roc.plot: Relative operating characteristic curve.

Description

This function creates Receiver Operating Characteristic (ROC) plots for one or more models. A ROC curve plots the false alarm rate against the hit rate for a probablistic forecast for a range of thresholds. The area under the curve is viewed as a measure of a forecast's accuracy. A measure of 1 would indicate a perfect model. A measure of 0.5 would indicate a random forecast.

Usage

# S3 method for default
roc.plot(x, pred, thresholds = NULL, binormal =
FALSE,   legend = FALSE, leg.text = NULL,  plot = "emp", CI = FALSE,
n.boot = 1000, alpha = 0.05, tck = 0.01, plot.thres = seq(0.1,
0.9, 0.1), show.thres = TRUE, main = "ROC Curve", xlab = "False Alarm Rate",
ylab = "Hit Rate", extra = FALSE,  ...)
# S3 method for prob.bin
roc.plot(x, ...)

Value

If assigned to an object, the following values are reported.

plot.data: The data used to generate the ROC plots. This is a array. Column headers are thresholds, empirical hit and false alarm rates, and binormal hit and false alarm rates. Each model is depicted on an array indexed by the third dimension.
roc.vol: The areas under the ROC curves. By default,this is printed on the plots. Areas and p-values are calculated with and without adjustments for ties along with the p-value for the area. These values are calculated using roc.area. The fifth column contains the area under the binormal curve, if binormal is selected.
A.boot: If confidence intervals are calculated, the area under the ROC curve are returned.

Arguments

x: A binary observation (coded {0, 1 } ) or a verification object.
pred: A probability prediction on the interval [0,1]. If multiple models are compared, this may be a matrix where each column represents a different prediction.
thresholds: Thresholds may be provided. These thresholds will be used to calculate the hit rate ($h$) and false alarm rate ($f$). If thresholds is NULL, all unique thresholds are used as a threshold. Alternatively, if the number of bins is specified, thresholds will be calculated using the specified numbers of quantiles.

binormal: If TRUE, in addition to the empirical ROC curve, the binormal ROC curve will be calculated. To get a plot draw, plot must be either ``binorm'' or ``both''.
legend: Binomial. Defaults to FALSE indicating whether a legend should be displayed.
leg.text: Character vector for legend. If NULL, models are labeled ``Model A", ``Model B",...
plot: Either ``emp'' (default), ``binorm'' or ``both'' to determine which plot is shown. If set to NULL, a plot is not created
CI: Confidence Intervals. Calculated by bootstrapping the observations and prediction, then calculating PODy and PODn values.
n.boot: Number of bootstrap samples.
alpha: Confidence interval. By default = 0.05
tck: Tick width on confidence interval whiskers.
plot.thres: By default, displays the threshold levels on the ROC diagrams. To surpress these values, set it equal to NULL. If confidence intervals (CI) is set to TRUE, levels specified here will determine where confidence interval boxes are placed.
show.thres: Show thresholds for points indicated by plot.thres. Defaults to TRUE.
main: Title for plot.
xlab, ylab: Plot axes labels. Defaults to ``Hit Rate'' and ``False Alarm Rate'', for the y and x axes respectively.
extra: Extra text describing binormal and empirical lines.
...: Additional plotting options.

Author

Matt Pocernich

References

Mason, I. (1982) ``A model for assessment of weather forecasts,'' Aust. Met. Mag 30 (1982) 291-303.

Mason, S.J. and N.E. Graham. (2002) ``Areas beneath the relative operating characteristics (ROC) and relative operating levels (ROL) curves: Statistical significance and interpretation, '' Q. J. R. Meteorol. Soc. 128 pp. 2145-2166.

Swets, John A. (1996) Signal Detection Theory and ROC Analysis in Psychology and Diagnostics, Lawrence Erlbaum Associates, Inc.

Examples

Run this code

# Data from Mason and Graham article.

a<- c(0,0,0,1,1,1,0,1,1,0,0,0,0,1,1)
b<- c(.8, .8, 0, 1,1,.6, .4, .8, 0, 0, .2, 0, 0, 1,1)
c<- c(.928,.576, .008, .944, .832, .816, .136, .584, .032, .016, .28, .024, 0, .984, .952)

A<- data.frame(a,b,c)
names(A)<- c("event", "p1", "p2")

## for model with ties
roc.plot(A$event, A$p1)

## for model without ties
roc.plot(A$event, A$p2)

### show binormal curve fit.

roc.plot(A$event, A$p2, binormal = TRUE)
if (FALSE) {
# icing forecast

data(prob.frcs.dat)
A <- verify(prob.frcs.dat$obs, prob.frcs.dat$frcst/100)
roc.plot(A, main = "AWG Forecast")


# plotting a ``prob.bin'' class object.
obs<- round(runif(100))
pred<- runif(100)

A<- verify(obs, pred, frcst.type = "prob", obs.type = "binary")

roc.plot(A, main = "Test 1", binormal = TRUE, plot = "both")

## show confidence intervals.  MAY BE SLOW
roc.plot(A, threshold = seq(0.1,0.9, 0.1), main = "Test 1", CI = TRUE,
alpha = 0.1)

###   example from forecast verification website. 
data(pop)
d <- pop.convert() ## internal function used to make binary observations for the pop figure.
### note the use of bins = FALSE !!
 mod24 <- verify(d$obs_norain, d$p24_norain, bins = FALSE)

 mod48 <- verify(d$obs_norain, d$p48_norain, bins = FALSE)

roc.plot(mod24, plot.thres = NULL)
lines.roc(mod48, col = 2, lwd = 2)
leg.txt <- c("24 hour forecast", "48 hour forecast")
legend( 0.6, 0.4, leg.txt, col = c(1,2), lwd = 2)
}

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