Compute the AUC (area under the Receiver Operating Characteristic curve) for a point pattern or other data.
auc(X, ...)# S3 method for ppp
auc(X, covariate, ..., high = TRUE, subset=NULL)
# S3 method for roc
auc(X, ...)
# S3 method for cdftest
auc(X, ..., high=TRUE)
# S3 method for bermantest
auc(X, ..., high=TRUE)
# S3 method for im
auc(X, covariate, ..., high=TRUE)
Numeric.
For auc.ppp, auc.cdftest, auc.bermantest
and auc.im, the result is a single number
giving the AUC value.
For auc.roc, the result is a numeric vector with one entry
for each column of function values of X.
Point pattern (object of class "ppp" or "lpp")
or fitted point process model
(object of class "ppm" or "kppm" or "lppm")
or fitted spatial logistic regression model
(object of class "slrm")
or an ROC curve
(object of class "roc" computed by roc).
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.
Arguments passed to roc,
and arguments passed to as.mask
controlling the pixel resolution for calculations,
Logical value indicating whether the threshold operation should favour high or low values of the covariate.
Optional. A spatial window (object of class "owin")
specifying a subset of the data, for which the AUC should be
calculated.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Ege Rubak rubak@math.aau.dk and Suman Rakshit Suman.Rakshit@curtin.edu.au.
This command computes the AUC, the area under the Receiver Operating
Characteristic curve. The ROC itself is computed by roc.
The function auc is generic. There are methods for
point patterns, fitted point process models, and many other kinds of
objects.
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.
Methods for calculating AUC for a point process model or
spatial logistic regression model are described in
auc.ppm and auc.lpp.
Some other kinds of objects in spatstat contain sufficient data to
compute the AUC. These include the objects returned by
rhohat,
cdf.test and berman.test. Methods are
provided here to compute the AUC from these objects.
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.
roc,
auc.ppm,
auc.lpp.
youden.