# linearpcfinhom

##### Inhomogeneous Linear Pair Correlation Function

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

- Keywords
- spatial, nonparametric

##### 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 \(g(r)\).

##### 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

##### Examples

```
# NOT RUN {
data(simplenet)
X <- rpoislpp(5, simplenet)
fit <- lppm(X ~x)
K <- linearpcfinhom(X, lambda=fit)
plot(K)
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*