"quad"
)
from point patterns of data and dummy points.quadscheme(data)
quadscheme(data, dummy=default.dummy(data), method="grid", ...)
"ppp"
or in a format recognised by as.ppp()
"ppp"
or in a format recognised by as.ppp()
"grid"
or "dirichlet"
."quad"
describing the quadrature scheme
(data points, dummy points, and quadrature weights)
suitable as the argument Q
of the function mpl()
for
fitting a point process model.mpl
.
The function mpl
fits a point process model to an
observed point pattern using
the Berman-Turner quadrature approximation (Berman and Turner, 1992;
Baddeley and Turner, 2000) to the pseudolikelihood of the model.
It requires a quadrature scheme consisting of
the original data point pattern, an additional pattern of dummy points,
and a vector of quadrature weights for all these points.
Such quadrature schemes are represented by objects of class
"quad"
. See quad.object
for a description of this class. Quadrature schemes are created by the function
quadscheme
.
The arguments data
and dummy
specify the data and dummy
points, respectively. There is a sensible default for the dummy
points (provided by default.dummy
).
Alternatively the dummy points
may be specified arbitrarily and given in any format recognised by
as.ppp
.
There are also functions for creating dummy patterns
including corners
,
gridcentres
,
stratrand
and
spokes
.
The quadrature region is the region over which we are
integrating, and approximating integrals by finite sums.
If dummy
is a point pattern object (class "ppp"
)
then the quadrature region is taken to be dummy$window
.
If dummy
is just a list of $x, y$ coordinates
then the quadrature region defaults to the observation window
of the data pattern, data$window
.
If method = "grid"
then the optional arguments (for ...
) are
(nx = default.ngrid(data), ny=nx)
.
The quadrature region (see below) is divided into
an nx
by ny
grid of rectangular tiles. The weight for each
quadrature point is the area of a tile divided by the number of
quadrature points in that tile.
If method="dirichlet"
then the optional arguments are
(exact=TRUE)
.
The quadrature points (both data and dummy) are used to construct the
Dirichlet tessellation. The quadrature weight of each point is the
area of its Dirichlet tile inside the quadrature region.
mpl
,
as.ppp
,
quad.object
,
gridweights
,
dirichlet.weights
,
corners
,
gridcentres
,
stratrand
,
spokes
library(spatstat)
data(simdat)
P <- simdat
D <- default.dummy(P, 100)
Q <- quadscheme(P, D, "grid")
mpl(Q, ~ x, Strauss(0.05), rbord=0.1)
Q <- quadscheme(P, , "grid")
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