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.
linearKcross(X, i, j, r=NULL, ..., correction="Ang")
| X | The observed point pattern, 
from which an estimate of the cross type K function
Kij(r) will be computed.
An object of class  | 
| i | Number or character string identifying the type (mark value)
of the points in  | 
| j | Number or character string identifying the type (mark value)
of the points in  | 
| r | numeric vector. The values of the argument r at which the K-function Kij(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  | 
| ... | Ignored. | 
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 Kij(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.
An object of class "fv" (see fv.object).
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. 
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
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), 63, 673–694.
data(chicago) K <- linearKcross(chicago, "assault", "robbery")
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