Kmulti.ls: Lotwick's and Silverman's combined estimator of the marked...

In ecespa: Functions for Spatial Point Pattern Analysis

Lotwick's and Silverman's combined estimator of the marked K-function

Description

For a multitype point pattern, calculates the combined estimator of the bivariate Kij(r) and Kji(r) functions.

Usage

Kmulti.ls(X, I, J, r = NULL, corre = "isotropic")

Arguments

X	Multitype marked point pattern. An object with the ppp format of spatstat.
I	Subset index specifying the points of the first pattern.
J	Subset index specifying the points of the second pattern.
r	Numeric vector. The values of the argument r at which the multitype K function K^*ij(r) should be evaluated.
corre	A character item selecting any of the options "border", "bord.modif", "isotropic", "Ripley" or "translate", as described in Kest. It specifies the edge correction(s) to be applied.

Details

As a consequence of edge effects, the estimators Kij(r) and Kji(r) of the same bivariate pattern could differ. K^*ij(r) is the combined estimator defined by Lotwick and Silverman (1982) as

nj*Kij(r)+ ni*Kji(r) / (ni + nj) ,

ni and nj being respectively the number of points in I and J.

Value

An object of class "fv" (see fv.object). Essentially a data frame containing numeric columns

r	The values of the argument r at which the function K^*ij(r) has been estimated

.

theo	The theoretical value of K*ij(r) for a marked Poisson process, namely pi * r^2

.

together with a column or columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function K^*ij(r) obtained by the edge corrections named.

Note

Kmulti.ls is a wrapper for a convenient use of the Kmulti function of spatstat. Please refer to its help page for additional documentation.

Author(s)

Marcelino de la Cruz

References

Lotwick,H.W. & Silverman, B. W. 1982. Methods for analysing spatial processes of several types of points. Journal of the Royal Statistical Society B, 44: 406-413. doi: 10.1111/j.2517-6161.1982.tb01221.x.

Examples

data(amacrine)

plot(Kmulti.ls(amacrine, I=amacrine$marks=="on", J=amacrine$marks=="off", 
	 corre="isotropic"), sqrt(./pi)-r~r, main="")

# compare with Kmulti

plot(Kmulti(amacrine, I=amacrine$marks=="on", J=amacrine$marks=="off"),
         sqrt(iso/pi)-r~r, add=TRUE, col=3)

plot(Kmulti(amacrine, J=amacrine$marks=="on", I=amacrine$marks=="off"),
      sqrt(iso/pi)-r~r, add=TRUE, col=4)

ecespa documentation built on Jan. 6, 2023, 1:21 a.m.