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Simultaneous Inference for Model Averaging of Derived Parameters

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  • Signe M. Jensen
  • Christian Ritz

Abstract

Model averaging is a useful approach for capturing uncertainty due to model selection. Currently, this uncertainty is often quantified by means of approximations that do not easily extend to simultaneous inference. Moreover, in practice there is a need for both model averaging and simultaneous inference for derived parameters calculated in an after‐fitting step. We propose a method for obtaining asymptotically correct standard errors for one or several model‐averaged estimates of derived parameters and for obtaining simultaneous confidence intervals that asymptotically control the family‐wise Type I error rate. The performance of the method in terms of coverage is evaluated using a simulation study and the applicability of the method is demonstrated by means of three concrete examples.

Suggested Citation

  • Signe M. Jensen & Christian Ritz, 2015. "Simultaneous Inference for Model Averaging of Derived Parameters," Risk Analysis, John Wiley & Sons, vol. 35(1), pages 68-76, January.
    • Handle: RePEc:wly:riskan:v:35:y:2015:i:1:p:68-76
    DOI: 10.1111/risa.12242
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    References listed on IDEAS

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    9. 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.
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    12. Steven B. Kim & Ralph L. Kodell & Hojin Moon, 2014. "A Diversity Index for Model Space Selection in the Estimation of Benchmark and Infectious Doses via Model Averaging," Risk Analysis, John Wiley & Sons, vol. 34(3), pages 453-464, March.
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    1. Signe M Jensen & Hanne Hauger & Christian Ritz, 2018. "Mediation analysis for logistic regression with interactions: Application of a surrogate marker in ophthalmology," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-7, February.
    2. Mirjana Glisovic‐Bensa & Walter W. Piegorsch & Edward J. Bedrick, 2024. "Bayesian benchmark dose risk assessment with mixed‐factor quantal data," Environmetrics, John Wiley & Sons, Ltd., vol. 35(5), August.
    3. Frank Schaarschmidt & Christian Ritz & Ludwig A. Hothorn, 2022. "The Tukey trend test: Multiplicity adjustment using multiple marginal models," Biometrics, The International Biometric Society, vol. 78(2), pages 789-797, June.
    4. Signe M. Jensen & Felix M. Kluxen & Christian Ritz, 2019. "A Review of Recent Advances in Benchmark Dose Methodology," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2295-2315, October.
    5. Florent Baty & Christian Ritz & Signe Marie Jensen & Lukas Kern & Michael Tamm & Martin Hugo Brutsche, 2017. "Multimodel inference applied to oxygen recovery kinetics after 6-min walk tests in patients with chronic obstructive pulmonary disease," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-12, November.

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