# linearKcross

0th

Percentile

##### 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 f
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 conditio
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.

linearKdot, linearK.
data(chicago)
K <- linearKcross(chicago, "assault", "robbery")