contagion {SpatEntropy}

Li and Reynolds' relative contagion index.

Description

This function computes Li and Reynold's contagion index, following Li and Reynolds (1993), starting from a data matrix. References can be found at SpatEntropy.

Usage

contagion(
  data,
  win = spatstat.geom::owin(xrange = c(0, ncol(data)), yrange = c(0, nrow(data))),
  plotout = T
)

Arguments

data

A data matrix or vector, can be numeric, factor, character, ...

win

Optional, an object of class owin, the observation window for data plotting

plotout

Logical. Default to TRUE, produces an informative plot as part of the function output.

Details

This index is based on the transformed variable Z identifying couples of realizations of the variable of interest. A distance of interest is fixed: the contagion index is originally thought for areas sharing a border, as O'Neill's entropy. Then, all contiguous couples of realizations of the variable of interest are counted and their relative frequencies are used to compute the index, which is 1-NO where NO is the relative version of O'Neill's entropy, i.e. O'Neill's entropy divided by its maximum \log(I^2), I being the number of categories of the variable under study. The relative contagion index ranges from 0 (no contagion, maximum entropy) to 1 (maximum contagion). The function is able to work with grids containing missing data, specified as NA values. All NAs are ignored in the computation and only couples of non-NA observations are considered.

Value

a list of two elements:

• contagion Li and Reynold's relative contagion index

• probabilities a table with absolute frequencies and estimated probabilities (relative frequencies) for all couple categories

Moreover, a plot of the dataset is produced.

Examples

#numeric data, square grid
data=matrix(sample(1:5, 100, replace=TRUE), nrow=10)
contagion(data)
#plot data
plot(as.im(data, W=square(nrow(data))),
     col=grDevices::gray(seq(1,0,length.out=length(unique(c(data))))),
     main="", ribbon=TRUE)

#character data, rectangular grid
data=matrix(sample(c("a","b","c"), 300, replace=TRUE), nrow=30)
contagion(data)
#plot data
plot(as.im(data, W=owin(xrange=c(0,ncol(data)), yrange=c(0,nrow(data)))),
     col=terrain.colors(length(unique(c(data)))),
     main="", ribbon=TRUE)