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

bw.relrisk {spatstat.core} | R Documentation

## Cross Validated Bandwidth Selection for Relative Risk Estimation

### Description

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

### Usage

       bw.relrisk(X, method = "likelihood", nh = spatstat.options("n.bandwidth"),
       hmin=NULL, hmax=NULL, warn=TRUE)

### Arguments

`X` | A multitype point pattern (object of class `"ppp"` which has factor valued marks).
`method` | Character string determining the cross-validation method. Current options are `"likelihood"`, `"leastsquares"` or `"weightedleastsquares"`.
`nh` | Number of trial values of smoothing bandwith `sigma` to consider. The default is 32.
`hmin, hmax` | Optional. Numeric values. Range of trial values of smoothing bandwith `sigma` to consider. There is a sensible default.
`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 selects an appropriate bandwidth for the nonparametric estimation of relative risk using `relrisk`.

Consider the indicators y[i,j] which equal 1 when data point x[i] belongs to type j, and equal 0 otherwise. For a particular value of smoothing bandwidth, let p*[j](u) be the estimated probabilities that a point at location u will belong to type j. Then the bandwidth is chosen to minimise either the negative likelihood, the squared error, or the approximately standardised squared error, of the indicators y[i,j] relative to the fitted values p*[j](x[i]). See Diggle (2003) or Baddeley et al (2015).

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 multiples of Stoyan's rule of thumb `bw.stoyan`.

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`.

Computation time depends on the number `nh` of trial values considered, and also on the range `[hmin, hmax]` of values considered, because larger values of `sigma` require calculations involving more pairs of data points.

### Value

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

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz.

### References

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

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

### See Also

`relrisk`, `bw.stoyan`

### Examples

      data(urkiola)

      b <- bw.relrisk(urkiola)
      b
      plot(b)
      b <- bw.relrisk(urkiola, hmax=20)
      plot(b)

[Package spatstat.core version 1.65-5 Index]