Given a fitted multiple point process model obtained by mppm,
evaluate the spatial trend and/or the conditional intensity of the
model. By default, predictions are evaluated over a grid of
locations, yielding pixel images of the trend and conditional intensity.
Alternatively predictions may be evaluated at specified
locations with specified values of the covariates.
# S3 method for mppm
predict(object, ..., newdata = NULL, type = c("trend", "cif"),
ngrid = 40, locations=NULL, verbose=FALSE)The fitted model. An object of class "mppm"
obtained from mppm.
Ignored.
New values of the covariates, for which the predictions should be computed.
If newdata=NULL, predictions are computed for the original
values of the covariates, to which the model was fitted.
Otherwise newdata should be a hyperframe
(see hyperframe) containing columns of covariates
as required by the model. If type includes "cif",
then newdata must also include a column of spatial point
pattern responses, in order to compute the conditional intensity.
Type of predicted values required. A character string or vector of
character strings. Options are "trend" for the spatial trend
(first-order term) and "cif" or "lambda" for the
conditional intensity.
Alternatively type="all" selects all options.
Dimensions of the grid of spatial locations at which prediction will be
performed (if locations=NULL). An integer or a pair of integers.
Optional. The locations at which
predictions should be performed. A list of point patterns, with one entry
for each row of newdata.
Logical flag indicating whether to print progress reports.
A hyperframe with columns named trend and cif.
If locations=NULL, the entries of the hyperframe are
pixel images.
If locations is not null, the entries are
marked point patterns constructed by attaching the predicted values
to the locations point patterns.
This function computes the spatial trend and the conditional intensity of a fitted multiple spatial point process model. See Baddeley and Turner (2000) and Baddeley et al (2007) for explanation and examples.
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 response point pattern X.
If locations=NULL, then predictions are performed
at an ngrid by ngrid grid of locations in the window
for each response point pattern. The result will be a hyperframe
containing a column of images of the trend (if selected)
and a column of images of the conditional intensity (if selected).
The result can be plotted.
If locations is given, then it should be a list of point
patterns (objects of class "ppp"). Predictions are performed at these
points. The result is a hyperframe containing a column of
marked point patterns where the locations
each point.
Baddeley, A. and Turner, R. Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42 (2000) 283--322.
Baddeley, A., Bischof, L., Sintorn, I.-M., Haggarty, S., Bell, M. and Turner, R. Analysis of a designed experiment where the response is a spatial point pattern. In preparation.
Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. London: Chapman and Hall/CRC Press.
# NOT RUN {
h <- hyperframe(Bugs=waterstriders)
fit <- mppm(Bugs ~ x, data=h, interaction=Strauss(7))
# prediction on a grid
p <- predict(fit)
plot(p$trend)
# prediction at specified locations
loc <- with(h, runifpoint(20, Window(Bugs)))
p2 <- predict(fit, locations=loc)
plot(p2$trend)
# }
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