spatialEco (version 1.3-0)

crossCorrelation: 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 = 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 (k=1000, default)

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

Examples

# NOT RUN {
  library(sp)
  library(spdep)
   
  data(meuse)
    coordinates(meuse) <- ~x+y  
 
  #### Providing a neighbor contiguity spatial weights matrix
  all.linked <- max(unlist(nbdists(knn2nb(knearneigh(coordinates(meuse))), 
                    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")	  

  #### 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 {
# }