# predict.mppm

##### Prediction for Fitted Multiple Point Process Model

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.

##### Usage

```
# S3 method for mppm
predict(object, ..., newdata = NULL, type = c("trend", "cif"),
ngrid = 40, locations=NULL, verbose=FALSE)
```

##### Arguments

- object
The fitted model. An object of class

`"mppm"`

obtained from`mppm`

.- …
Ignored.

- newdata
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
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.- ngrid
Dimensions of the grid of spatial locations at which prediction will be performed (if

`locations=NULL`

). An integer or a pair of integers.- locations
Optional. The locations at which predictions should be performed. A list of point patterns, with one entry for each row of

`newdata`

.- verbose
Logical flag indicating whether to print progress reports.

##### Details

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.

##### Value

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.

##### References

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.

##### See Also

##### Examples

```
# 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)
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*