spatstat (version 1.63-0)

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

## Description

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

## Usage

`effectfun(model, covname, …, se.fit=FALSE, nvalues=256)`

## Arguments

model

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

covname

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.

se.fit

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

nvalues

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.

## Value

A data frame containing a column of values of the covariate and a column of values of the fitted trend. If `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 `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.

## Details

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 `se.fit=TRUE`, 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`.

`ppm`, `predict.ppm`, `fv.object`

## Examples

```# NOT RUN {
X <- copper\$SouthPoints
D <- distfun(copper\$SouthLines)
fit <- ppm(X ~ polynom(D, 5))
effectfun(fit)
plot(effectfun(fit, se.fit=TRUE))

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