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 class '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 class 'prob.bin':
roc.plot(x, \dots)

Arguments

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 sp

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

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

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.

Value

If assigned to an object, the following values are reported.
plot.dataThe 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.volThe 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.bootIf confidence intervals are calculated, the area under the ROC curve are returned.

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)
# 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)