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 $X o Y$ upper X right arrow upper Y , does not preclude the reverse direction ( Y -> X $Y o X$ 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 & strns; -> A & strns; $\bar {B} o \bar {A}$ upper B overbar right arrow upper A overbar ), in addition to the main assertion ( A -> B $A o B$ 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.
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