# linearpcf: Linear Pair Correlation Function In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

 linearpcf R Documentation

## Linear Pair Correlation Function

### Description

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

### Usage

```linearpcf(X, r=NULL, ..., correction="Ang", ratio=FALSE)
```

### Arguments

 `X` Point pattern on linear network (object of class `"lpp"`). `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. `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 linear pair correlation function from point pattern data on a linear network.

The pair correlation function is estimated from the shortest-path distances between each pair of data points, using the fixed-bandwidth kernel smoother `density.default`, with a bias correction at each end of the interval of r values. To switch off the bias correction, set `endcorrect=FALSE`.

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`.

If `correction="none"`, the calculations do not include any correction for the geometry of the linear network. The result is an estimate of the first derivative of the network K function defined by Okabe and Yamada (2001).

If `correction="Ang"`, the pair counts are weighted using Ang's correction (Ang, 2010). The result is an estimate of the pair correlation function in the linear network.

### 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.

### 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.

`linearK`, `linearpcfinhom`, `lpp`

### Examples

```  data(simplenet)
X <- rpoislpp(5, simplenet)
linearpcf(X)
linearpcf(X, correction="none")
```

spatstat.linnet documentation built on March 18, 2022, 6:40 p.m.