Churn Prediction: why are churners usually selected as the positive class and not vice versa?

Question

Is it just because churners usually form the minority class in the binary classification setting? Would it make sense to turn the non-churners group of customers into the positive class instead if churners form the majority class?

Answer 1

I believe that this is a question of a habit and not of mathematics. Most measure (e.g., precision, recall) are defined with respect to the positive class. Of course that you can use the related measures with respect to the negative class but by sticking with the norm you communication is less confusing.

In the case of churn there is another benefit from the actionability of the results. In most cases the goal of the churn research is to find ways to reduce churn by applying various actions on the potential churners. By treating them as the positives, the actions and the predictions are aligned.

Answer 2

I have a small experience in churn prediction modeling and initially I had the same question in my mind. First of all, even if the labels are switched, the only thing that changes would be the interpretation of the model. Here is a quick R example:

set.seed(1)
x <- matrix(rnorm(100*2), 100, 2)
y <- sample(0:1, 100, replace = TRUE)


coef(glm(as.logical(y) ~ x, family = "binomial"))  # 0: retain, 1: churn
(Intercept)          x1          x2 
-0.11876127 -0.02344758 -0.02995008 

coef(glm(!as.logical(y) ~ x, family = "binomial")) # 0: churn, 1: retain
(Intercept)          x1          x2 
 0.11876127  0.02344758  0.02995008 

In the first example, x1 and x2 have negative sign so I would consider those as features that reduce the churn probability.

If I switch the labels and proceed tho second example, I would have to conclude that x1 and x2 are features that increase the retention probability.

Since the object is called "churn modeling" rather than "retention modeling", I think it makes sense to keep settings as (0: churn, 1: retain), regardless of the ratio of the "Churn" labels.