SpatEntropy (version 0.1.0)

karlstrom: Karlstrom and Ceccato's entropy.

Description

This function computes Karlstrom and Ceccato's spatial entropy for a chosen neighbourhood distance, following Karlstrom and Ceccato (2002), see also Altieri et al (2017) (references are under the topic SpatEntropy).

Usage

karlstrom(data, data.assign, category, G.coords, neigh.dist)

Arguments

data

A data matrix or vector, can be numeric, factor, character, ... If the dataset is a point pattern, data is the mark vector.

data.assign

A three column matrix, containing the data coordinates (centroids when pixels) and the id of the corresponding sub-area. Provided by user or returned by areapart().

category

A character string, the exact name of the category for which Karlstrom and Ceccato's spatial entropy is computed, as in data.

G.coords

A point pattern (an object of class ppp see package spatstat), or a two column matrix with the area centroids' coordinates. Provided by user or returned by areapart().

neigh.dist

A scalar, the chosen neighbourhood Euclidean distance.

Value

Karlstrom and Ceccato's spatial entropy value as well as a table with information about each sub-area:

• area.id the sub-area id

• abs.freq the number of points/pixels presenting the category of interest for each sub-area

• rel.freq the proportion of points/pixels presenting the category of interest in each sub-area, with regard to the total number of points/pixels with the category of interest

• p.tilde the probability of occurrence over area \(g\) weighted with its neighbours.

Details

Karlstrom and Ceccato's spatial entropy measures the heterogeneity in the spatial distribution of a phenomenon of interest, with regard to an area partition and accounting for the neighbourhood. It is similar to Batty's entropy (see batty()) discarding the sub-area size, with the difference that the probability of occurrence of the phenomenon over area \(g\) is actually a weighted sum of the neighbouring probabilities. When data are categorical, the phenomenon of interest corresponds to one category, which must be specified. If data are an unmarked point pattern, a fake mark vector must be created with the same category for all points.

Examples

# NOT RUN {
#LATTICE DATA
data.lat=matrix(sample(c("a","b","c"), 100, replace=TRUE), nrow=10)
ccc=coords_pix(area=square(10), nrow=10, ncol=10)
partition=areapart(square(10), G=5, data.coords=ccc)
karlstrom(data.lat, partition$data.assign, category="a",
G.coords=partition$G.coords, neigh.dist=2)
plot_areapart(partition$data.assign, square(10), is.pointdata=FALSE,
add.data=TRUE, data.bin=TRUE, category="a",
data=data.lat, G.coords=partition$G.coords, main="")

#POINT DATA
data.pp=runifpoint(100, win=square(10))
marks(data.pp)=sample(c("a","b","c"), 100, replace=TRUE)
ccc=coords(data.pp)
partition=areapart(square(10), G=4, data.coords=ccc)
karlstrom(marks(data.pp), partition$data.assign,
category="b", G.coords=partition$G.coords, neigh.dist=4)
plot_areapart(partition$data.assign, square(10), is.pointdata=TRUE,
add.data=TRUE, data.bin=TRUE, category="b",
data=data.pp, G.coords=partition$G.coords, main="")

# }