C Statistic (Area Under the ROC Curve)

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).

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.

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.

Value

numeric value

Author

Andri Signorell <andri@signorell.net>

References

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

Examples

d.titanic = Untable(Titanic)
r.glm <- glm(Survived ~ ., data=d.titanic, family=binomial)
Cstat(r.glm)
#> Warning: This function will be moved to the package ModTools. Please update.
#> [1] 0.7597259

# default interface
Cstat(x = predict(r.glm, method="response"), 
      resp = model.response(model.frame(r.glm)))
#> Warning: This function will be moved to the package ModTools. Please update.
#> [1] 0.7597287
  
      
# calculating bootstrap confidence intervals
FUN <- function(d.set, i) {
   r.glm <- glm(Survived ~ ., data=d.set[i,], family=binomial)
   Cstat(r.glm)
   }
   
if (FALSE) {
library(boot)
boot.res <- boot(d.titanic, FUN, R=999) 

# the percentile confidence intervals
boot.ci(boot.res, type="perc")

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 999 bootstrap replicates
##
## CALL : 
## boot.ci(boot.out = res, type = "perc")
## 
## Intervals : 
## Level     Percentile     
## 95%   ( 0.7308,  0.7808 )  
## Calculations and Intervals on Original Scale
}