ecespa (version 1.1-1)

Kmulti.ls: 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.

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.

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 $J$.

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.

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)