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A Bayes-Factor-Guided Approach to Post-Double Selection with Bootstrapped Multiple Imputation

Author

Listed:
  • Johannes Bleher

    (Department of Econometrics and Empirical Economics & Computational Science Hub, University of Hohenheim)

  • Claudia Tarantola

    (Department of Economics, Management and Quantitative Methods, University of Milan)

Abstract

When variable selection methods are applied to bootstrapped and multiply imputed datasets, the set of selected variables typically varies across iterations. Aggregating results via the union rule can lead to overly dense models. We propose a sequential evidence aggregation procedure that models detection outcomes across perturbation iterations as Bernoulli trials and accumulates evidence for variable relevance through a likelihood-ratio process admitting an approximate Bayes-factor interpretation. The procedure provides both a variable inclusion criterion and a stopping rule that eliminates the need to fix the number of bootstrap-imputation iterations ex ante. A Monte Carlo study across 126 scenarios and an empirical illustration demonstrate the method's performance relative to existing aggregation approaches.

Suggested Citation

  • Johannes Bleher & Claudia Tarantola, 2026. "A Bayes-Factor-Guided Approach to Post-Double Selection with Bootstrapped Multiple Imputation," Papers 2604.12783, arXiv.org, revised Apr 2026.
    • Handle: RePEc:arx:papers:2604.12783
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    File URL: http://arxiv.org/pdf/2604.12783
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    References listed on IDEAS

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    1. Sierra A. Bainter & Thomas G. McCauley & Mahmoud M. Fahmy & Zachary T. Goodman & Lauren B. Kupis & J. Sunil Rao, 2023. "Comparing Bayesian Variable Selection to Lasso Approaches for Applications in Psychology," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 1032-1055, September.
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