# linearKcross.inhom

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##### Inhomogeneous multitype K Function (Cross-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 type $j$ within a given distance of a point of type $i$.

Keywords
spatial, nonparametric
##### Usage
linearKcross.inhom(X, i, j, lambdaI, lambdaJ,
r=NULL, …, correction="Ang", normalise=TRUE)
##### 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).

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" or "lppm").

lambdaJ

Intensity values for the points of type j. 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" or "lppm").

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.

Arguments passed to lambdaI and lambdaJ 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, the denominator is the length of the network.

##### Details

This is a counterpart of the function Kcross.inhom 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.

If lambdaI or lambdaJ 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 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.

##### Aliases
• linearKcross.inhom
##### Examples
# NOT RUN {
lam <- table(marks(chicago))/(summary(chicago)\$totlength)
lamI <- function(x,y,const=lam[["assault"]]){ rep(const, length(x)) }
lamJ <- function(x,y,const=lam[["robbery"]]){ rep(const, length(x)) }

K <- linearKcross.inhom(chicago, "assault", "robbery", lamI, lamJ)

# }
# NOT RUN {
fit <- lppm(chicago, ~marks + x)
linearKcross.inhom(chicago, "assault", "robbery", fit, fit)

# }

Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)

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