predict.ppm {spatstat} | R Documentation |
Given a fitted point process model obtained by mpl
,
evaluate the spatial trend and the conditional intensity of the model
at new locations.
predict.ppm(object, nx = 40, ny = NULL, type="trend") predict.ppm(object, newdata, type="trend")
object |
A fitted point process model, typically obtained from
the maximum pseudolikelihood algorithm mpl . An object of
class "ppm" (see ppm.object ).
|
newdata |
optional data frame giving the values of any spatial covariates
for the locations at which the trend and conditional intensity should be
computed. (Incompatible with nx,ny )
|
nx |
predictions are to be made at
an (nx by ny ) rectangular grid of positions in the
original window of observation.
(Incompatible with newdata )
|
ny |
see nx above; ny defaults to the same value as nx
|
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.
|
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
maximum pseudolikelihood algorithm mpl
. 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
.
This is feasible in such generality because the Berman-Turner-Baddeley method
(Berman and Turner, 1992; Baddeley and Turner, 2000)
reduces maximum pseudolikelihood estimation to the fitting
of a GLM or GAM, and because Splus/R contains predict
methods for
glm
and gam
objects. The current implementation
invokes predict.glm
.
The default action is to create a rectangular 40 by 40 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.
The argument newdata
, if given, is a data frame
giving the values of any spatial covariates
at the locations where the trend and conditional intensity should be
computed.
If the trend formula in the fitted model
involves spatial covariates (other than
the Cartesian coordinates x
, y
)
then newdata
is required.
If newdata
is present then it must contain variables
matching all the variable names featuring in the trend formula
and the Cartesian coordinates x
and y
and the mark values marks
.
[This is different from the role of the data
argument in mpl
which must not contain
x
and y
variables.]
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 newdata
is given:
a vector of predicted values for the spatial locations
(and marks and covariates) given in the rows of newdata
.
If newdata
is not given:
a list with components
x
, y
, z
giving the
coordinates and predicted values for a rectangular grid of points.
If object
is an unmarked point process,
z
is a matrix such that z[i,j]
gives the predicted value at location (x[i],y[j])
;
for marked point processes,
z
is a three-dimensional array
such that z[i,j,m]
gives the predicted value for a
point at location (x[i],y[j])
with mark m
.
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 newdata
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) 283322.
Berman, M. and Turner, T.R. Approximating point process likelihoods with GLIM. Applied Statistics 41 (1992) 3138.
mpl
,
ppm.object
,
plot.ppm
,
print.ppm
library(spatstat) data(cells) m <- mpl(cells, ~ polynom(x,y,2), Strauss(0.05), rbord=0.05) trend <- predict(m, type="trend") image(trend) points(cells) cif <- predict(m, type="cif") persp(cif)