auc(X, ...)
"auc"(X, covariate, ..., high = TRUE)
"auc"(X, ...)
"auc"(X, ...)
"auc"(X, covariate, ..., high = TRUE)
"auc"(X, ...)"ppp" or "lpp")
or fitted point process model (object of class "ppm"
or "kppm" or "lppm").
function(x,y),
a pixel image (object of class "im"), or
one of the strings "x" or "y" indicating the
Cartesian coordinates.
as.mask controlling the
pixel resolution for calculations.
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).
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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