roc.area: Area under curve (AUC) calculation for Response Operating Characteristic curve.

Description

This function calculates the area underneath a ROC curve following the process outlined in Mason and Graham (2002). The p-value produced is related to the Mann-Whitney U statistics. The p-value is calculated using the wilcox.test function which automatically handles ties and makes approximations for large values.

The p-value addresses the null hypothesis $H_o:$ The area under the ROC curve is 0.5 i.e. the forecast has no skill.

Usage

roc.area(obs, pred)

Arguments

obs

A binary observation (coded {0, 1 } ).

pred

A probability prediction on the interval [0,1].

Value

A: Area under ROC curve, adjusted for ties in forecasts, if present
n.total: Total number of records
n.events: Number of events
n.noevents: Number of non-events
p.value: Unadjusted p-value

References

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

Examples

Run this code

a<- c(1981, 1982, 1983, 1984, 1985, 1986, 1987, 1988, 1989, 1990,
 1991, 1992, 1993, 1994, 1995)
b<- c(0,0,0,1,1,1,0,1,1,0,0,0,0,1,1)
c<- c(.8, .8, 0, 1,1,.6, .4, .8, 0, 0, .2, 0, 0, 1,1)
d<- c(.928,.576, .008, .944, .832, .816, .136, .584, .032, .016, .28, .024, 0, .984, .952)

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

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

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

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