# linearKdot.inhom

##### Inhomogeneous multitype K Function (Dot-type) for Linear Point Pattern

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

- Keywords
- spatial, nonparametric

##### Usage

```
linearKdot.inhom(X, i, lambdaI, lambdadot, r=NULL, ...,
correction="Ang", normalise=TRUE)
```

##### Arguments

- X
- The observed point pattern,
from which an estimate of the dot type $K$ function
$K_{i\bullet}(r)$ will be computed.
An object of class
`"lpp"`

which must be a multitype point pattern (a marked point pattern whose marks are - 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)`

. - lambdaI
- Intensity values for the points of type
`i`

. Either a numeric vector, a`function`

, a pixel image (object of class`"im"`

or`"linim"`

) or a fitted point process model (object of class`"ppm"`

- lambdadot
- Intensity values for all points of
`X`

. Either a numeric vector, a`function`

, a pixel image (object of class`"im"`

or`"linim"`

) or a fitted point process model (object of class`"ppm"`

- r
- numeric vector. The values of the argument $r$ at which the $K$-function $K_{i\bullet}(r)$ should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important co
- correction
- Geometry correction.
Either
`"none"`

or`"Ang"`

. See Details. - ...
- Arguments passed to
`lambdaI`

and`lambdadot`

if they are functions. - normalise
- Logical. If
`TRUE`

(the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the points of type`i`

), which reduces the sampling variability. If`FALSE`

##### Details

This is a counterpart of the function `Kdot.inhom`

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

).

The argument `i`

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

.
If `i`

is missing, it defaults to the first
level of the marks factor.

The argument `r`

is the vector of values for the
distance $r$ at which $K_{i\bullet}(r)$ 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.

If `lambdaI`

or `lambdadot`

is a fitted point process model,
the default behaviour is to update the model by re-fitting it to
the data, before computing the fitted intensity.
This can be disabled by setting `update=FALSE`

.

##### Value

- An object of class
`"fv"`

(see`fv.object`

).

##### Warnings

The argument `i`

is interpreted as a
level 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

```
lam <- table(marks(chicago))/(summary(chicago)$totlength)
lamI <- function(x,y,const=lam[["assault"]]){ rep(const, length(x)) }
lam. <- function(x,y,const=sum(lam)){ rep(const, length(x)) }
K <- linearKdot.inhom(chicago, "assault", lamI, lam.)
fit <- lppm(chicago, ~marks + x)
linearKdot.inhom(chicago, "assault", fit, fit)
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*