# precision recall breakeven point

There are two popular measures that aggregate $Precision$ and $Recall$, there are $F1$ and $\text{Precision Recall Breakeven point}$.

$F1$ can be calculated easily by formula, but how to calculate $\text{breakeven point}$?

I have some experiment and get all four values: true positive, false positive, true negative, false negative, so now I can calculate Precision and Recall but how to find breakeven point in this case.

There is an excellent post (Obtaining predicted values (Y=1 or 0) from a logistic regression model fit) about the break-even point of precision (or sensitivity) and specificity. The latter is not the same as recall, but it should be easy to generalize from there.

If you look at the plot you will see a point where the metrics cross, this is your optimal cutoff point.

EDIT I have updated the code to include precision, recall, and F1

perf = function(cut, mod, y)
{
yhat = (mod\$fit>cut)
w = which(y==1)
sensitivity = mean( yhat[w] == 1 )
specificity = mean( yhat[-w] == 0 )
c.rate = mean( y==yhat )
d = cbind(sensitivity,specificity)-c(1,1)
d = sqrt( d[1]^2 + d[2]^2 )

# F-score
retrieved <- sum(yhat)
precision <- sum(yhat & y) / retrieved
recall <- sum(yhat & y) / sum(y)
Fmeasure <- 2 * precision * recall / (precision + recall)
out = t(as.matrix(c(sensitivity, specificity, c.rate,d, Fmeasure)))
colnames(out) = c("sensitivity", "specificity", "c.rate", "distance", "F-score")
return(out)
}

y3.mod <- glm(y3 ~ x1 + x2 + x3 + x4 + x5 + x6, family=binomial())

par(mfrow=c(1,1))
s = seq(.01,.99,length=100)
OUT = matrix(0,100,5)
for(i in 1:100) OUT[i,]=perf(s[i],y3.mod,y3)
plot(s,OUT[,1],xlab="Cutoff",ylab="Value",cex.lab=1.5,cex.axis=1.5,ylim=c(0,1),type="l",lwd=2,axes=FALSE,col=2)
axis(1,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.)
axis(2,seq(0,1,length=5),seq(0,1,length=5),cex.lab=1.)
lines(s,OUT[,2],col="darkgreen",lwd=2)
lines(s,OUT[,3],col=4,lwd=2)
lines(s,OUT[,4],col="darkred",lwd=2)
lines(s,OUT[,5],col="black",lwd=2)
grid()
box()
legend("topleft",col=c(2,"darkgreen",4,"darkred","black"),lwd=c(2,2,2,2,2),c("Sensitivity","Specificity","Classification Rate","Distance","F-score"))

• Thank you very much for your answer, the problem is I had an experiment and got Precision, Recall, I have no idea what to do with the data in order to get a lot of Precision Recall value and find where there are equal. – user16168 Jun 12 '14 at 17:54
• If you only have 1 set of outputs then you will only have 1 precision, recall, and F1 score. The idea is that for each model you would compare these scores to determine which model is the best. – mike1886 Jun 12 '14 at 18:24
• In addition to comparing models, you can use these measures to compare decision thresholds applied to a single model in order to choose a threshold that balances errors based on their costs and the specifics of your problem. Maybe that is what the questioner wants to do? – MattBagg Jun 12 '14 at 22:26