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Selective inference for additive and linear mixed models

Author

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  • Rügamer, David
  • Baumann, Philipp F.M.
  • Greven, Sonja

Abstract

After model selection, subsequent inference in statistical models tends to be overconfident if selection is not accounted for. One possible solution to address this problem is selective inference, which constitutes a post-selection inference framework and yields valid inference statements by conditioning on the selection event. Existing work on selective inference is, however, not directly applicable to additive and linear mixed models. A novel extension to recent work on selective inference to the class of additive and linear mixed models is thus presented. The approach can be applied for any type of model selection mechanism that can be expressed as a function of the outcome variable (and potentially of covariates on which the model conditions). Properties of the method are validated in simulation studies and in an application to a data set in monetary economics. The approach is particularly useful in cases of non-standard selection procedures, as present in the motivating application.

Suggested Citation

  • Rügamer, David & Baumann, Philipp F.M. & Greven, Sonja, 2022. "Selective inference for additive and linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
  • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321001845
    DOI: 10.1016/j.csda.2021.107350
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    References listed on IDEAS

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    6. Ryan J. Tibshirani & Jonathan Taylor & Richard Lockhart & Robert Tibshirani, 2016. "Exact Post-Selection Inference for Sequential Regression Procedures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 600-620, April.
    7. Giampiero Marra & Simon N. Wood, 2012. "Coverage Properties of Confidence Intervals for Generalized Additive Model Components," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(1), pages 53-74, March.
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    Cited by:

    1. Kramlinger, Peter & Schneider, Ulrike & Krivobokova, Tatyana, 2023. "Uniformly valid inference based on the Lasso in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    2. Anna Gottard & Giulia Vannucci & Leonardo Grilli & Carla Rampichini, 2023. "Mixed-effect models with trees," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 431-461, June.

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