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, ..., se.fit=FALSE)
- A fitted point process model (object of class
- The name of the covariate. A character string.
- 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.
model should be an object of class
"ppm" representing a point process model fitted to
point pattern data.
The model's trend formula should involve a spatial covariate
covname. This could be
representing one of the Cartesian coordinates.
More commonly the covariate
is another, external variable that was supplied when fitting the model.
effectfun computes the fitted trend
of the point process
model as a function of the covariate
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
then these covariates will be held fixed. Values for
these other covariates must be provided as arguments
effectfun in the form
se.fit=TRUE, the algorithm also calculates
the asymptotic standard error of the fitted trend,
and a (pointwise) asymptotic 95% confidence interval for the
This command is just a wrapper for the prediction method
predict.ppm. For more complicated computations
about the fitted intensity, use
- A data frame containing a column of values of the covariate and a column
of values of the fitted trend.
se.fit=TRUE, there are 3 additional columns containing the standard error and the upper and lower limits of a confidence interval.
If the covariate named
covnameis 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.
data(copper) X <- copper$SouthPoints D <- distmap(copper$SouthLines) fit <- ppm(X, ~polynom(Z, 5), covariates=list(Z=D)) plot(effectfun(fit, "Z")) plot(effectfun(fit, "Z", se.fit=TRUE), shade=c("hi", "lo")) fit <- ppm(X, ~x + polynom(Z, 5), covariates=list(Z=D)) plot(effectfun(fit, "Z", x=20)) fit <- ppm(X, ~x) plot(effectfun(fit, "x"))