predict.ppm

Prediction from a Fitted Point Process Model

Given a fitted point process model obtained by ppm, evaluate the spatial trend or the conditional intensity of the model at new locations.

Usage

## S3 method for class 'ppm':
predict(object, window, ngrid=NULL, locations=NULL,
   covariates=NULL, type="trend", X=data.ppm(object),
   ..., new.coef=NULL, check=TRUE, repair=TRUE)

Details

This function computes the spatial trend and the conditional intensity of a fitted spatial point process model, and the standard error of the estimate of spatial trend. 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 model-fitting algorithm ppm. 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.

The default action is to create a rectangular grid of points in the observation window of the data point pattern, and evaluate the spatial trend at these locations.

The argument type specifies the values that are computed: [object Object],[object Object],[object Object] Note that the ``spatial trend'' is the same as the intensity function if the fitted model object is a Poisson point process. However, if the model is not a Poisson process, then the ``spatial trend'' is 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 $\beta$, while the intensity is a smaller value that is not easy to compute. ]

The spatial locations where predictions are required, are determined by the (incompatible) arguments ngrid and locations.

• If the argumentngridis present, then predictions are performed at a rectangular grid of locations in the windowwindow. The result of prediction will be a pixel image or images.
• Iflocationsis present, then predictions will be performed at the spatial locations given by this dataset. These may be an arbitrary list of spatial locations, or they may be a rectangular grid. The result of prediction will be either a numeric vector or a pixel image or images.
• If neitherngridnorlocationsis given, thenngridis assumed. The value ofngriddefaults tospatstat.options("npixel"), which is initialised to 128 whenspatstatis loaded.

If locations is a point pattern (object of class "ppp"), then prediction will be performed at the points of the point pattern. The result of prediction will be a vector of predicted values, one value for each point. If the model is a marked point process, then locations should be a marked point pattern, with marks of the same kind as the model; prediction will be performed at these marked points. The result of prediction will be a vector of predicted values, one value for each (marked) point.

If locations is a data frame or list, then it must contain vectors locations$x and locations$y specifying the $x,y$ coordinates of the prediction locations. Additionally, if the model is a marked point process, then locations must also contain a factor locations$marks specifying the marks of the prediction locations. These vectors must have equal length. The result of prediction will be a vector of predicted values, of the same length. If locations is a binary image mask, then prediction will be performed at each pixel in this binary image where the pixel value is TRUE (in other words, at each pixel that is inside the window). If the fitted model is an unmarked point process, then the result of prediction will be an image. If the fitted model is a marked point process, then prediction will be performed for each possible value of the mark at each such location, and the result of prediction will be a list of images, one for each mark value. The argument covariates gives the values of any spatial covariates at the prediction locations. If the trend formula in the fitted model involves spatial covariates (other than the Cartesian coordinates x, y) then covariates is required.

The format and use of covariates are analogous to those of the argument of the same name in ppm. It is either a data frame or a list of images. If covariates is a list of images, then the names of the entries should correspond to the names of covariates in the model formula trend. Each entry in the list must be an image object (of class "im", see im.object). The software will look up the pixel values of each image at the quadrature points.

If covariates is a data frame, then the ith row of covariates is assumed to contain covariate data for the ith location. When locations is a data frame, this just means that each row of covariates contains the covariate data for the location specified in the corresponding row of locations. When locations is a binary image mask, the row covariates[i,] must correspond to the location x[i],y[i] where x = as.vector(raster.x(locations)) and y = as.vector(raster.y(locations)).

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.

Warnings

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 covariates argument and the function crashes, it is advisable to start by checking that all the conditions listed above are satisfied.

References

Baddeley, A. and Turner, R. Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42 (2000) 283--322. Berman, M. and Turner, T.R. Approximating point process likelihoods with GLIM. Applied Statistics 41 (1992) 31--38.

See Also

ppm, ppm.object, plot.ppm, print.ppm, fitted.ppm, spatstat.options

Aliases

• predict.ppm

Examples

data(cells)
  <testonly>op <- spatstat.options(npixel=32)</testonly>
  m <- ppm(cells, ~ polynom(x,y,2), Strauss(0.05))
  trend <- predict(m, type="trend")
  image(trend)
  points(cells)
  cif <- predict(m, type="cif")
  persp(cif)
  data(japanesepines)
  mj <- ppm(japanesepines, ~harmonic(x,y,2))
  se <- predict(mj, type="se")

  # prediction at arbitrary locations
  predict(mj, locations=data.frame(x=0.3, y=0.4))

  X <- runifpoint(5, as.owin(japanesepines))
  predict(mj, locations=X)
  predict(mj, locations=X, type="se")

  # multitype
  data(amacrine)
  ma <- ppm(amacrine, ~marks,
     MultiStrauss(c("off","on"),matrix(0.06, 2, 2)))
  Z <- predict(ma)
  Z <- predict(ma, type="cif")
  predict(ma, locations=data.frame(x=0.8, y=0.5,marks="on"), type="cif")

  <testonly>spatstat.options(op)</testonly>