There have been few attempts to devise suitable methods of analysis for the implications grid devised by Hinkle (1965). As Hinkle noted (Hinkle, 1965, p. 63), there are three implications needed to define a hierarchical relationship (A → B, B → C, and A → C). Hinkle did not attempt to test this requirement, as neither did the only other published use of the technique (Fransella, 1972). Subsequently, Caputi, Breiger, and Pattison (1990) published a technique that explicitly sought to model implications data with respect to this requirement. In this study we use this technique to both (a) evaluate some of the choice points in the technique using data from the 28 implications grids collected by Hinkle and published as an appendix to his thesis, and (b) subsequently analyze this data to examine the hierarchical relationships as defined above. Our evaluation of the choice points showed that the joint modification approach worked best and that there was a clear cut-off to most fully represent the relationships in the raw data. Our analysis via the modeling approach found that there was no difference between the mean number of transitive superordinate constructs implied by subordinate constructs and the mean number of transitive subordinate constructs implied by superordinate constructs in the modeled data, suggesting that the laddered constructs in this study were not necessarily superordinate to the generating constructs.
Bell, R. C., Caputi, P. & Miller, L. (2016). Modeling hierarchical relationships in Hinkle's implications grid data. Journal of Constructivist Psychology, 29 (4), 407-416.