A Note on High-Dimensional Linear Regression With Interactions

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13 Scopus citations


The problem of interaction selection in high-dimensional data analysis has recently received much attention. This note aims to address and clarify several fundamental issues in interaction selection for linear regression models, especially when the input dimension p is much larger than the sample size n. We first discuss how to give a formal definition of “importance” for main and interaction effects. Then we focus on two-stage methods, which are computationally attractive for high-dimensional data analysis but thus far have been regarded as heuristic. We revisit the counterexample of Turlach and provide new insight to justify two-stage methods from the theoretical perspective. In the end, we suggest new strategies for interaction selection under the marginality principle and provide some simulation results.

Original languageEnglish (US)
Pages (from-to)291-297
Number of pages7
JournalAmerican Statistician
Issue number4
StatePublished - Oct 2 2017


  • Heredity condition
  • Hierarchical structure
  • Interaction effects
  • Linear model
  • Marginality principle

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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