# lppm

##### Fit Point Process Model to Point Pattern on Linear Network

Fit a point process model to a point pattern dataset on a linear network

##### Usage

`lppm(X, ...)`# S3 method for formula
lppm(X, interaction=NULL, ..., data=NULL)

# S3 method for lpp
lppm(X, ..., eps=NULL, nd=1000, random=FALSE)

##### Arguments

- X
Either an object of class

`"lpp"`

specifying a point pattern on a linear network, or a`formula`

specifying the point process model.- …
Arguments passed to

`ppm`

.- interaction
An object of class

`"interact"`

describing the point process interaction structure, or`NULL`

indicating that a Poisson process (stationary or nonstationary) should be fitted.- data
Optional. The values of spatial covariates (other than the Cartesian coordinates) required by the model. A list whose entries are images, functions, windows, tessellations or single numbers.

- eps
Optional. Spacing between dummy points along each segment of the network.

- nd
Optional. Total number of dummy points placed on the network. Ignored if

`eps`

is given.- random
Logical value indicating whether the grid of dummy points should be placed at a randomised starting position.

##### Details

This function fits a point process model to data that specify
a point pattern on a linear network. It is a counterpart of
the model-fitting function `ppm`

designed
to work with objects of class `"lpp"`

instead of `"ppp"`

.

The function `lppm`

is generic, with methods for
the classes `formula`

and `lppp`

.

In `lppm.lpp`

the first argument `X`

should be an object of class `"lpp"`

(created by the command `lpp`

) specifying a point pattern
on a linear network.

In `lppm.formula`

,
the first argument is a `formula`

in the R language
describing the spatial trend model to be fitted. It has the general form
`pattern ~ trend`

where the left hand side `pattern`

is usually
the name of a point pattern on a linear network
(object of class `"lpp"`

)
to which the model should be fitted, or an expression which evaluates
to such a point pattern;
and the right hand side `trend`

is an expression specifying the
spatial trend of the model.

Other arguments `...`

are passed from `lppm.formula`

to `lppm.lpp`

and from `lppm.lpp`

to `ppm`

.

##### Value

An object of class `"lppm"`

representing the fitted model.
There are methods for `print`

, `predict`

,
`coef`

and similar functions.

##### References

Ang, Q.W. (2010)
*Statistical methodology for events on a network*.
Master's thesis, School of Mathematics and Statistics, 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.

McSwiggan, G., Nair, M.G. and Baddeley, A. (2012) Fitting Poisson point process models to events on a linear network. Manuscript in preparation.

##### See Also

##### Examples

```
# NOT RUN {
X <- runiflpp(15, simplenet)
lppm(X ~1)
lppm(X ~x)
marks(X) <- factor(rep(letters[1:3], 5))
lppm(X ~ marks)
lppm(X ~ marks * x)
# }
```

*Documentation reproduced from package spatstat, version 1.62-2, License: GPL (>= 2)*