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Controlling the familywise error rate when performing multiple comparisons in a linear latent variable model

Author

Listed:
  • Brice Ozenne

    (University of Copenhagen
    Rigshospitalet and University of Copenhagen)

  • Esben Budtz-Jørgensen

    (University of Copenhagen)

  • Sebastian Elgaard Ebert

    (Rigshospitalet and University of Copenhagen)

Abstract

In latent variable models (LVMs) it is possible to analyze multiple outcomes and to relate them to several explanatory variables. In this context many parameters are estimated and it is common to perform multiple tests, e.g. to investigate outcome-specific effects using Wald tests or to check the correct specification of the modeled mean and variance using a forward stepwise selection (FSS) procedure based on Score tests. Controlling the family-wise error rate (FWER) at its nominal level involves adjustment of the p-values for multiple testing. Because of the correlation between test statistics, the Bonferroni procedure is often too conservative. In this article, we extend the max-test procedure to the LVM framework for Wald and Score tests. Depending on the correlation between the test statistics, the max-test procedure is equivalent or more powerful than the Bonferroni procedure while also providing, asymptotically, a strong control of the FWER for non-iterative procedures. Using simulation studies, we assess the finite sample behavior of the max-test procedure for Wald and Score tests in LVMs. We apply our procedure to quantify the neuroinflammatory response to mild traumatic brain injury in nine brain regions.

Suggested Citation

  • Brice Ozenne & Esben Budtz-Jørgensen & Sebastian Elgaard Ebert, 2023. "Controlling the familywise error rate when performing multiple comparisons in a linear latent variable model," Computational Statistics, Springer, vol. 38(1), pages 1-23, March.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01214-7
    DOI: 10.1007/s00180-022-01214-7
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    References listed on IDEAS

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    1. Brice Ozenne & Patrick M. Fisher & Esben Budtz‐J⊘rgensen, 2020. "Small sample corrections for Wald tests in latent variable models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 841-861, August.
    2. Christian Bressen Pipper & Christian Ritz & Hans Bisgaard, 2012. "A versatile method for confirmatory evaluation of the effects of a covariate in multiple models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 61(2), pages 315-326, March.
    3. Armengol Gasull & José López-Salcedo & Frederic Utzet, 2015. "Maxima of Gamma random variables and other Weibull-like distributions and the Lambert $$\varvec{W}$$ W function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 714-733, December.
    4. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    5. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    6. Klaus Holst & Esben Budtz-Jørgensen, 2013. "Linear latent variable models: the lava-package," Computational Statistics, Springer, vol. 28(4), pages 1385-1452, August.
    7. DiCiccio, Cyrus J. & DiCiccio, Thomas J. & Romano, Joseph P., 2020. "Exact tests via multiple data splitting," Statistics & Probability Letters, Elsevier, vol. 166(C).
    8. Westfall, Peter H. & Tobias, Randall D., 2007. "Multiple Testing of General Contrasts: Truncated Closure and the Extended ShafferRoyen Method," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 487-494, June.
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