On the Optimality of the LR Test for Mediation
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 transfo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/1/178 |
| _version_ | 1797490031751856128 |
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| author | Kees Jan Van Garderen Noud Van Giersbergen |
| author_facet | Kees Jan Van Garderen Noud Van Giersbergen |
| author_sort | Kees Jan Van Garderen |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T00:26:09Z |
| format | Article |
| id | doaj.art-e330b714f4e84327bae76a5f842a4055 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T00:26:09Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e330b714f4e84327bae76a5f842a40552023-11-23T15:34:39ZengMDPI AGSymmetry2073-89942022-01-0114117810.3390/sym14010178On the Optimality of the LR Test for MediationKees Jan Van Garderen0Noud Van Giersbergen1UvA Econometrics, Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The NetherlandsUvA Econometrics, Amsterdam School of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The NetherlandsTesting 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> 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.https://www.mdpi.com/2073-8994/14/1/178coherenceindirect effectmaximal invariantSobelstatistics |
| spellingShingle | Kees Jan Van Garderen Noud Van Giersbergen On the Optimality of the LR Test for Mediation Symmetry coherence indirect effect maximal invariant Sobel statistics |
| title | On the Optimality of the LR Test for Mediation |
| title_full | On the Optimality of the LR Test for Mediation |
| title_fullStr | On the Optimality of the LR Test for Mediation |
| title_full_unstemmed | On the Optimality of the LR Test for Mediation |
| title_short | On the Optimality of the LR Test for Mediation |
| title_sort | on the optimality of the lr test for mediation |
| topic | coherence indirect effect maximal invariant Sobel statistics |
| url | https://www.mdpi.com/2073-8994/14/1/178 |
| work_keys_str_mv | AT keesjanvangarderen ontheoptimalityofthelrtestformediation AT noudvangiersbergen ontheoptimalityofthelrtestformediation |