How to Take Both Non-Linearity and Asymmetry (Skewness) into Account in Binary Decision Making: Skew-Probit and Skew-Logit in Binary Kink Regression

Abstract

In many practical situations, it is desirable to predict binary (“yes”–“no”) decisions made by people. The traditional approach to this prediction assumes that the utility linearly depends on the corresponding parameters, and that the distribution of the difference between predicted and actual utility is symmetric — usually normal or logistic; the corresponding techniques are known as, correspondingly, probit and logit. In real life, utility often non-linearly depends on the parameters, and the corresponding distributions are asymmetric (skewed). There are techniques for dealing with non-linearity; the most widely used such technique — called kink regression — uses piece-wise linear approximations to the utility. There are also techniques that take into account the distribution’s asymmetry; usually, they are based on using special asymmetric distributions: skew-normal and skew-logistic. In this paper, we show how these two techniques to be combined to take into account both non-linearity and asymmetry. On a real-life example, we show that the new technique indeed leads to a better description of human binary decision-making.