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

Maarten De Schryver (UGent) and Jan De Neve (UGent)
(2019) PSYCHOLOGICAL METHODS. 24(4). p.403-418
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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.
Keywords
MANN-WHITNEY TEST, INTUITIVE NONPARAMETRIC APPROACH, SEMIPARAMETRIC REGRESSION, common language effect size, probability of superiority, regression, rank tests, probability of superiority

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MLA
De Schryver, Maarten, and Jan De Neve. “A Tutorial on Probabilistic Index Models : Regression Models for the Effect Size P(Y1 < Y2).” PSYCHOLOGICAL METHODS, vol. 24, no. 4, 2019, pp. 403–18.
APA
De Schryver, M., & De Neve, J. (2019). A tutorial on probabilistic index models : regression models for the effect size P(Y1 < Y2). PSYCHOLOGICAL METHODS, 24(4), 403–418.
Chicago author-date
De Schryver, Maarten, and Jan De Neve. 2019. “A Tutorial on Probabilistic Index Models : Regression Models for the Effect Size P(Y1 < Y2).” PSYCHOLOGICAL METHODS 24 (4): 403–18.
Chicago author-date (all authors)
De Schryver, Maarten, and Jan De Neve. 2019. “A Tutorial on Probabilistic Index Models : Regression Models for the Effect Size P(Y1 < Y2).” PSYCHOLOGICAL METHODS 24 (4): 403–418.
Vancouver
1.
De Schryver M, De Neve J. A tutorial on probabilistic index models : regression models for the effect size P(Y1 < Y2). PSYCHOLOGICAL METHODS. 2019;24(4):403–18.
IEEE
[1]
M. De Schryver and J. De Neve, “A tutorial on probabilistic index models : regression models for the effect size P(Y1 < Y2),” PSYCHOLOGICAL METHODS, vol. 24, no. 4, pp. 403–418, 2019.
@article{8566381,
  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.},
  author       = {De Schryver, Maarten and De Neve, Jan},
  issn         = {1082-989X},
  journal      = {PSYCHOLOGICAL METHODS},
  keywords     = {MANN-WHITNEY TEST,INTUITIVE NONPARAMETRIC APPROACH,SEMIPARAMETRIC REGRESSION,common language effect size,probability of superiority,regression,rank tests,probability of superiority},
  language     = {eng},
  number       = {4},
  pages        = {403--418},
  title        = {A tutorial on probabilistic index models : regression models for the effect size P(Y1 < Y2)},
  url          = {http://dx.doi.org/10.1037/met0000194},
  volume       = {24},
  year         = {2019},
}

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