Kappa Regression: An Alternative to Logistic Regression

Abstract

In this study, a new regression method called Kappa regression is introduced to model conditional probabilities. The regression function is based on Dombi’s Kappa function, which is well known in fuzzy theory. Here, we discuss how the Kappa function relates to the Logistic function as well as how it can be used to approximate the Logistic function. We introduce the so-called Generalized Kappa Differential Equation and show that both the Kappa and the Logistic functions can be derived from it. Kappa regression, like binary Logistic regression, models the conditional probability of the event that a dichotomous random variable takes a particular value at a given value of an explanatory variable. This new regression method may be viewed as an alternative to binary Logistic regression, but while in binary Logistic regression the explanatory variable is defined over the entire Euclidean space, in the Kappa regression model the predictor variable is defined over a bounded subset of the Euclidean space. We will also show that asymptotic Kappa regression is Logistic regression. The advantages of this novel method are demonstrated by means of an example, and afterwards some implications are discussed.