# Ldot.inhom

##### Inhomogeneous Multitype L Dot Function

For a multitype point pattern, estimate the inhomogeneous version of the dot \(L\) function.

- Keywords
- spatial, nonparametric

##### Usage

`Ldot.inhom(X, i, …)`

##### Arguments

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

- i
The type (mark value) of the points in

`X`

from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of`marks(X)`

.- …
Other arguments passed to

`Kdot.inhom`

.

##### Details

This a generalisation of the function `Ldot`

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

.

All the arguments are passed to `Kdot.inhom`

, which
estimates the inhomogeneous multitype K function
\(K_{i\bullet}(r)\) for the point pattern.
The resulting values are then
transformed by taking \(L(r) = \sqrt{K(r)/\pi}\).

##### Value

An object of class `"fv"`

(see `fv.object`

).

Essentially a data frame containing numeric columns

the values of the argument \(r\) at which the function \(L_{i\bullet}(r)\) has been estimated

the theoretical value of \(L_{i\bullet}(r)\) for a marked Poisson process, identical to \(r\).

##### Warnings

The argument `i`

is interpreted as
a level of the factor `X$marks`

. It is converted to a character
string if it is not already a character string.
The value `i=1`

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

##### References

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

##### See Also

##### Examples

```
# NOT RUN {
# Lansing Woods data
lan <- lansing
lan <- lan[seq(1,npoints(lan), by=10)]
ma <- split(lan)$maple
lg <- unmark(lan)
# Estimate intensities by nonparametric smoothing
lambdaM <- density.ppp(ma, sigma=0.15, at="points")
lambdadot <- density.ppp(lg, sigma=0.15, at="points")
L <- Ldot.inhom(lan, "maple", lambdaI=lambdaM,
lambdadot=lambdadot)
# synthetic example: type A points have intensity 50,
# type B points have intensity 50 + 100 * x
lamB <- as.im(function(x,y){50 + 100 * x}, owin())
lamdot <- as.im(function(x,y) { 100 + 100 * x}, owin())
X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
L <- Ldot.inhom(X, "B", lambdaI=lamB, lambdadot=lamdot)
# }
```

*Documentation reproduced from package spatstat, version 1.49-0, License: GPL (>= 2)*