Description Usage Arguments Details Value Warnings Author(s) References See Also Examples

For a multitype point pattern,
estimate the inhomogeneous version of the cross-type *L* function.

1 | ```
Lcross.inhom(X, i, j, ...)
``` |

`X` |
The observed point pattern,
from which an estimate of the inhomogeneous cross type |

`i` |
The type (mark value)
of the points in |

`j` |
The type (mark value)
of the points in |

`...` |
Other arguments passed to |

This is a generalisation of the function `Lcross`

to include an adjustment for spatially inhomogeneous intensity,
in a manner similar to the function `Linhom`

.

All the arguments are passed to `Kcross.inhom`

, which
estimates the inhomogeneous multitype K function
*Kij(r)* for the point pattern.
The resulting values are then
transformed by taking *L(r) = sqrt(K(r)/pi)*.

An object of class `"fv"`

(see `fv.object`

).

Essentially a data frame containing numeric columns

`r` |
the values of the argument |

`theo` |
the theoretical value of |

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 *Lij(r)*
obtained by the edge corrections named.

The arguments `i`

and `j`

are always interpreted as
levels of the factor `X$marks`

. They are converted to character
strings if they are not already character strings.
The value `i=1`

does **not**
refer to the first level of the factor.

and \rolf

Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
# Lansing Woods data
woods <- lansing
ma <- split(woods)$maple
wh <- split(woods)$whiteoak
# method (1): estimate intensities by nonparametric smoothing
lambdaM <- density.ppp(ma, sigma=0.15, at="points")
lambdaW <- density.ppp(wh, sigma=0.15, at="points")
L <- Lcross.inhom(woods, "whiteoak", "maple", lambdaW, lambdaM)
# method (2): fit parametric intensity model
fit <- ppm(woods ~marks * polynom(x,y,2))
# evaluate fitted intensities at data points
# (these are the intensities of the sub-processes of each type)
inten <- fitted(fit, dataonly=TRUE)
# split according to types of points
lambda <- split(inten, marks(woods))
L <- Lcross.inhom(woods, "whiteoak", "maple",
lambda$whiteoak, lambda$maple)
# synthetic example: type A points have intensity 50,
# type B points have intensity 100 * x
lamB <- as.im(function(x,y){50 + 100 * x}, owin())
X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
L <- Lcross.inhom(X, "A", "B",
lambdaI=as.im(50, Window(X)), lambdaJ=lamB)
``` |

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