ppm
,
evaluate the spatial trend or the conditional intensity of the model
at new locations.## S3 method for class 'ppm':
predict(object, window=NULL, ngrid=NULL, locations=NULL,
covariates=NULL,
type=c("trend", "cif", "intensity", "count"),
se=FALSE,
interval=c("none", "confidence", "prediction"),
level = 0.95,
X=data.ppm(object), correction,
..., new.coef=NULL, check=TRUE, repair=TRUE)
ppm
. An object of
class "ppm"
(see ppm.object
)."owin"
)
delimiting the locations where predictions
should be computed. Defaults to the window of the
original data used to fit the model object
.window
where the predictions should be computed.
An integer, or an integer vector of length 2,
specifying the number of grid points in the $y$ and $x$
directions. x
and
y
, or a binary imag"trend"
for the spatial trend,
"cif"
or "lambda"
for the conditional intensity,
"intensity"
interval="none"
, the default)
or a confidence interval (interval="confidence"
)
or a prediction interval (interval="prediction"
)."ppp"
)
to be taken as the data point pattern when calculating the
conditional intensity. The default is to use the original data
to which the model was fitted."border"
and "none"
.
Other options may include "periodic"
,
"isotropic"
and "translat
coef(object)
.object
. If there is any possibility that this object
has been restored from a dump file, or has otherwise lost track of
the environment where it was originally compuobject
, if it is found to be damaged.total
is given:
a numeric vector or matrix.
If locations
is given and is a data frame:
a vector of predicted values for the spatial locations
(and marks, if required) given in locations
. If ngrid
is given, or if locations
is given
and is a binary image mask or a pixel image:
If object
is an unmarked point process,
the result is a pixel image object (of class "im"
, see
im.object
) containing the predictions.
If object
is a multitype point process,
the result is a list of pixel images, containing the predictions
for each type at the same grid of locations.
The ``predicted values'' are either values of the spatial trend
(if type="trend"
), values of the conditional intensity
(if type="cif"
or type="lambda"
),
values of the intensity (if type="intensity"
)
or numbers of points (if type="count"
).
If se=TRUE
, then the result is a list with two entries,
the first being the predicted values in the format described above,
and the second being the standard errors in the same format.
predict.glm
so that prediction is wrong if the trend formula in
object
involves terms in ns()
,
bs()
or poly()
.
This is a weakness of predict.glm
itself!
Error messages may be very opaque,
as they tend to come from deep in the workings of
predict.glm
.
If you are passing the covariates
argument
and the function crashes,
it is advisable to start by checking that all the conditions
listed above are satisfied."ppm"
). For a Poisson point process
it can compute the fitted intensity function, or the expected number of
points in a region. For a Gibbs point process it can compute the
spatial trend (first order potential), conditional intensity,
and approximate intensity of the process.
Point estimates, standard errors,
confidence intervals and prediction intervals are available.
Given a point pattern dataset, we may fit
a point process model to the data using the
model-fitting algorithm ppm
. This
returns an object of class "ppm"
representing
the fitted point process model (see ppm.object
).
The parameter estimates in this fitted model can be read off
simply by printing the ppm
object.
The spatial trend, conditional intensity and intensity of the
fitted model are evaluated using this function predict.ppm
.The default action is to create a rectangular grid of points in the observation window of the data point pattern, and evaluate the spatial trend at these locations.
The argument type
specifies the values that are desired:
[object Object],[object Object],[object Object],[object Object]
The spatial trend, conditional intensity, and intensity
are all equivalent if the fitted model is a Poisson point process.
However, if the model is not a Poisson process, then they are
all different. The ``spatial trend'' is the (exponentiated)
first order potential, and not the intensity of the process.
[For example if we fit the
stationary Strauss process with parameters
$\beta$ and $\gamma$,
then the spatial trend is constant and equal to $\beta$,
while the intensity is a smaller value.]
The default is to compute an estimate of the desired quantity.
If interval="confidence"
or interval="prediction"
,
the estimate is replaced by a confidence interval or prediction interval.
If se=TRUE
, then a standard error is also calculated,
and is returned together with the (point or interval) estimate.
The spatial locations where predictions are required,
are determined by the (incompatible)
arguments ngrid
and locations
.
ngrid
is present, then
predictions are performed at a rectangular
grid of locations in the windowwindow
.
The result of prediction will be a pixel image or images.locations
is present, then predictions
will be performed at the spatial locations given by
this dataset. These may be an arbitrary list of spatial locations,
or they may be a rectangular grid.
The result of prediction will be either a numeric vector
or a pixel image or images.ngrid
norlocations
is given, thenngrid
is assumed. The value ofngrid
defaults tospatstat.options("npixel")
, which is initialised to 128
whenlocations
may be a point pattern,
a data frame or a list specifying arbitrary locations;
or it may be a binary image mask (an object of class "owin"
with type "mask"
) or a pixel image (object of class
"im"
) specifying (a subset of) a rectangular
grid of locations.
locations
is a point pattern (object of class"ppp"
),
then prediction will be performed at the points of the point pattern.
The result of prediction will be a vector of predicted values,
one value for each point.
If the model is a marked point process, thenlocations
should be a marked point pattern, with marks of the
same kind as the model; prediction will be performed at these
marked points.
The result of prediction will be a vector of predicted values,
one value for each (marked) point.locations
is a data frame or list, then it must contain
vectorslocations$x
andlocations$y
specifying the$x,y$coordinates of the prediction locations. Additionally, if
the model is a marked point process, thenlocations
must also contain
a factorlocations$marks
specifying the marks of the
prediction locations. These vectors must have equal length.
The result of prediction will be a vector of predicted values,
of the same length.locations
is a binary image mask, then prediction will be
performed at each pixel in this binary image where the pixel value
isTRUE
(in other words, at each pixel that is inside the
window). If the fitted model is an unmarked point process, then the
result of prediction will be an image. If the fitted model is a
marked point process, then prediction will
be performed for each possible value of the mark at each such
location, and the result of prediction will be a
list of images, one for each mark value.locations
is a pixel image (object of class"im"
),
then prediction will be performed at each pixel in this image where
the pixel value is defined (i.e.\ where the pixel value is notNA
).covariates
gives the values of any spatial covariates
at the prediction locations.
If the trend formula in the fitted model
involves spatial covariates (other than
the Cartesian coordinates x
, y
)
then covariates
is required.
The format and use of covariates
are analogous to those of the
argument of the same name in ppm
.
It is either a data frame or a list of images.
covariates
is a list of images, then
the names of the entries should correspond to
the names of covariates in the model formulatrend
.
Each entry in the list must be an image object (of class"im"
,
seeim.object
).
The software will look up
the pixel values of each image at the quadrature points.covariates
is a data frame, then thei
th row ofcovariates
is assumed to contain covariate data for thei
th location.
Whenlocations
is a data frame,
this just means that each row ofcovariates
contains the
covariate data for the location specified in the corresponding row oflocations
. Whenlocations
is a binary image
mask, the rowcovariates[i,]
must correspond to the locationx[i],y[i]
wherex = as.vector(raster.x(locations))
andy = as.vector(raster.y(locations))
. Note that if you only want to use prediction in order to
generate a plot of the predicted values,
it may be easier to use plot.ppm
which calls
this function and plots the results.
ppm
,
ppm.object
,
plot.ppm
,
print.ppm
,
fitted.ppm
,
spatstat.options
<testonly>op <- spatstat.options(npixel=32)</testonly>
m <- ppm(cells ~ polynom(x,y,2), Strauss(0.05))
trend <- predict(m, type="trend")
image(trend)
points(cells)
cif <- predict(m, type="cif")
persp(cif)
data(japanesepines)
mj <- ppm(japanesepines ~ harmonic(x,y,2))
se <- predict(mj, se=TRUE)
# prediction interval for total number of points
predict(mj, type="count", interval="p")
# prediction at arbitrary locations
predict(mj, locations=data.frame(x=0.3, y=0.4))
X <- runifpoint(5, Window(japanesepines))
predict(mj, locations=X, se=TRUE)
# multitype
rr <- matrix(0.06, 2, 2)
ma <- ppm(amacrine ~ marks, MultiStrauss(rr))
Z <- predict(ma)
Z <- predict(ma, type="cif")
predict(ma, locations=data.frame(x=0.8, y=0.5,marks="on"), type="cif")
<testonly>spatstat.options(op)</testonly>
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