On dimensional implication graphs

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 on , frequently interpreted as evidence of a directed dependence , does not preclude the reverse direction ( ).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 ), in addition to the main assertion ( ).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 paper 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.