point.interactions: Calculate point interactions for area-interaction models In ppmlasso: Point Process Models with LASSO Penalties

Description

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

Usage

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

Arguments

 dat.ppm A design matrix generated using the ppmdat function. r The radius of point interactions. availability An optional binary matrix used in calculating point interactions indicating whether locations are available (availability = 1) or not (availability = 0). If no such matrix is provided, availability is automatically generated with all values set to 1 at a special resolution of half of r.

Details

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.

Value

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

Ian W. Renner

References

Baddeley, A.J. & Turner, R. (2005). Spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software 12, 1-42.