x/1-x expression

[saminny]

I see a number of places where ppl use this sort of computation:
x = 0.2 // or some percent

s = x/(1-x) * size

In general, what is the theory behind using x/(1-x) if x is a random percentage value?


thx
Sam

[squareandrare]

Most often, you see log(x/(1-x)), which is often written as logit(x). This extends the domain of x. If you just keep it as a proportion, x is bounded between 0 and 1. Using x/(1-x) extends the domain to all non-negative numbers. Then, taking logit(x) extends it to all real numbers.

Read about logistic regression if you want more info. Using logit(x) is helpful because if x is the response variable in regression, you can make predictions for any values of the independent variables. Without using logit, the only valid predictions are those that fall between 0 and 1.