DescTools (version 0.99.39)

Cstat: C Statistic (Area Under the ROC Curve)

Description

Calculate the C statistic, a measure of goodness of fit for binary outcomes in a logistic regression or any other classification model. The C statistic is equivalent to the area under the ROC-curve (Receiver Operating Characteristic).

Usage

Cstat(x, ...)
# S3 method for glm
Cstat(x, ...)
# S3 method for default
Cstat(x, resp, ...)

Arguments

x

the logistic model for the glm interface or the predicted probabilities of the model for the default.

resp

the response variable (coded as c(0, 1))

…

further arguments to be passed to other functions.

Value

numeric value

Details

Values for this measure range from 0.5 to 1.0, with higher values indicating better predictive models. A value of 0.5 indicates that the model is no better than chance at making a prediction of membership in a group and a value of 1.0 indicates that the model perfectly identifies those within a group and those not. Models are typically considered reasonable when the C-statistic is higher than 0.7 and strong when C exceeds 0.8.

Confidence intervals for this measure can be calculated by bootstrap.

References

Hosmer D.W., Lemeshow S. (2000) Applied Logistic Regression (2nd Edition). New York, NY: John Wiley & Sons

See Also

BrierScore

Examples

# NOT RUN {
r.glm <- glm(Survived ~ ., data=Untable(Titanic), family=binomial)
Cstat(r.glm)

# default interface
Cstat(x = predict(r.glm, method="response"), 
      resp = model.response(model.frame(r.glm)))
# }