Year: 2026
Type: article
Abstract: Classical symmetric association measures, such as correlation and chi-square indices, are widely used in applied psychology. However, these indices have limitations in identifying asymmetric implicative relationships. Standard regression analysis of Y on X , frequently interpreted as evidence of a directed dependence X → Y $X\to Y$ upper X right arrow upper Y , does not preclude the reverse direction ( Y → X $Y\to X$ upper Y right arrow upper X ). While various proposals in the literature have sought to provide non-symmetric association measures between binary events, most have overlooked the potential information in the contrapositive ( B ¯ → A ¯ $\bar {B}\to \bar {A}$ upper B overbar right arrow upper A overbar ), in addition to the main assertion ( A → B $A\to B$ upper A right arrow upper B ). When multiple variables are involved, asymmetric dependence is frequently represented as intricate dependency networks, which can be challenging to summarize and interpret in terms of higher-order clusters or latent dimensions. This article introduces a novel statistical implication index designed to address both limitations. The efficacy of this asymmetric index is demonstrated through its ability to detect one-way implication relationships, using both positive and contrapositive evidence. It also facilitates dimensional reduction by establishing aligned sets of nodes in a graph representation, under the condition that a Rasch model holds on these nodes, thus filling the gap between graphical and dimensional models. The efficacy of this index is substantiated through both simulated and real-world data illustrations.
Source: Psychometrika
Author: Yvonnick Noel
Institution: Université Rennes 2
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7162070147
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