# intensity_pspline: Intensity Estimation on Geometric Networks with Penalized... In geonet: Intensity Estimation on Geometric Networks with Penalized Splines

 intensity_pspline R Documentation

## Intensity Estimation on Geometric Networks with Penalized Splines

### Description

This is the main function of the `geonet` package. `intensity_pspline` estimates the intensity of a point pattern on a geometric network employing penalized splines as outlined in Schneble and Kauermann (2020). In distinction to `density.lpp` from the `spatstat.linnet` package, which provides kernel based tools for intensity estimation of point patterns on linear networks, `intensity_pspline` allows to incorporate covariates while also estimating the baseline intensity. Covariates can be either internal or external. External covariates can also be incorporated as a smooth term using penalized splines with the same syntax as in `gam`.

### Usage

```intensity_pspline(
X,
...,
formula = ~1,
delta = "0",
h = "0.5",
r = 2,
scale = NULL,
density = FALSE,
verbose = FALSE,
control = list()
)
```

### Arguments

 `X` A point pattern on a geometric network (object of class `gnpp`). The data (`X\$data`) must contain information on all covariates included in `formula`. `...` Other arguments. The following arguments must match exactly. `formula` A one-sided formula (if a two-sided formula is supplied, the left hand side of the formula is ignored). The formula can consist of either linear terms as in linear models (`lm`) or smooth terms as in `gam` formulae, where the usage is restricted to smooth terms constructed with `s` and the argument `bs` is set to `bs = "ps"` by default, i.e. `intensity_pspline` can handle penalized spline based smooth terms. `delta` The global knot distance δ, a numerical vector of length one. If not supplied, delta will be chosen properly according to the geometric network `X` which is supplied. `h` The global bin width h, a numerical vector of length one. If not supplied, `h` will be chosen properly according to the geometric network `X` which is supplied. `r` The order of the penalty of the baseline intensity on the geometric network, default to a penalty of order `r = 2`. `scale` A named list which specifies the rescaling of network related covariates. Currently, only x- and y-coordinates can be scaled. `density` `TRUE` if the intensity should be normalized such that it can be interpreted as a density, i.e. the integral over the estimated density is equal to one. `verbose` If `TRUE`, prints information on the process of the fitting algorithm. `control` A list of optional arguments which control the convergence of the fitting algorithm. See "Details".

### Value

A fitted geometric network (object of class `gnppfit`).

### Author(s)

Marc Schneble marc.schneble@stat.uni-muenchen.de

### References

Schneble, M. and G. Kauermann (2020). Intensity estimation on geometric networks with penalized splines. arXiv preprint arXiv:2002.10270 .

### Examples

```library(geonet)
X <- runifgn(50, small_gn)
delta <- 0.2
model <- intensity_pspline(X, delta = delta)
summary(model)
plot(model)
```

geonet documentation built on July 11, 2022, 9:08 a.m.