R: Cross Validated Bandwidth Selection for Relative Risk...

bw.relrisklpp {spatstat.linnet} | R Documentation

## Cross Validated Bandwidth Selection for Relative Risk Estimation on a Network

### Description

Uses cross-validation to select a smoothing bandwidth for the estimation of relative risk on a linear network.

### Usage

      bw.relrisklpp(X, ...,
        method = c("likelihood", "leastsquares", "KelsallDiggle", "McSwiggan"),
        distance=c("path", "euclidean"),
        hmin = NULL, hmax = NULL, nh = NULL,
        fast = TRUE, fastmethod = "onestep",
        floored = TRUE, reference = c("thumb", "uniform", "sigma"),
        allow.infinite = TRUE, epsilon = 1e-20, fudge = 0,
        verbose = FALSE, warn = TRUE)

### Arguments

`X` | A multitype point pattern on a linear network (object of class `"lpp"` which has factor-valued marks).
`...` | Arguments passed to `density.lpp` to control the resolution of the algorithm.
`method` | Character string (partially matched) determining the cross-validation method. See Details.
`distance` | Character string (partially matched) specifying the type of smoothing kernel. See `density.lpp`.
`hmin,hmax` | Optional. Numeric values. Range of trial values of smoothing bandwith `sigma` to consider. There is a sensible default.
`nh` | Number of trial values of smoothing bandwidth `sigma` to consider.
`fast` | Logical value specifying whether the leave-one-out density estimates should be computed using a fast approximation (`fast=TRUE`, the default) or exactly (`fast=FALSE`).
`fastmethod, floored` | Developer use only.
`reference` | Character string (partially matched) specifying the bandwidth for calculating the reference intensities used in the McSwiggan method (modified Kelsall-Diggle method). `reference="sigma"` means the maximum bandwidth considered, which is given by the argument `sigma`. `reference="thumb"` means the bandwidths selected by Scott's rule of thumb `bw.scott.iso`. `reference="uniform"` means infinite bandwidth corresponding to uniform intensity.
`allow.infinite` | Logical value indicating whether an infinite bandwidth (corresponding to a constant relative risk) should be permitted as a possible choice of bandwidth.
`epsilon` | A small constant value added to the reference density in some of the cross-validation calculations, to improve performance.
`fudge` | Fudge factor to prevent very small density estimates in the leave-one-out calculation. If `fudge > 0`, then the lowest permitted value for a leave-one-out estimate of intensity is `fudge/L`, where `L` is the total length of the network.
`verbose` | Logical value indicating whether to print progress reports,
`warn` | Logical. If `TRUE`, issue a warning if the minimum of the cross-validation criterion occurs at one of the ends of the search interval.

### Details

This function computes an optimal value of smoothing bandwidth for the nonparametric estimation of relative risk on a linear network using `relrisk.lpp`. The optimal value is found by optimising a cross-validation criterion.

The cross-validation criterion is selected by the argument `method`:

`method="likelihood"` | likelihood cross-validation
`method="leastsquares"` | least squares cross-validation
`method="KelsallDiggle"` | Kelsall and Diggle (1995) density ratio cross-validation
`method="McSwiggan"` | McSwiggan et al (2019) modified density ratio cross-validation

See McSwiggan et al (2019) for details.

The result is a numerical value giving the selected bandwidth `sigma`. The result also belongs to the class `"bw.optim"` allowing it to be printed and plotted. The plot shows the cross-validation criterion as a function of bandwidth.

The range of values for the smoothing bandwidth `sigma` is set by the arguments `hmin, hmax`. There is a sensible default, based on the linear network version of Scott's rule `bw.scott.iso`.

If the optimal bandwidth is achieved at an endpoint of the interval `[hmin, hmax]`, the algorithm will issue a warning (unless `warn=FALSE`). If this occurs, then it is probably advisable to expand the interval by changing the arguments `hmin, hmax`.

The cross-validation procedure is based on kernel estimates of intensity, which are computed by `density.lpp`. Any arguments `...` are passed to `density.lpp` to control the kernel estimation procedure. This includes the argument `distance` which specifies the type of kernel. The default is `distance="path"`; the fastest option is `distance="euclidean"`.

### 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 and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### References

Kelsall, J.E. and Diggle, P.J. (1995) Kernel estimation of relative risk. Bernoulli 1, 3–16.

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.

### See Also

`relrisk.lpp`

### Examples

       set.seed(2020)
       X <- superimpose(A=runiflpp(20, simplenet),
                        B=runifpointOnLines(20, as.psp(simplenet)[1]))
       plot(bw.relrisklpp(X, hmin=0.1, hmax=0.25, method="McSwiggan"))
       plot(bw.relrisklpp(X, hmin=0.1, hmax=0.3, nh=8, distance="euclidean"))

[Package spatstat.linnet version 2.3-1 Index]