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.

- X
Point pattern (object of class

`"ppp"`

or`"lpp"`

) or fitted point process model (object of class`"ppm"`

,`"kppm"`

,`"slrm"`

or`"lppm"`

).- 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.- high
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`