auc {PresenceAbsence}

Area Under the Curve

Description

auc calculates the area under the ROC curve approximated with a Mann-Whitney U statistic, and (optionally) the associated standard deviation.

Usage

auc(DATA, st.dev = TRUE, which.model = 1, na.rm = FALSE)

Arguments

DATA

a matrix or dataframe of observed and predicted values where each row represents one plot and where columns are:

			DATA[,1]	plot ID	text
			DATA[,2]	observed values	zero-one values
			DATA[,3]	predicted probabilities from first model	numeric (between 0 and 1)
			DATA[,4]	predicted probabilities from second model, etc...

st.dev

a logical indicating whether the associated standard deviation should be calculated

which.model

a number indicating which model from DATA should be used

na.rm

a logical indicating whether missing values should be removed

Details

auc approximates the area under the ROC curve with a Mann-Whitney U statistic (Delong et al., 1988) to calculate the area under the curve.

The standard errors from auc are only valid for comparing an individual model to random assignment (i.e. AUC=.5). To compare two models to each other it is necessary to account for correlation due to the fact that they use the same test set. If you are interested in pair wise model comparisons see the Splus ROC library from Mayo clinic. auc is a much simpler function than what is available from the Splus ROC library from Mayo clinic.

The observed values (column 2 in DATA) can be given as 0/1 values to represent absence and presence. If this column contains actual values (i.e. basal area, biomass, etc...), any value of zero will be treated as absence and any value greater than zero will be treated as presence.

If observed values are all the same, in other words, if the data consists entirely of observed Presences or entirely of observed Absences, auc will return NaN.

Value

if st.dev = FALSE, returns: AUC area under the curve.

if st.dev = TRUE, returns a dataframe where:

[1,1]	AUC	area under the curve
[1,2]	AUC.sd	standard deviation of AUC

Author(s)

Elizabeth Freeman [e-mail]

References

DeLong, E.R., Delong, D.M. and Clarke-Pearson, D.L., 1988. Comparing areas under two or more correlated Receiver Operating Characteristic curves: a nonparametric approach. Biometrics, 44(3):837-845.

Splus ROC library developed by Beth Atkinson and Doug Mahoney at the Mayo Clinic is available at: http://www.stats.ox.ac.uk/pub/MASS3/Winlibs/ for windows.

See Also

cmx, pcc, sensitivity, specificity, Kappa, auc.roc.plot

Examples

data(SIM3DATA)

auc(SIM3DATA)

auc(SIM3DATA,st.dev=FALSE,which.model=2)