spatstat.Knet (version 3.1-2)

Knetinhom: Geometrically-Corrected Inhomogeneous K Function on Network

Description

Compute the geometrically-corrected inhomogeneous \(K\) function for a point pattern on a linear network.

Usage

Knetinhom(X, lambda, r = NULL, freq, ..., verbose=FALSE)

Value

Function value table (object of class "fv").

Arguments

X

Point pattern on a linear network (object of class "lpp").

lambda

Fitted intensity of the point process. Either a numeric vector giving values of the fitted intensity at each data point of X, or an object of class "linim", "linfun" or "lppm" from which the fitted intensity at each data point can be extracted.

r

Optional. Numeric vector of values of the function argument \(r\). There is a sensible default.

freq

Vector of frequencies corresponding to the point events on the network. The length of this vector should be equal to the number of points on the network. The default frequency is one for every point on the network.

...

Ignored.

verbose

Logical value indicating whether to print progress reports during the computation.

Author

Suman Rakshit (modified by Adrian Baddeley)

Details

This command computes the inhomogeneous version of the geometrically-corrected \(K\) function, proposed by Ang et al (2012), from point pattern data on a linear network.

The algorithm used in this computation is described in Rakshit et al (2019).

The spatstat function linearKinhom is usable (and slightly faster) for this purpose for small datasets, but requires substantial amounts of memory. For larger datasets, the function Knetinhom is much more efficient.

References

Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591--617.

Rakshit, S., Baddeley, A. and Nair, G. (2019) Efficient code for second order analysis of events on a linear network. Journal of Statistical Software 90 (1) 1--37. DOI: 10.18637/jss.v090.i01

Examples

   UC <- unmark(chicago)
   fit <- lppm(UC ~ x+y)
   r <- seq(0, 1000, length = 41)
   K <- Knetinhom(UC, lambda=fit, r = r)