R: Prediction for Fitted Multiple Point Process Model

predict.mppm {spatstat} | R Documentation

## Prediction for Fitted Multiple Point Process Model

### Description

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 class '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.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Ida-Maria Sintorn and Leanne Bischoff. Implemented by Adrian Baddeley Adrian.Baddeley@curtin.edu.au

Rolf Turner r.turner@auckland.ac.nz

and Ege Rubak rubak@math.aau.dk

### 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

`mppm`, `fitted.mppm`, `hyperframe`

### Examples

      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)

[Package spatstat version 1.54-0 Index]