spatstat.linnet (version 3.3-1)

roc.lpp: Receiver Operating Characteristic for Data on a Network

Description

Computes the Receiver Operating Characteristic curve for a point pattern on a linear network or a fitted point process model on a linear network.

Usage

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

Value

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

Arguments

X

Point pattern on a network (object of class "lpp") or fitted point process model on a network (object of class "lppm").

covariate

Spatial covariate. Either a function(x,y), a pixel image (object of class "im" or "linim"), 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" or "linim") giving the baseline intensity at any location on the network. Alternatively a point pattern on the network (object of class "lpp") giving the locations of the reference population.

high

Logical value indicating whether the threshold operation should favour high or low values of the covariate.

weights

Optional. Numeric vector of weights attached to the data points.

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.

subset

Optional. A spatial window (object of class "owin") specifying a subset of the data, from which the ROC should be calculated.

leaveoneout

Logical value specifying (for roc.lppm) whether the fitted intensity of the model at each of the original data points should be computed by the leave-one-out procedure (i.e. by removing the data point in question from the point pattern, re-fitting the model to the reduced point pattern, and computing the intensity of this modified model at the point in question) as described in Baddeley et al (2025). It is also possible to specify leaveoneout=c(TRUE,FALSE) so that both versions are calculated.

Author

Adrian Baddeley , Rolf Turner and Ege Rubak .

Details

The command roc computes the Receiver Operating Characteristic curve. The area under the ROC is computed by auc.

The function roc is generic, with methods for point patterns, fitted point process models and other kinds of data.

This help file describes the methods for classes "lpp" and "lppm".

For a point pattern X and a covariate Z, the ROC is a plot showing the ability of the covariate to separate the spatial domain into areas of high and low density of points. For each possible threshold \(z\), the algorithm calculates the fraction \(a(z)\) of area in the study region where the covariate takes a value greater than \(z\), and the fraction \(b(z)\) of data points for which the covariate value is greater than \(z\). The ROC is a plot of \(b(z)\) against \(a(z)\) for all thresholds \(z\).

For a fitted point process model, the ROC shows the ability of the fitted model intensity to separate the spatial domain into areas of high and low density of points. The ROC is not a diagnostic for the goodness-of-fit of the model (Lobo et al, 2007).

References

Baddeley, A., Rubak, E., Rakshit, S. and Nair, G. (2025) ROC curves for spatial point patterns and presence-absence data. tools:::Rd_expr_doi("10.48550/arXiv.2506.03414")..

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

auc

Examples

  plot(roc(spiders, "x"))
  fit <- lppm(spiders ~ x)
  plot(roc(fit))