auc(X, ...)## S3 method for class 'ppp':
auc(X, covariate, \dots, high = TRUE)
## S3 method for class 'ppm':
auc(X, \dots)
"ppp"
)
or fitted point process model (object of class "ppm"
).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,
roc
fit <- ppm(swedishpines ~ x+y)
auc(fit)
auc(swedishpines, "x")
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