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 ofY on X, frequently interpreted as evidence of a directed dependence X→Y, does not preclude the reverse direction (Y→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), in addition to the main assertion (A→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 detectone-wayimplicationrelationships,usingbothpositiveandcontrapositiveevidence.Italsofacilitates dimensionalreductionbyestablishingalignedsetsofnodesinagraphrepresentation,underthecondition that a Rasch model holds on these nodes, thus filling the gap between graphical and dimensional models. Theefficacyofthisindexissubstantiatedthroughbo thsimulatedandreal-worlddataillustrations.