Compute the AUC (area under the Receiver Operating Characteristic curve) for an observed point pattern.
auc(X, ...)# S3 method for ppp
auc(X, covariate, ..., high = TRUE)
Numeric.
For auc.ppp and auc.lpp, the result is a single number
giving the AUC value.
Point pattern (object of class "ppp" or "lpp")
or fitted point process model (object of class "ppm",
"kppm", "slrm" or "lppm").
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.
Logical value indicating whether the threshold operation should favour high or low values of the covariate.
Arguments passed to as.mask controlling the
pixel resolution for calculations.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
This command computes the AUC, the area under the Receiver Operating
Characteristic curve. The ROC itself is computed by roc.
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.
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