Computes the Receiver Operating Characteristic curve for a fitted point process model.
# S3 method for ppm
roc(X, covariate=NULL,
..., baseline=NULL, high=TRUE,
method = "raw",
CI = "none", alpha=0.05,
leaveoneout=FALSE, subset=NULL)# S3 method for slrm
roc(X, covariate=NULL,
..., baseline=NULL, high=TRUE,
method = "raw",
CI = "none", alpha=0.05,
leaveoneout=FALSE, subset=NULL)
# S3 method for kppm
roc(X, covariate=NULL,
..., baseline=NULL, high=TRUE,
method = "raw",
CI = "none", alpha=0.05,
leaveoneout=FALSE, subset=NULL)
Function value table (object of class "fv")
which can be plotted to show the ROC curve.
Also belongs to class "roc".
Fitted point process model
(object of class "ppm" or "kppm")
or fitted spatial logistic regression model
(object of class "slrm").
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.
Traditionally omitted when X is a fitted model.
Arguments passed to as.mask controlling the
pixel resolution for calculations.
Optional. A spatial object giving a baseline intensity.
Usually a function(x,y) or
a pixel image (object of class "im")
giving the baseline intensity at
any location within the observation window.
Alternatively a point pattern (object of class "ppp")
with the locations of the reference population.
Logical value indicating whether the threshold operation should favour high or low values of the covariate.
The method or methods that should be used to estimate the ROC curve.
A character vector: current choices are
"raw", "monotonic", "smooth" and "all".
See Details.
Character string (partially matched) specifying whether confidence intervals should be computed, and for which method. See Details.
Numeric value between 0 and 1. The confidence intervals will have
confidence level 1-alpha. The default gives 95%
confidence intervals.
Logical value specifying (for roc.ppm, roc.slrm,
roc.kppm and roc.lppm) whether the fitted intensity
of the model at each of the original data points should be computed
by the leave-one-out procedure
(i.e. by removing the data point in question from the point pattern,
re-fitting the model to the reduced point pattern, and computing the
intensity of this modified model at the point in question)
as described in Baddeley et al (2025).
It is also possible to specify leaveoneout=c(TRUE,FALSE)
so that both versions are calculated.
Optional. A spatial window (object of class "owin")
specifying a subset of the data, from which the ROC should be
calculated.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Ege Rubak rubak@math.aau.dk and Suman Rakshit Suman.Rakshit@curtin.edu.au.
The generic function roc
computes the Receiver Operating Characteristic (ROC)
curve. The area under the ROC is computed by auc.
For a fitted model X
and a spatial covariate Z, two ROC curves are computed and
plotted together. The first curve is obtained by
extracting the original point pattern data to which the model X
was fitted, and computing the raw ROC curve as described above.
The second curve is the predicted value of the raw curve according to
the model, as described in Baddeley et al (2025).
For a fitted model X, if covariate
is missing or NULL, the default is to take the covariate
to be the fitted probability of presence (if X is a spatial
logistic regression model) or the fitted point process intensity
(for other models).
This is the standard use of the ROC curve in spatial ecology.
The ROC shows the ability of the
fitted model to separate the spatial domain
into areas of high and low density of points.
For a fitted spatial logistic regression model,
similarly the ROC shows the ability of the fitted presence
probabilities to segregate the spatial domain into pixels
with high and low probability of presence.
The ROC is not a diagnostic for the goodness-of-fit of the model
(Lobo et al, 2007).
There are currently three methods to estimate the ROC curve:
"raw"uses the raw empirical spatial cummulative distribution function of the covariate.
"monotonic"uses a monotonic regression to estimate the relation between the covariate and the point process intensity and then calculates the ROC from that. This corresponds to a either a convex minorant or a concave majorant of the raw ROC curve.
"smooth"uses a smooth estimate of the relation between the covariate and the point
process intensity and then calculates the ROC from that. See
roc.rhohat for details.
"all"uses all of the above methods.
If CI is one of the strings 'raw',
'monotonic' or 'smooth', then
pointwise 95% confidence intervals for the true ROC curve
will be computed based on the raw, monotonic or
smooth estimates, respectively.
The confidence level is 1-alpha, so that for example
alpha=0.01 would give 99% confidence intervals.
By default, confidence bands for the ROC curve are not computed.
Baddeley, A., Rubak, E., Rakshit, S. and Nair, G. (2025) ROC curves for spatial point patterns and presence-absence data. tools:::Rd_expr_doi("10.48550/arXiv.2506.03414")..
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,
roc.lpp,
roc.rhohat.
addROC,
dropROC,
addapply,
dropply for adding or removing variables from a model.
auc
gold <- rescale(murchison$gold, 1000, "km")
faults <- rescale(murchison$faults, 1000, "km")
dfault <- distfun(faults)
fit <- ppm(gold ~ dfault)
plot(roc(fit, method="all"))
## compare raw estimates with and without using leave-one-out intensity
plot(roc(fit, leaveoneout=c(FALSE, TRUE)))
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