# Logistic regression with non-negative parameter

I want to model the probability of a binary variable x given some predictor, d. It needs two parameters:

• One parameter that sets the "break point", at which p(x=1 | d) = 0.5.
• One parameter that sets the "softness", i.e. how abruptly the probability changes around the break point.

(Sorry I'm sure there's standard terminology for this, but I'm a bit of a novice.)

A logistic regression model feels like the right approach, but the domain of d is [0, inf] (d is a distance metric). Is there a standard way to transform d to [-inf, inf] so a logistic regression can be used (e.g. f(x) = x-1/x)? Or is there another common model for this kind of scenario?

• Is d a parameter of the logistic regression or a predictor used in logistic regression? It sounds like a predictor but you call it a parameter. If it is a predictor, then its domain is irrelevant. – Rob Hyndman Nov 10 '10 at 2:27
• d is the predictor. Thanks for correcting me, I've updated the question. – redmoskito Nov 10 '10 at 2:29