DescTools (version 0.99.37)

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

Run this code
# 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)))
# }

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