Description Usage Arguments Details Value Author(s) References See Also Examples

This function calculates point interactions at presence locations and quadrature points required for fitting a regularisation path of area-interaction models.

1 | ```
point.interactions(dat.ppm, r, availability = NA)
``` |

`dat.ppm` |
A design matrix generated using the |

`r` |
The radius of point interactions. |

`availability` |
An optional binary matrix used in calculating point interactions indicating
whether locations are available ( |

Theoretically, the point interaction *t(y)* at a point *y* is calculated
as the proportion of available area in a circular region *Y* or radius *r* centred
at *y* that overlaps with circles of radius *r* centred at other presence locations
(Baddeley & Turner, 2005).

This function discretises the study region at the same spatial resolution
as `availability`

by defining the matrix `occupied`

, a fine grid of locations
spanning the study region initialised to zero. The values of `occupied`

within a
distance of `r`

of each presence location are then augmented by `1`

, such that
`occupied`

then contains the total number of presence locations with which each
grid location interacts. To prevent unavailable areas from being included in the
calculation of point interactions, the values of `occupied`

at grid locations for which
`availability = 0`

are set to zero.

*t(y)* is then estimated as the proportion of available grid locations within *Y*
that overlap circular regions around other presence locations.

The availability matrix is particularly useful for regions that have inaccessible areas
(**e.g.** due to the presence of ocean or urban areas).

Finer resolutions of the `availability`

matrix will yield more precise estimates but
at a cost of greater computation time.

A vector of point interactions corresponding to the locations contained in the
`dat.ppm`

argument.

Ian W. Renner

Baddeley, A.J. & Turner, R. (2005). Spatstat: an `R`

package for analyzing spatial
point patterns. *Journal of Statistical Software* **12**, 1-42.

`ppmlasso`

for fitting a regularisation path of area-interaction models

1 2 3 4 | ```
data(BlueMountains)
species.ppm = ppmdat(sp.xy = BlueMountains$eucalypt, back.xy = BlueMountains$env,
sp.scale = 1, file.name = "Sp PPM Data") # generate design matrix
species.int = point.interactions(species.ppm, 2, BlueMountains$availability)
``` |

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