roc.ppm: Receiver Operating Characteristic For Fitted Point Process...

In spatstat.model: Parametric Statistical Modelling and Inference for the 'spatstat' Family

Receiver Operating Characteristic For Fitted Point Process Model

Description

Computes the Receiver Operating Characteristic curve for a fitted point process model.

Usage

## S3 method for class 'ppm'
roc(X, covariate=NULL,
                  ..., baseline=NULL, high=TRUE,
                  method = "raw",
                  CI = "none", alpha=0.05,
                  leaveoneout=FALSE, subset=NULL)

## S3 method for class 'slrm'
roc(X, covariate=NULL,
                  ..., baseline=NULL, high=TRUE,
                  method = "raw",
                  CI = "none", alpha=0.05,
                  leaveoneout=FALSE, subset=NULL)

## S3 method for class 'kppm'
roc(X, covariate=NULL,
                  ..., baseline=NULL, high=TRUE,
                  method = "raw",
                  CI = "none", alpha=0.05,
                  leaveoneout=FALSE, subset=NULL)

## S3 method for class 'dppm'
roc(X, covariate=NULL,
                  ..., baseline=NULL, high=TRUE,
                  method = "raw",
                  CI = "none", alpha=0.05,
                  leaveoneout=FALSE, subset=NULL)

Arguments

X	Fitted point process model (object of class "ppm", "kppm" or "dppm") or fitted spatial logistic regression model (object of class "slrm").
covariate	Spatial covariate. Either a function(x,y), a pixel image (object of class "im"), or one of the strings "x" or "y" indicating the Cartesian coordinates. Traditionally omitted when X is a fitted model.
...	Arguments passed to as.mask controlling the pixel resolution for calculations.
baseline	Optional. A spatial object giving a baseline intensity. Usually a function(x,y) or a pixel image (object of class "im") giving the baseline intensity at any location within the observation window. Alternatively a point pattern (object of class "ppp") with the locations of the reference population.
high	Logical value indicating whether the threshold operation should favour high or low values of the covariate.
method	The method or methods that should be used to estimate the ROC curve. A character vector: current choices are "raw", "monotonic", "smooth" and "all". See Details.
CI	Character string (partially matched) specifying whether confidence intervals should be computed, and for which method. See Details.
alpha	Numeric value between 0 and 1. The confidence intervals will have confidence level 1-alpha. The default gives 95% confidence intervals.
leaveoneout	Logical value specifying whether the fitted intensity or presence probability should be computed by the leave-one-out procedure (see Details). It is also possible to specify leaveoneout=c(TRUE,FALSE) so that both versions are calculated.
subset	Optional. A spatial window (object of class "owin") specifying a subset of the data, from which the ROC should be calculated.

Details

The generic function roc computes the Receiver Operating Characteristic (ROC) curve. The area under the ROC is computed by auc.

For a fitted model X and a spatial covariate Z, two ROC curves are computed and plotted together. The first curve is obtained by extracting the original point pattern data to which the model X was fitted, and computing the raw ROC curve as described above. The second curve is the predicted value of the raw curve according to the model, as described in \rocpapercite.

For a fitted model X, if covariate is missing or NULL, the default is to take the covariate to be the fitted probability of presence (if X is a spatial logistic regression model) or the fitted point process intensity (for other models). This is the standard use of the ROC curve in spatial ecology. The ROC shows the ability of the fitted model to separate the spatial domain into areas of high and low density of points. For a fitted spatial logistic regression model, similarly the ROC shows the ability of the fitted presence probabilities to segregate the spatial domain into pixels with high and low probability of presence. The ROC is not a diagnostic for the goodness-of-fit of the model (Lobo et al, 2007, page 146; \rocpapercitealp, Sections 5.3.3 and 6.5).

If leaveoneout=TRUE, then the fitted presence probability or fitted intensity is computed using a leave-one-out procedure proposed in \rocpapercite.

• leave-one-point-out: if X is a point process model (class 'ppm', 'kppm', 'dppm' or 'lppm') then the intensity value at each data point X[i] is computed by removing this data point from the point pattern, re-fitting the model to the reduced point pattern X[-i], and computing the intensity of this modified model at the query point X[i].

• leave-one-pixel-out: if X is a spatial logistic regression model (class 'slrm', then the presence probability at each pixel is computed by removing this pixel from the data, re-fitting the model to the reduced data, and predicting the presence probability at the pixel in question.

The leave-one-out calculation reduces the effects of overfitting. It is possible to specify leaveoneout=c(TRUE,FALSE) to obtain the results with and without the leave-one-out calculation.

There are currently three methods to estimate the ROC curve:

"raw"

uses the raw empirical spatial cummulative distribution function of the covariate.

"monotonic"

uses a monotonic regression to estimate the relation between the covariate and the point process intensity and then calculates the ROC from that. This corresponds to a either a convex minorant or a concave majorant of the raw ROC curve.

"smooth"

uses a smooth estimate of the relation between the covariate and the point process intensity and then calculates the ROC from that. See roc.rhohat for details.

"all"

uses all of the above methods.

Confidence bands for the ROC curve are not computed by default. If CI is one of the strings 'raw', 'monotonic' or 'smooth', then pointwise 95% confidence intervals for the true ROC curve will be computed based on the raw, monotonic or smooth estimates, respectively. The confidence level is 1-alpha, so that for example alpha=0.01 would give 99% confidence intervals.

Value

Function value table (object of class "fv") which can be plotted to show the ROC curve. Also belongs to class "roc".

Author(s)

\rocketAuthors

.

References

\rocpaper

.

Lobo, J.M., \Jimenez-Valverde, A. and Real, R. (2007) AUC: a misleading measure of the performance of predictive distribution models. Global Ecology and Biogeography 17(2) 145–151.

Nam, B.-H. and D'Agostino, R. (2002) Discrimination index, the area under the ROC curve. Pages 267–279 in Huber-Carol, C., Balakrishnan, N., Nikulin, M.S. and Mesbah, M., Goodness-of-fit tests and model validity, \Birkhauser, Basel.

See Also

roc, roc.lpp, roc.rhohat.

addROC, dropROC, addapply, dropply for adding or removing variables from a model.

auc

Examples

  gold <- rescale(murchison$gold, 1000, "km")
  faults <- rescale(murchison$faults, 1000, "km")
  dfault <- distfun(faults)
  
  fit <- ppm(gold ~ dfault)
  plot(roc(fit, method="all"))

  ## compare raw estimates with and without using leave-one-out intensity
  plot(roc(fit, leaveoneout=c(FALSE, TRUE)))

spatstat.model documentation built on Nov. 28, 2025, 9:06 a.m.