Performs a concordance/disconcordance (C-statistic) test on binomial models.
concordance(y, p)
| y | vector of binomial response variable used in model |
|---|---|
| p | estimated probabilities from fit binomial model |
list object with: concordance, discordance, tied and pairs
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
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
Jeffrey S. Evans <jeffrey_evans@tnc.org>
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"))#> $concordance #> [1] 0.9087302 #> #> $discordance #> [1] 0.09126984 #> #> $tied #> [1] 1.387779e-17 #> #> $pairs #> [1] 252 #>