spatstat.linnet: bw.lppl – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

bw.lppl

Likelihood Cross Validation Bandwidth Selection for Kernel Density on a Linear Network

Description

Uses likelihood cross-validation to select a smoothing bandwidth for the kernel estimation of point process intensity on a linear network.

Usage

bw.lppl(X, ..., srange=NULL, ns=16, sigma=NULL, weights=NULL,
           distance=c("euclidean", "path"), shortcut=TRUE, warn=TRUE)

Arguments

`X`	A point pattern on a linear network (object of class `"lpp"`).
`srange`	Optional numeric vector of length 2 giving the range of values of bandwidth to be searched.
`ns`	Optional integer giving the number of values of bandwidth to search.
`sigma`	Optional. Vector of values of the bandwidth to be searched. Overrides the values of `ns` and `srange`.
`weights`	Optional. Numeric vector of weights for the points of `X`. Argument passed to `density.lpp`.
`distance`	Argument passed to `density.lpp` controlling the type of kernel estimator.
`...`	Additional arguments passed to `density.lpp`.
`shortcut`	Logical value indicating whether to speed up the calculation by omitting the integral term in the cross-validation criterion.
`warn`	Logical. If `TRUE`, issue a warning if the maximum of the cross-validation criterion occurs at one of the ends of the search interval.

Details

This function selects an appropriate bandwidth sigma for the kernel estimator of point process intensity computed by density.lpp.

The argument X should be a point pattern on a linear network (class "lpp").

The bandwidth σ is chosen to maximise the point process likelihood cross-validation criterion

LCV(σ) = sum[i] log(λ[-i](x[i])) - integral[L] λ(u) du

where the sum is taken over all the data points x[i], where λ[-i](x_i) is the leave-one-out kernel-smoothing estimate of the intensity at x[i] with smoothing bandwidth σ, and λ(u) is the kernel-smoothing estimate of the intensity at a spatial location u with smoothing bandwidth σ. See Loader(1999, Section 5.3).

The value of LCV(σ) is computed directly, using density.lpp, for ns different values of σ between srange[1] and srange[2].

The result is a numerical value giving the selected bandwidth. The result also belongs to the class "bw.optim" which can be plotted to show the (rescaled) mean-square error as a function of sigma.

If shortcut=TRUE, the computation is accelerated by omitting the integral term in the equation above. This is valid because the integral is approximately constant.

Value

A numerical value giving the selected bandwidth. The result also belongs to the class "bw.optim" which can be plotted.

Author(s)

Greg McSwiggan, Suman Rakshit and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

References

Loader, C. (1999) Local Regression and Likelihood. Springer, New York.

McSwiggan, G., Baddeley, A. and Nair, G. (2019) Estimation of relative risk for events on a linear network. Statistics and Computing 30 (2) 469–484.

Examples

if(interactive()) {
    b <- bw.lppl(spiders)
    plot(b, main="Likelihood cross validation for spiders")
    plot(density(spiders, b, distance="e"))
  } else {
    b1 <- bw.lppl(spiders, ns=2)
    b2 <- bw.lppl(spiders, ns=2, shortcut=TRUE)
  }

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