# concordance

##### Concordance test for binomial models

Performs a concordance/disconcordance (C-statistic) test on binomial models.

##### Usage

`concordance(y, p)`

##### Arguments

- y
vector of binomial response variable used in model

- p
estimated probabilities from fit binomial model

##### Value

list object with: concordance, discordance, tied and pairs

##### Note

Test of binomial regression for the hypothesis that probabilities of all positives [1], are greater than the probabilities of the nulls [0]. The concordance would be 100 inverse of concordance, representing the null. The C-statistic has been show to be comparable to the area under an ROC

Results are: concordance - percent of positives that are greater than probabilities of nulls. discordance - concordance inverse of concordance representing the null class, tied - number of tied probabilities and pairs - number of pairs compared

##### References

Austin, P.C. & E.W. Steyerberg (2012) Interpreting the concordance statistic of a logistic regression model: relation to the variance and odds ratio of a continuous explanatory variable. BMC Medical Research Methodology, 12:82

Harrell, F.E. (2001) Regression modelling strategies. Springer, New York, NY.

Royston, P. & D.G. Altman (2010) Visualizing and assessing discrimination in the logistic regression model. Statistics in Medicine 29(24):2508-2520

##### Examples

```
# NOT RUN {
data(mtcars)
dat <- subset(mtcars, select=c(mpg, am, vs))
glm.reg <- glm(vs ~ mpg, data = dat, family = binomial)
concordance(dat$vs, predict(glm.reg, type = "response"))
# }
```

*Documentation reproduced from package spatialEco, version 1.3-2, License: GPL-3*