Function to fit CAS-ANOVA method of Bondell and Reich (2009): When performing an analysis of variance, the investigator often has two main goals: to determine which of the factors have a significant effect on the response, and to detect differences among the levels of the significant factors. Level comparisons are done via a post-hoc analysis based on pairwise differences. This article proposes a novel constrained regression approach to simultaneously accomplish both goals via shrinkage within a single automated procedure. The form of this shrinkage has the ability to collapse levels within a factor by setting their effects to be equal, while also achieving factor selection by zeroing out entire factors. Using this approach also leads to the identification of a structure within each factor, as levels can be automatically collapsed to form groups. In contrast to the traditional pairwise comparison methods, these groups are necessarily nonoverlapping so that the results are interpretable in terms of distinct subsets of levels. The proposed procedure is shown to have the oracle property in that asymptotically it performs as well as if the exact structure were known beforehand. A simulation and real data examples show the strong performance of the method.

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Devriendt, Sander; Antonio, Katrien; Reynkens, Tom; Verbelen, Roel: Sparse regression with multi-type regularized feature modeling (2021)
  2. Jeon, Jong-June; Kim, Yongdai; Won, Sungho; Choi, Hosik: Primal path algorithm for compositional data analysis (2020)
  3. Egami, Naoki; Imai, Kosuke: Causal interaction in factorial experiments: application to conjoint analysis (2019)
  4. Groll, Andreas; Hambuckers, Julien; Kneib, Thomas; Umlauf, Nikolaus: LASSO-type penalization in the framework of generalized additive models for location, scale and shape (2019)
  5. Pauger, Daniela; Wagner, Helga: Bayesian effect fusion for categorical predictors (2019)
  6. Malsiner-Walli, Gertraud; Pauger, Daniela; Wagner, Helga: Effect fusion using model-based clustering (2018)
  7. Tutz, Gerhard; Berger, Moritz: Tree-structured modelling of categorical predictors in generalized additive regression (2018)
  8. Jeon, Jong-June; Kwon, Sunghoon; Choi, Hosik: Homogeneity detection for the high-dimensional generalized linear model (2017)
  9. Oelker, Margret-Ruth; Tutz, Gerhard: A uniform framework for the combination of penalties in generalized structured models (2017)
  10. Schauberger, Gunther; Tutz, Gerhard: Subject-specific modelling of paired comparison data: a Lasso-type penalty approach (2017)
  11. Farcomeni, A.: A general class of recapture models based on the conditional capture probabilities (2016)
  12. Choi, Hosik; Koo, Ja-Yong; Park, Changyi: Fused least absolute shrinkage and selection operator for credit scoring (2015)
  13. Maj-Kańska, Aleksandra; Pokarowski, Piotr; Prochenka, Agnieszka: Delete or merge regressors for linear model selection (2015)
  14. Neely, Megan L.; Bondell, Howard D.; Tzeng, Jung-Ying: A penalized likelihood approach for investigating gene-drug interactions in pharmacogenetic studies (2015)
  15. Oelker, Margret-Ruth; Pößnecker, Wolfgang; Tutz, Gerhard: Selection and fusion of categorical predictors with (L_0)-type penalties (2015)
  16. Tutz, Gerhard; Schauberger, Gunther: Extended ordered paired comparison models with application to football data from German Bundesliga (2015)
  17. Abbadi, Mohamed; Di Giacomo, Francesco; Orsini, Renzo; Plaat, Aske; Spronck, Pieter; Maggiore, Giuseppe: Resource entity action: a generalized design pattern for RTS games (2014)
  18. Oelker, Margret-Ruth; Gertheiss, Jan; Tutz, Gerhard: Regularization and model selection with categorical predictors and effect modifiers in generalized linear models (2014)
  19. Tutz, Gerhard; Gertheiss, Jan: Rating scales as predictors -- the old question of scale level and some answers (2014)
  20. Zhao, Weihua; Zhang, Riquan; Liu, Jicai: Regularization and model selection for quantile varying coefficient model with categorical effect modifiers (2014)

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