spatstat (version 1.23-1)

Lcross: Multitype L-function (cross-type)

Description

Calculates an estimate of the cross-type L-function for a multitype point pattern.

Usage

Lcross(X, i, j, ...)

Arguments

X

The observed point pattern, from which an estimate of the cross-type $L$ function $L_{ij}(r)$ will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.

i

Number or character string identifying the type (mark value) of the points in X from which distances are measured.

j

Number or character string identifying the type (mark value) of the points in X to which distances are measured.

...

Arguments passed to Kcross.

Value

• An object of class "fv", see fv.object, which can be plotted directly using plot.fv.

  Essentially a data frame containing columns

• r
  the vector of values of the argument $r$ at which the function $L_{ij}$ has been estimated
• theo
  the theoretical value $L_{ij}(r) = r$ for a stationary Poisson process
• together with columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function $L_{ij}$ obtained by the edge corrections named.

Details

The cross-type L-function is a transformation of the cross-type K-function, $$L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}$$ where $K_{ij}(r)$ is the cross-type K-function from type i to type j. See Kcross for information about the cross-type K-function.

The command Lcross first calls Kcross to compute the estimate of the cross-type K-function, and then applies the square root transformation.

For a marked point pattern in which the points of type i are independent of the points of type j, the theoretical value of the L-function is $L_{ij}(r) = r$. The square root also has the effect of stabilising the variance of the estimator, so that $L_{ij}$ is more appropriate for use in simulation envelopes and hypothesis tests.

See Also

Kcross, Ldot, Lest

Examples

data(amacrine)
 L <- Lcross(amacrine, "off", "on")
 plot(L)