# Cstat: C Statistic (Area Under the ROC Curve) In DescTools: Tools for Descriptive Statistics

## 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

 ```1 2 3 4 5 6 7``` ```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.

numeric value

## Author(s)

Andri Signorell <andri@signorell.net>

## References

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

`BrierScore`

## Examples

 ```1 2 3 4 5 6``` ```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))) ```

### Example output

```[1] 0.8113533
[1] 0.8113533
```

DescTools documentation built on Sept. 8, 2020, 1:07 a.m.