# 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 ppp
auc(X, covariate, …, high = TRUE)

# S3 method for ppm
auc(X, …)

# S3 method for kppm
auc(X, …)

# S3 method for lpp
auc(X, covariate, …, high = TRUE)

# S3 method for lppm
auc(X, …)

##### Arguments

- X
Point pattern (object of class

`"ppp"`

or`"lpp"`

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

or`"kppm"`

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.- …
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

Numeric.
For `auc.ppp`

and `auc.lpp`

, the result is a single number
giving the AUC value.
For `auc.ppm`

, `auc.kppm`

and `auc.lppm`

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

##### References

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

##### Examples

```
# NOT RUN {
fit <- ppm(swedishpines ~ x+y)
auc(fit)
auc(swedishpines, "x")
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*