auc | R Documentation |

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

auc(X, ...) ## S3 method for class 'ppp' auc(X, covariate, ..., high = TRUE) ## S3 method for class 'ppm' auc(X, ...) ## S3 method for class 'kppm' auc(X, ...) ## S3 method for class 'slrm' auc(X, ...)

`X` |
Point pattern (object of class |

`covariate` |
Spatial covariate. Either a |

`...` |
Arguments passed to |

`high` |
Logical value indicating whether the threshold operation should favour high or low values of the covariate. |

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 *λ(u)* is the intensity function of the model.
The AUC is the probability that
*λ(x[i]) > λ(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).

(For spatial logistic regression models (class `"slrm"`

)
replace “intensity” by “probability of presence”
in the text above.)

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.

.

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`

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

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