R: Inhomogeneous Linear Pair Correlation Function

linearpcfinhom {spatstat} | R Documentation

## Inhomogeneous Linear Pair Correlation Function

### Description

Computes an estimate of the inhomogeneous linear pair correlation function for a point pattern on a linear network.

### Usage

    linearpcfinhom(X, lambda=NULL, r=NULL, ..., correction="Ang",
                   normalise=TRUE, normpower=1,
    	       update = TRUE, leaveoneout = TRUE,
    	       ratio = FALSE)

### Arguments

`X` | Point pattern on linear network (object of class `"lpp"`).
`lambda` | Intensity values for the point pattern. Either a numeric vector, a `function`, a pixel image (object of class `"im"`) or a fitted point process model (object of class `"ppm"` or `"lppm"`).
`r` | Optional. Numeric vector of values of the function argument r. There is a sensible default.
`...` | Arguments passed to `density.default` to control the smoothing.
`correction` | Geometry correction. Either `"none"` or `"Ang"`. See Details.
`normalise` | Logical. If `TRUE` (the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the data points, raised to `normpower`), which reduces the sampling variability. If `FALSE`, the denominator is the length of the network.
`normpower` | Integer (usually either 1 or 2). Normalisation power. See explanation in `linearKinhom`.
`update` | Logical value indicating what to do when `lambda` is a fitted model (class `"lppm"` or `"ppm"`). If `update=TRUE` (the default), the model will first be refitted to the data `X` (using `update.lppm` or `update.ppm`) before the fitted intensity is computed. If `update=FALSE`, the fitted intensity of the model will be computed without re-fitting it to `X`.
`leaveoneout` | Logical value (passed to `fitted.lppm` or `fitted.ppm`) specifying whether to use a leave-one-out rule when calculating the intensity, when `lambda` is a fitted model. Supported only when `update=TRUE`.
`ratio` | Logical. If `TRUE`, the numerator and denominator of each estimate will also be saved, for use in analysing replicated point patterns.

### Details

This command computes the inhomogeneous version of the linear pair correlation function from point pattern data on a linear network.

If `lambda = NULL` the result is equivalent to the homogeneous pair correlation function `linearpcf`. If `lambda` is given, then it is expected to provide estimated values of the intensity of the point process at each point of `X`. The argument `lambda` may be a numeric vector (of length equal to the number of points in `X`), or a `function(x,y)` that will be evaluated at the points of `X` to yield numeric values, or a pixel image (object of class `"im"`) or a fitted point process model (object of class `"ppm"` or `"lppm"`).

If `lambda` 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`.

If `correction="none"`, the calculations do not include any correction for the geometry of the linear network. If `correction="Ang"`, the pair counts are weighted using Ang's correction (Ang, 2010).

The bandwidth for smoothing the pairwise distances is determined by arguments `...` passed to `density.default`, mainly the arguments `bw` and `adjust`. The default is to choose the bandwidth by Silverman's rule of thumb `bw="nrd0"` explained in `density.default`.

### Value

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

If `ratio=TRUE` then the return value also has two attributes called `"numerator"` and `"denominator"` which are `"fv"` objects containing the numerators and denominators of each estimate of g(r).

### Author(s)

Ang Qi Wei aqw07398@hotmail.com and Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### References

Ang, Q.W. (2010) Statistical methodology for spatial point patterns on a linear network. MSc thesis, University of Western Australia.

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.

Okabe, A. and Yamada, I. (2001) The K-function method on a network and its computational implementation. Geographical Analysis 33, 271-290.

### See Also

`linearpcf`, `linearKinhom`, `lpp`

### Examples

      data(simplenet)
      X <- rpoislpp(5, simplenet)
      fit <- lppm(X ~x)
      K <- linearpcfinhom(X, lambda=fit)
      plot(K)

[Package spatstat version 1.54-0 Index]