Confirmatory Person-Oriented Mediation Analysis in Categorical Variables-Options and Limitations.

In this article, we propose three new approaches to analyzing person-oriented mediation hypotheses. First, we propose using relevance logic instead of classical logic. Relevance logic (1) rejects the ex falso sequitur quodlibet ("from a falsehood anything follows") rule and (2) requires that the premise and the outcome of an implication exhibit variable sharing, that is, possess a substantive link. Propositions are declared irrelevant when the premise is false, when there is no substantive link, or both. Second, we discuss, based on relevance logic, alternative concepts of mediation. Specifically, we discuss that mediation can be based on conjunctive as well as on implicative relations. In contrast to conjunctive mediation models, implicative mediation models do allow one to distinguish between full and partial mediation. Third, we propose using confirmatory Configural Frequency Analysis to test hypotheses of full or partial mediation. This is illustrated using data on adolescent development.