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 $X\to Y$
, does not preclude the reverse direction ($Y\to X$
). 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 ($\bar {B}\to \bar {A}$
), in addition to the main assertion ($A\to B$
). 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.