Prediction from a Fitted Point Process Model

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

predict.ppm(object, window, ngrid=NULL, locations=NULL,
   covariates=NULL, type="trend", ...)
A fitted point process model, typically obtained from the model-fitting algorithm ppm. An object of class "ppm" (see ppm.object).
window delimiting the locations where predictions should be computed. Defaults to the window of the original data used to fit the model object.
dimensions (either (ngrid[1] by ngrid[2] or ngrid by ngrid) of a rectangular grid of locations inside window where predictions should be computed. (Incompatible with locati
data giving the $x,y$ coordinates (and marks, if required) at which predictions should be computed. Either a data frame or a binary image mask. (Incompatible with ngrid)
Values of external covariates required by the model. Either a data frame or a list of images. See Details.
character string. Indicates which property of the fitted model should be predicted. Options are "trend" for the spatial trend, and "cif" or "lambda" for the conditional intensity.

This function computes the spatial trend and the conditional intensity of a fitted spatial point process model. 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 and conditional intensity at these locations.

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 data point pattern $X$.

If the argument ngrid is present, then predictions are performed at an ngrid by ngrid pixel grid of locations in the window window. The result of prediction will be a pixel image or images. If locations is present, then predictions will be performed at the spatial locations given by this dataset. The result of prediction will be either a vector of values or a pixel image or a list of images, depending on the format of locations.

The argument locations may be either a data frame or list specifying arbitrary locations, or a binary image mask (an object of class "owin" with type "mask") specifying (a subset of) a rectangular grid of locations.

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. If neither ngrid nor locations is given, then ngrid is assumed. It defaults to 50.

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.


  • If locations is given and is a data frame: a vector of predicted values for the spatial locations (and marks, if required) given in locations.

    If ngrid is given, or if locations is given and is a binary image mask: If object is an unmarked point process, the result is an image object (of class "im", see im.object) containing the predictions. If object is a multitype point process, the result is a list of images, containing the predictions for each type at the same grid of locations.

    The ``predicted values'' are either values of the spatial trend (if type="trend") or values of the conditional intensity (if type="cif" or type="lambda").


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.


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

  • predict.ppm
  m <- ppm(cells, ~ polynom(x,y,2), Strauss(0.05), rbord=0.05)
  trend <- predict(m, type="trend")
  cif <- predict(m, type="cif")
Documentation reproduced from package spatstat, version 1.6-5, License: GPL version 2 or newer

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