# auc

##### Area Under ROC Curve

Compute the AUC (area under the Receiver Operating Characteristic curve) for a fitted point process model.

- Keywords
- spatial

##### Usage

`auc(X, ...)`## S3 method for class 'ppp':
auc(X, covariate, \dots, high = TRUE)

## S3 method for class 'ppm':
auc(X, \dots)

##### Arguments

- X
- Point pattern (object of class
`"ppp"`

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

). - 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. - ...
- 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.

##### Details

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.
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).

##### Value

- A numeric vector of length 2 giving the AUC value and the theoretically expected AUC value for this model.

##### References

Lobo, J.M.,
*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*,

##### See Also

##### Examples

```
fit <- ppm(swedishpines ~ x+y)
auc(fit)
auc(swedishpines, "x")
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*