Saturday, October 29, 2011

Plotting gain chart

Gain chart is a popular method to visually inspect model performance in binary prediction. It presents the percentage of captured positive responses as a function of selected percentage of a sample. It is easy to obtain it using ROCR package plotting "tpr" against "rpp". However, it is worth to note that gain chart can be equivalently interpreted as empirical cumulative distribution function of random variable representing rank of randomly selected positive response divided by sample size. This equivalence is presented in the following code:

library(ROCR)
gain.chart <- function(n) {
    score <- runif(n)
    y <- (runif(n) < score)
    plot(performance(prediction(score, y)"tpr""rpp"),
         lwd = 7, main = paste("N =", n))
    lines(ecdf((rank(-score)[y == T]) / n),
          verticals = T, do.points = F, col = "red", lwd = 3)
}

set.seed(1)
par(mfrow = c(12))
gain.chart(10)
gain.chart(10000)

The code plots the following gain charts:


For small samples the two methods do not produce identical plots as ecdf returns step function and ROCR plot provides linear interpolation at jumps.

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