when simulated (k>0), a list containing:

• I Global autocorrelation statistic

• SCI A data.frame with two columns representing the xy and yx autocorrelation

• nsim value representing number of simulations

• global.p p-value of global autocorrelation statistic

• local.p Probability based simulated data using successful rejection of t-test

• range.p Probability based on range of probabilities resulting from paired t-test

• clusters If "clust" argument TRUE, vector representing lisa clusters

##### References

Chen., Y. (2015) A New Methodology of Spatial Cross-Correlation Analysis. PLoS One 10(5):e0126158. doi:10.1371/journal.pone.0126158

##### Aliases
• crossCorrelation
##### Examples
# NOT RUN {
library(sp)
library(spdep)

data(meuse)
coordinates(meuse) <- ~x+y

#### Providing a neighbor contiguity spatial weights matrix
coordinates(meuse))))
nb <- nb2listw(dnearneigh(meuse, 0, all.linked), style = "B", zero.policy = TRUE)
Wij <- as.matrix( as(nb, "symmetricMatrix") )
( I <- crossCorrelation(meuse$zinc, meuse$copper, w = Wij,
clust=TRUE, k=99) )
meuse$lisa <- I$SCI[,"lsci.xy"]
meuse$lisa.clust <- as.factor(I$cluster)
spplot(meuse, "lisa")
spplot(meuse, "lisa.clust")

#### Using a default spatial weights matrix method (inverse power function)
( I <- crossCorrelation(meuse$zinc, meuse$copper, coords = coordinates(meuse),
clust = TRUE, k=99) )
meuse$lisa <- I$SCI[,"lsci.xy"]
meuse$lisa.clust <- as.factor(I$cluster)
spplot(meuse, "lisa")
spplot(meuse, "lisa.clust")

# }
# NOT RUN {
#### Simulate spatially autocorrelated random normal variables
####   using eigen-decomposition, requires ncf package
library(sp)
library(ncf)
x=expand.grid(1:20, 1:20)[,1]
y=expand.grid(1:20, 1:20)[,2]
sdat <- data.frame(x =x,y=y,
z1=ncf::rmvn.spa(x=x, y=y, p=2, method="exp"),
z2=ncf::rmvn.spa(x=x, y=y, p=2, method="exp"))
coordinates(sdat) <- ~x+y
( I <- crossCorrelation(sdat$z1, sdat$z2, coords=coordinates(sdat),
k=99, clust = TRUE) )
sdat$lisa <- I$SCI[,"lsci.xy"]
sdat$lisa.clust <- as.factor(I$cluster)
spplot(sdat, "lisa")
spplot(sdat, "lisa.clust")

#### 1st order polygon contingency example
####   requires UScensus2000tract package
library(sp)
library(spdep)
library(UScensus2000tract)

data(oregon.tract)
nb <- spdep::nb2listw(poly2nb(oregon.tract), style = "B", zero.policy = TRUE)
Wij <- as.matrix( as(nb, "symmetricMatrix") )

X = oregon.tract$white Y = oregon.tract$black

# Simulated bivariate lisa
I <- crossCorrelation(X, Y, w=Wij, k=99)
oregon.tract$lisa <-I$SCI[,"lsci.xy"]
oregon.tract$lisa.clust <- as.factor(I$cluster)
spplot(oregon.tract, "lisa")
spplot(oregon.tract, "lisa.clust")
# }
# NOT RUN {
# }

Documentation reproduced from package spatialEco, version 1.3-2, License: GPL-3

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