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 class 'glm'
Cstat(x, ...)

# Default S3 method
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

See also

BrierScore

Examples

d.titanic = Untable(Titanic)
r.glm <- glm(Survived ~ ., data=d.titanic, family=binomial)
Cstat(r.glm)
#> [1] 0.7597259

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