roc.area {verification} | R Documentation

## 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

### Note

This function is used internally in the `roc.plot` command to calculate areas.

### Author(s)

Matt Pocernich <pocernic@rap.ucar.edu>

### References

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. 30 (1982) 291-303.

### See Also

`roc.plot`, `verify`, `wilcox.test`

### Examples

    # Data used from Mason and Graham (2002).
    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)

[Package verification version 1.20 Index]