spatstat (version 1.63-0)

effectfun: Compute Fitted Effect of a Spatial Covariate in a Point Process Model


Compute the trend or intensity of a fitted point process model as a function of one of its covariates.


effectfun(model, covname, …,, nvalues=256)



A fitted point process model (object of class "ppm", "kppm", "lppm", "dppm", "rppm" or "profilepl").


The name of the covariate. A character string. (Needed only if the model has more than one covariate.)

The fixed values of other covariates (in the form name=value) if required.

Logical. If TRUE, asymptotic standard errors of the estimates will be computed, together with a 95% confidence interval.


Integer. The number of values of the covariate (if it is numeric) for which the effect function should be evaluated. We recommend at least 256.


A data frame containing a column of values of the covariate and a column of values of the fitted trend. If, there are 3 additional columns containing the standard error and the upper and lower limits of a confidence interval.

If the covariate named covname is numeric (rather than a factor or logical variable), the return value is also of class "fv" so that it can be plotted immediately.

Trend and intensity

For a Poisson point process model, the trend is the same as the intensity of the point process. For a more general Gibbs model, the trend is the first order potential in the model (the first order term in the Gibbs representation). In Poisson or Gibbs models fitted by ppm, the trend is the only part of the model that depends on the covariates.

Determinantal point process models with fixed intensity

The function dppm which fits a determinantal point process model allows the user to specify the intensity lambda. In such cases the effect function is undefined, and effectfun stops with an error message.


The object model should be an object of class "ppm", "kppm", "lppm", "dppm", "rppm" or "profilepl" representing a point process model fitted to point pattern data.

The model's trend formula should involve a spatial covariate named covname. This could be "x" or "y" representing one of the Cartesian coordinates. More commonly the covariate is another, external variable that was supplied when fitting the model.

The command effectfun computes the fitted trend of the point process model as a function of the covariate named covname. The return value can be plotted immediately, giving a plot of the fitted trend against the value of the covariate.

If the model also involves covariates other than covname, then these covariates will be held fixed. Values for these other covariates must be provided as arguments to effectfun in the form name=value.

If, the algorithm also calculates the asymptotic standard error of the fitted trend, and a (pointwise) asymptotic 95% confidence interval for the true trend.

This command is just a wrapper for the prediction method predict.ppm. For more complicated computations about the fitted intensity, use predict.ppm.

See Also

ppm, predict.ppm, fv.object


  X <- copper$SouthPoints
  D <- distfun(copper$SouthLines)
  fit <- ppm(X ~ polynom(D, 5))

  fitx <- ppm(X ~ x + polynom(D, 5))
  plot(effectfun(fitx, "D", x=20))
# }