Grant Hillier, Kees Jan van Garderen, Noud van Giersbergen
arXiv 4 Mar 2024 · Econometrics
arXiv:2403.02144 · PDF · DOI · OpenAlex · Extracted main text
Testing for a mediation effect is important in many disciplines, but is made difficult - even asymptotically - by the influence of nuisance parameters. Classical tests such as likelihood ratio (LR) and Wald (Sobel) tests have very poor power properties in parts of the parameter space, and many attempts have been made to produce improved tests, with limited success. In this paper we show that augmenting the critical region of the LR test can produce a test with much improved behavior everywhere. In fact, we first show that there exists a test of this type that is (asymptotically) exact for certain test levels $\alpha $, including the common choices $\alpha =.01,.05,.10.$ The critical region of this exact test has some undesirable properties. We go on to show that there is a very simple class of augmented LR critical regions which provides tests that are nearly exact, and avoid the issues inherent in the exact test. We suggest an optimal and coherent member of this class, provide the table needed to implement the test and to report p-values if desired. Simulation confirms validity with non-Gaussian disturbances, under heteroskedasticity, and in a nonlinear (logit) model. A short application of the method to an entrepreneurial attitudes study is included for illustration.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Van Garderen, K. J. and N. P. A. Van Giersbergen (2021) A nearly similar powerful test for mediation | 0.843 | 3 | 3 | 100% |
| 2 | White, H (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity | 0.737 | 3 | 2 | 100% |
| 3 | MacKinnon, D. P., C. M. Lockwood, C. H. Brown, W. Wang, and J. M. Ho… (2007) The intermediate endpoint effect in logistic and probit regression | 0.511 | 2 | 1 | 100% |
| 4 | Vaughan, R. J. and W. N. Venables (1972) Permanent expressions for order statistic densities | 0.511 | 2 | 1 | 100% |
| 5 | Hayes, A. F (2017) Introduction to mediation, moderation, and conditional process analysis: A regression-based approach | 0.511 | 2 | 1 | 100% |
| 6 | Aggarwal, S (2019) A survey-cum-tutorial on approximations to Gaussian $Q$ function for symbol error probability analysis over Nakagami-$m$ fading… | 0.405 | 1 | 1 | 100% |
| 7 | Alwin, D. F. and R. M. Hauser (1975) The decomposition of effects in path analysis | 0.405 | 1 | 1 | 100% |
| 8 | Baron, R. M. and D. A. Kenny (1986) The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerati… | 0.405 | 1 | 1 | 100% |
| 9 | Bezanson, J., A. Edelman, S. Karpinski, and V. B. Shah (2017) Julia: A fresh approach to numerical computing | 0.405 | 1 | 1 | 100% |
| 10 | Cohen, J. D (1988) Noncentral chi-square: Some observations on recurrence | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 25 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Nearly Similar Powerful Test for Mediation | 0.843 | 4 | 3 |
| 2 | Inference under First-Order Degeneracy | 0.405 | 1 | 1 |