spatstat.linnet: linearKdot.inhom – R documentation

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linearKdot.inhom

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

Description

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.

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.](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)`.
`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"`).
`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"` or `"lppm"`).
`r`	numeric vector. The values of the argument r at which the K-function K[i.](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 `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`, the denominator is the length of the network.

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 Ki.(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.

Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

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.

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.)

   # using fitted models for the intensity
   # fit <- lppm(chicago ~marks + x)
   # linearKdot.inhom(chicago, "assault", fit, fit)

spatstat.linnet

Linear Networks Functionality of the 'spatstat' Family

v2.1-1

GPL (>= 2)

Authors

Adrian Baddeley [aut, cre], Rolf Turner [aut], Ege Rubak [aut], Ottmar Cronie [ctb], Tilman Davies [ctb], Greg McSwiggan [ctb], Suman Rakshit [ctb]

Initial release

2021-03-28