This function calculates point interactions at presence locations and quadrature points required for fitting a regularisation path of area-interaction models.
A design matrix generated using the
The radius of point interactions.
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
availability by defining the matrix
occupied, a fine grid of locations
spanning the study region initialised to zero. The values of
occupied within a
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
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
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