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.
Optional. New values of the covariates, for which the predictions should be computed. See Details.
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/or 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.
The point process model that is described by an mppm object
may be a different point process for each row of the original
hyperframe of data. This occurs if
the model formula includes the variable id (representing
row number) or if the model has a different interpoint interaction on
each row.
If the point process model is different on each row of the original data, then either
newdata is missing. Predictions are computed for
each row of the original data using the point process model
that applies on each row.
newdata must have the same number of rows
as the original data. Each row of newdata is assumed
to be a replacement for the corresponding row of the original data.
The prediction for row i of newdata
will be computed for the point process model that applies to row i
of the original data.
newdata must include a column called id
specifying the row number, and therefore identifying which
of the point process models should apply.
The predictions for row i
of newdata will be computed for the point process model that applies
to row k of the original data, where k = newdata$id[i].
This function computes the spatial trend and the conditional intensity of a spatial point process model that has been fitted to several spatial point patterns. See Chapter 16 of Baddeley, Rubak and Turner (2015) 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 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.
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, and the results are returned as mark values attached to the
locations. The result is a hyperframe containing columns
called trend and/or cif. The column called trend
contains marked point patterns in which the point locations are
the locations and the mark value is the predicted trend.
The column called cif
contains marked point patterns in which the point locations are
the locations and the mark value is the predicted conditional
intensity.
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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