On the Optimality of the LR Test for Mediation

Autor: Kees Jan Van Garderen, Noud Van Giersbergen
Jazyk: angličtina
Rok vydání: 2022
Předmět:
Zdroj: Symmetry, Vol 14, Iss 1, p 178 (2022)
Druh dokumentu: article
ISSN: 14010178
2073-8994
DOI: 10.3390/sym14010178
Popis: Testing for mediation, or indirect effects, is empirically very important in many disciplines. It has two obvious symmetries that the testing procedure should be invariant to. The ordered absolute t-statistics from two ordinary regressions are maximal invariant under the associated groups of transformations. Sobel’s (1982) Wald-type and the LR test statistic are both functions of this maximal invariant and satisfy two logical coherence requirements: (1) size coherence: rejection at level α implies rejection at all higher significance levels; and (2) information coherence: more (less) evidence against the null implies continued (non) rejection of the null. The LR test statistic is simply the smallest of the two absolute t-statistics, and we show that the LR test is the Uniformly Most Powerful (information and size) Coherent Invariant (UMPCI) test. In short: the LR test for mediation is simple and best.
Databáze: Directory of Open Access Journals
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