# linearKcross: Multitype K Function (Cross-type) for Linear Point Pattern In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

 linearKcross R Documentation

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

### Description

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.

### 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 Kij(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 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 `"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 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.

### 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), 63, 673–694.

`linearKdot`, `linearK`.
```   data(chicago)