Area Under ROC Curve
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, ...)
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).
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
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.
fit <- ppm(swedishpines ~ x+y) auc(fit) auc(swedishpines, "x")
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