linearpcfinhom | R Documentation |

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

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

`X` |
Point pattern on linear network (object of class |

`lambda` |
Intensity values for the point pattern. Either a numeric vector,
a |

`r` |
Optional. Numeric vector of values of the function argument |

`...` |
Arguments passed to |

`correction` |
Geometry correction.
Either |

`normalise` |
Logical. If |

`normpower` |
Integer (usually either 1 or 2).
Normalisation power. See explanation in |

`update` |
Logical value indicating what to do when |

`leaveoneout` |
Logical value (passed to |

`ratio` |
Logical.
If |

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`

.

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)*.

and \adrian.

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.

`linearpcf`

,
`linearKinhom`

,
`lpp`

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

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