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.
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References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Maj-Kańska, Aleksandra; Pokarowski, Piotr; Prochenka, Agnieszka: Delete or merge regressors for linear model selection (2015)
- Tutz, Gerhard; Gertheiss, Jan: Rating scales as predictors -- the old question of scale level and some answers (2014)
- Post, Justin B.; Bondell, Howard D.: Factor selection and structural identification in the interaction ANOVA model (2013)
- Gertheiss, Jan; Tutz, Gerhard: Regularization and model selection with categorial effect modifiers (2012)
- Masarotto, Guido; Varin, Cristiano: The ranking lasso and its application to sport tournaments (2012)
- Ueki, Masao; Kawasaki, Yoshinori: Automatic grouping using smooth-threshold estimating equations (2011)
- Gertheiss, Jan; Tutz, Gerhard: Sparse modeling of categorial explanatory variables (2010)
- Bondell, Howard D.; Reich, Brian J.: Simultaneous factor selection and collapsing levels in ANOVA (2009)