# linearKcross

##### Multitype K Function (Cross-type) for Linear Point Pattern

For a multitype point pattern on a linear network, estimate the multitype \(K\) function which counts the expected number of points of type \(j\) within a given distance of a point of type \(i\).

- Keywords
- spatial, nonparametric

##### Usage

`linearKcross(X, i, j, r=NULL, …, correction="Ang")`

##### Arguments

- X
The observed point pattern, from which an estimate of the cross type \(K\) function \(K_{ij}(r)\) will be computed. An object of class

`"lpp"`

which must be a multitype point pattern (a marked point pattern whose marks are a factor).- i
Number or character string identifying the type (mark value) of the points in

`X`

from which distances are measured. Defaults to the first level of`marks(X)`

.- j
Number or character string identifying the type (mark value) of the points in

`X`

to which distances are measured. Defaults to the second level of`marks(X)`

.- r
numeric vector. The values of the argument \(r\) at which the \(K\)-function \(K_{ij}(r)\) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on \(r\).

- correction
Geometry correction. Either

`"none"`

or`"Ang"`

. See Details.- …
Ignored.

##### Details

This is a counterpart of the function `Kcross`

for a point pattern on a linear network (object of class `"lpp"`

).

The arguments `i`

and `j`

will be interpreted as
levels of the factor `marks(X)`

.
If `i`

and `j`

are missing, they default to the first
and second level of the marks factor, respectively.

The argument `r`

is the vector of values for the
distance \(r\) at which \(K_{ij}(r)\) should be evaluated.
The values of \(r\) must be increasing nonnegative numbers
and the maximum \(r\) value must not exceed the radius of the
largest disc contained in the window.

##### Value

An object of class `"fv"`

(see `fv.object`

).

##### Warnings

The arguments `i`

and `j`

are interpreted as
levels of the factor `marks(X)`

. Beware of the usual
trap with factors: numerical values are not
interpreted in the same way as character values.

##### References

Baddeley, A, Jammalamadaka, A. and Nair, G. (to appear)
Multitype point process analysis of spines on the
dendrite network of a neuron.
*Applied Statistics* (Journal of the Royal Statistical
Society, Series C), In press.

##### See Also

##### Examples

```
# NOT RUN {
data(chicago)
K <- linearKcross(chicago, "assault", "robbery")
# }
```

*Documentation reproduced from package spatstat, version 1.60-1, License: GPL (>= 2)*