Demonstration of how to construct a bespoke regression to determine the optimal cutoff value for constructing a categorical variable for a logistic regression

find_best_cutoff.r

# Finding best cut-off for constructing a categorical variable 
# logistic regression

data(iris)

x0 = iris[iris$Species != 'setosa',]
plot(x0, col=x0$Species)

# Keep things simple for this demo
form = "is_virginica ~ Petal.Length + Petal.Width"
x = subset(x0, select=Petal.Length)
x$is_virginica = x0$Species=='virginica'

# Find best cut-off for Petal.Width
v = x0$Petal.Width
c0 = quantile(v, 0.5) # initialization = 1.6
names(c0) = "cutoff"

cost_fn = function(c_i){
  x_i = x
  x_i$Petal.Width = v < c_i
  mod = glm(form, data=x_i, family=binomial)
  -logLik(mod)
}

cutoff = optim(c0, cost_fn)
cutoff$par # 1.68

plot(x0$Petal.Length, x0$Petal.Width, col=x0$Species)
abline(h=c0, lty=2)  # initialization
abline(h=cutoff$par) # best cutoff