| predict.ppm {spatstat} | R Documentation |
Given a fitted point process model obtained by ppm,
evaluate the spatial trend and the conditional intensity of the model
at new locations.
## S3 method for class 'ppm': predict(object, window, ngrid=NULL, locations=NULL, covariates=NULL, type="trend", ..., check=TRUE, repair=TRUE)
object |
A fitted point process model, typically obtained from
the model-fitting algorithm ppm. An object of
class "ppm" (see ppm.object).
|
window |
window delimiting the locations where predictions
should be computed. Defaults to the window of the
original data used to fit the model object.
|
ngrid |
dimensions (either (ngrid[1] by ngrid[2]
or ngrid by ngrid) of a rectangular grid of locations
inside window where predictions should be computed.
(Incompatible with locations)
|
locations |
data giving the x,y coordinates (and marks, if required)
at which predictions should be computed. Either a data frame
or a binary image mask.
(Incompatible with ngrid)
|
covariates |
Values of external covariates required by the model. Either a data frame or a list of images. See Details. |
type |
character string.
Indicates which property of the fitted model should be predicted.
Options are "trend" for the spatial trend, and
"cif" or "lambda" for the conditional intensity.
|
... |
Ignored. |
check |
Logical value indicating whether to check the internal format
of 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 computed, set
check=TRUE.
|
repair |
Logical value indicating whether to repair the internal format
of object, if it is found to be damaged.
|
This function computes the spatial trend and the conditional intensity of a fitted spatial point process model. See Baddeley and Turner (2000) for explanation and examples.
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 and conditional 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 and conditional intensity at these locations.
Note that by ``spatial trend'' we mean 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. ] The conditional intensity lambda(u,X) of the fitted model is evaluated at each required spatial location u, with respect to the data point pattern X.
If the argument ngrid is present, then
predictions are performed at an ngrid by ngrid
pixel grid of locations in the window window.
The result of prediction will be a pixel image or images.
If locations is present, then predictions
will be performed at the spatial locations given by
this dataset. The result of prediction will be either a
vector of values or a pixel image or a list of images, depending
on the format of locations.
The argument locations may be either a data frame or list
specifying arbitrary locations,
or a binary image mask (an object of class "owin"
with type "mask") specifying (a subset of) a rectangular
grid of locations.
If locations is a data frame or list, then it must contain
vectors locations$x and locations$y specifying the
x,y coordinates of the prediction locations. Additionally, if
the model is a marked point process, then locations must also contain
a factor locations$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.
If locations is a binary image mask, then prediction will be
performed at each pixel in this binary image where the pixel value
is TRUE (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.
If neither ngrid nor locations is given, then
ngrid is assumed. It defaults to 50.
The argument 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.
If covariates is a list of images, then
the names of the entries should correspond to
the names of covariates in the model formula trend.
Each entry in the list must be an image object (of class "im",
see im.object).
The software will look up
the pixel values of each image at the quadrature points.
If covariates is a data frame, then the
ith row of covariates
is assumed to contain covariate data for the ith location.
When locations is a data frame,
this just means that each row of covariates contains the
covariate data for the location specified in the corresponding row of
locations. When locations is a binary image
mask, the row covariates[i,] must correspond to the location
x[i],y[i] where x = as.vector(raster.x(locations))
and y = 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.
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:
If object is an unmarked point process,
the result is an image object (of class "im", see
im.object) containing the predictions.
If object is a multitype point process,
the result is a list of 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") or values of the conditional intensity
(if type="cif" or type="lambda").
The current implementation invokes 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.
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
Baddeley, A. and Turner, R. Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42 (2000) 283–322.
Berman, M. and Turner, T.R. Approximating point process likelihoods with GLIM. Applied Statistics 41 (1992) 31–38.
ppm,
ppm.object,
plot.ppm,
print.ppm,
fitted.ppm
data(cells) m <- ppm(cells, ~ polynom(x,y,2), Strauss(0.05), rbord=0.05) trend <- predict(m, type="trend") ## Not run: image(trend) points(cells) ## End(Not run) cif <- predict(m, type="cif") ## Not run: persp(cif) ## End(Not run)