C Statistic (Area Under the ROC Curve)
Calculate the C statistic (equivalent to the area under the Receiver Operating Characteristic Curver ROC) for a logistic regression model, a measure of goodness of fit for binary outcomes in a logistic regression model.
Cstat(x, ...)"Cstat"(x, ...)"Cstat"(x, resp, ...)
- the linear model
- the response variable
- further arguments to be passed to other functions.
Values for this measure range from 0.5 to 1.0. 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.
Hosmer D.W., Lemeshow S. (2000) Applied Logistic Regression (2nd Edition). New York, NY: John Wiley & Sons
r.glm <- glm(Survived ~ ., data=Untable(Titanic), family=binomial) Cstat(r.glm)