A tutorial on probabilistic index models: Regression models for the effect size P(Y1 < Y2).

Abstract

The probabilistic index (PI), also known as the probability of superiority or the common language effect size, refers to the probability that the outcome of a randomly selected subject exceeds the outcome of another randomly selected subject, conditional on the covariate values of both subjects. This summary measure has a long history, especially for the 2-sample design where the covariate value typically refers to 1 of 2 treatments. Despite some of the attractive features of the PI, it is often not used beyond the 2-sample design. One reason is the lack of a flexible regression framework that embeds the PI and that allows the user to estimate it for more complicated designs. However, Thas, De Neve, Clement, and Ottoy (2012) recently developed such a regression framework, named probabilistic index models (PIMs). In this tutorial we provide an introduction to PIMs where we discuss several theoretical properties, motivate why we think PIMs could be useful for behavioral sciences, and illustrate how it can be used in practice using the R package pim. (PsycINFO Database Record (c) 2019 APA, all rights reserved).