crossCorrelation {spatialEco}

Spatial cross correlation

Description

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 = 999,
  dist.function = c("inv.power", "neg.exponent", "none"),
  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 w = 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", "none") If w = NULL, the default method for deriving spatial weights matrix, options are: inverse power or negative exponent, none is for use with a provided matrix

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

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

Details

In specifying a distance matrix, you can pass a coordinates matrix or spatial object to coords or alternately, pass a distance or spatial weights matrix to the w argument. If the w matrix represents spatial weights dist.function="none" should be specified. Otherwise, w is assumed to represent distance and will be converted to spatial weights using inv.power or neg.exponent. The w distances can represent an alternate distance hypothesis (eg., road, stream, network distance) Here are example argument usages for defining a matrix.

• IF coords=x, w=NULL, dist.function= c("inv.power", "neg.exponent") A distance matrix is derived using the data passed to coords then spatial weights derived using one of the dist.function options

• IF cords=NULL, w=x, dist.function= c("inv.power", "neg.exponent") It is expected that the distance matrix specified with w represent some form of distance then the spatial weights are derived using one of the dist.function options

• IF cords=NULL, w=x, dist.function="none" It is assumed that the matrix passed to w already represents the spatial weights

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.G. (2012) On the four types of weight functions for spatial contiguity matrix. Letters in Spatial and Resource Sciences 5(2):65-72

Chen, Y.G. (2013) New approaches for calculating Moran’s index of spatial autocorrelation. PLoS ONE 8(7):e68336

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

Examples

# replicate Chen (2015)
 data(chen)
( r <- crossCorrelation(x=chen[["X"]], y=chen[["Y"]], w = chen[["M"]],  
                        clust=TRUE, type = "LSCI", k=0, 
                        dist.function = "inv.power") ) 


library(sf)
library(spdep)
 
  if (require(sp, quietly = TRUE)) {
   data(meuse, package = "sp")
   meuse <- st_as_sf(meuse, coords = c("x", "y"), crs = 28992, agr = "constant")
  } 

#### Using a default spatial weights matrix method (inverse power function)
( I <- crossCorrelation(meuse$zinc, meuse$copper, 
             coords = st_coordinates(meuse)[,1:2], k=99) )
  meuse$lisa <- I$SCI[,"lsci.xy"]
    plot(meuse["lisa"], pch=20)

#### Providing a distance matrix
if (require(units, quietly = TRUE)) {
  Wij <- units::drop_units(st_distance(meuse))
 ( I <- crossCorrelation(meuse$zinc, meuse$copper, w = Wij, k=99) )

#### Providing an inverse power function weights matrix
  Wij <- 1 / Wij
    diag(Wij) <- 0 
      Wij <- Wij / sum(Wij) 
        diag(Wij) <- 0
 ( I <- crossCorrelation(meuse$zinc, meuse$copper, w = Wij, 
                         dist.function = "none", k=99) )
}