Journal
BIOMETRICS
Volume 64, Issue 1, Pages 115-123Publisher
BLACKWELL PUBLISHING
DOI: 10.1111/j.1541-0420.2007.00843.x
Keywords
correlation; penalization; predictive group; regression; shrinkage; supervised clustering; variable selection
Funding
- NIEHS NIH HHS [R01 ES014843, R01 ES014843-01A2] Funding Source: Medline
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Variable selection can be challenging, particularly in situations with a large number of predictors with possibly high correlations, such as gene expression data. In this article, a new method called the OSCAR (octagonal shrinkage and clustering algorithm for regression) is proposed to simultaneously select variables while grouping them into predictive clusters. In addition to improving prediction accuracy and interpretation, these resulting groups can then be investigated further to discover what contributes to the group having a similar behavior. The technique is based on penalized least squares with a geometrically intuitive penalty function that shrinks some coefficients to exactly zero. Additionally, this penalty yields exact equality of some coefficients, encouraging correlated predictors that have a similar effect on the response to form predictive clusters represented by a single coefficient. The proposed procedure is shown to compare favorably to the existing shrinkage and variable selection techniques in terms of both prediction error and model complexity, while yielding the additional grouping information.
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