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, ...)
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. |
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.
numeric value
Andri Signorell <andri@signorell.net>
Hosmer D.W., Lemeshow S. (2000) Applied Logistic Regression (2nd Edition). New York, NY: John Wiley & Sons
d.titanic = Untable(Titanic)
r.glm <- glm(Survived ~ ., data=d.titanic, family=binomial)
Cstat(r.glm)
# default interface
Cstat(x = predict(r.glm, method="response"),
resp = model.response(model.frame(r.glm)))
# calculating bootstrap confidence intervals
FUN <- function(d.set, i) {
r.glm <- glm(Survived ~ ., data=d.set[i,], family=binomial)
Cstat(r.glm)
}
## Not run:
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
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.