kpqfun: Multiscale second-order neigbourhood analysis of a multivariate spatial point pattern

Description

(Formerly kijfun) Computes a set of K- and K12-functions for all possible pairs of marks $(p,q)$ in a multivariate spatial point pattern defined in a simple (rectangular or circular) or complex sampling window (see Details).

Usage

kpqfun(p, upto, by)

Arguments

a "spp" object defining a multivariate spatial point pattern in a given sampling window (see spp).

upto

maximum radius of the sample circles (see Details).

interval length between successive sample circles radii (see Details).

Value

A list of class "fads" with essentially the following components:
ra vector of regularly spaced distances (seq(by,upto,by)).
labpqa vector containing the $(p,q)$ paired levels of p$marks.
gpqa data frame containing values of the pair density functions $g(r)$ and $g12(r)$.
npqa data frame containing values of the local neighbour density functions $n(r)$ and $n12(r)$.
kpqa data frame containing values of the $K(r)$ and $K12(r)$ functions.
lpqa data frame containing values of the modified $L(r)$ and $L12(r)$ functions.
Each component except r is a data frame with the following variables:
obsa vector of estimated values for the observed point pattern.
theoa vector of theoretical values expected under the null hypotheses of spatial randomness (see kfun) and population independence (see k12fun).

encoding

latin1

Details

Function kpqfun is simply a wrapper to kfun and k12fun, which computes either K(r) for points of mark $p$ when $p=q$ or K12(r) between the marks $p$ and $q$ otherwise.

Examples

Run this code

data(BPoirier)
  BP <- BPoirier
  # multivariate spatial point pattern in a rectangle sampling window 
  swrm <- spp(BP$trees, win=BP$rect, marks=BP$species)
  kpqswrm <- kpqfun(swrm, 25, 1)
  plot(kpqswrm)
  
 # multivariate spatial point pattern in a circle with radius 50 centred on (55,45)
  swcm <- spp(BP$trees, win=c(55,45,45), marks=BP$species)
  kpqswcm <- kpqfun(swcm, 25, 1)
  plot(kpqswcm)
  
  # multivariate spatial point pattern in a complex sampling window
  swrtm <- spp(BP$trees, win=BP$rect, tri=BP$tri2, marks=BP$species)
  kpqswrtm <- kpqfun(swrtm, 25, 1)
  plot(kpqswrtm)

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