spatstat.linnet (version 3.3-1)

auc.lpp: Area Under ROC Curve for Network Data

Description

Compute the AUC (area under the Receiver Operating Characteristic curve) for a point pattern on a network, or a fitted point process model on a network.

Usage

# S3 method for lpp
auc(X, covariate, ..., high = TRUE,
                     subset=NULL)
# S3 method for lppm
auc(X, ..., subset=NULL)

Value

Numeric. For auc.lpp, the result is a single number giving the AUC value.

For auc.lppm, the result is a numeric vector of length 2 giving the AUC value and the theoretically expected AUC value for this model.

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.

...

Arguments passed to roc, and arguments passed to as.mask controlling the pixel resolution for calculations.

high

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

subset

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

Author

Adrian Baddeley , Ege Rubak and Suman Rakshit .

Details

The generic auc computes the AUC, the area under the curve of the Receiver Operating Characteristic. The ROC curve itself is computed by the generic roc.

The functions auc.lpp and auc.lppm are methods for auc for point patterns on a linear network (class "lpp") and fitted point process models on a linear network (class "lppm").

For a point pattern X and a covariate Z, the AUC is a numerical index that measures the ability of the covariate to separate the spatial domain into areas of high and low density of points. Let \(x_i\) be a randomly-chosen data point from X and \(U\) a randomly-selected location in the study region. The AUC is the probability that \(Z(x_i) > Z(U)\) assuming high=TRUE. That is, AUC is the probability that a randomly-selected data point has a higher value of the covariate Z than does a randomly-selected spatial location. The AUC is a number between 0 and 1. A value of 0.5 indicates a complete lack of discriminatory power.

For a fitted point process model X, the AUC measures the ability of the fitted model intensity to separate the spatial domain into areas of high and low density of points. Suppose \(\lambda(u)\) is the intensity function of the model. The AUC is the probability that \(\lambda(x_i) > \lambda(U)\). That is, AUC is the probability that a randomly-selected data point has higher predicted intensity than does a randomly-selected spatial location. The AUC is not a measure of 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

roc.

auc, auc.ppm.

youden.

Examples

  Crimes <- unmark(chicago)
  fit <- lppm(Crimes ~ x)
  auc(fit)
  auc(Crimes, "x")