A penalized likelihood approach to rotation of principal components

Research output: Contribution to journalArticlepeer-review


A new paradigm for enhancing the interpretability of principal components through rotation is presented within the framework of penalized likelihood. The rotated components are computed as the maximizers of a Gaussian-based profile log-likelihood function plus a penalty term defined by a standard rotation criterion. This method enjoys a number of advantages over other methods for principal component rotation, notably (1) the rotation specifically targets ill-defined principal components, which may benefit the most from rotation, and (2) the connection with likelihood allows assessment of the fidelity of the rotated components to the data, thereby guiding the choice of penalty parameter. The method is illustrated with an application to a small functional dataset. Efficient computation of the penalized likelihood solution is possible using recently developed algorithms for optimization under orthogonality constraints.

Original languageEnglish (US)
Pages (from-to)867-888
Number of pages22
JournalJournal of Computational and Graphical Statistics
Issue number4
StatePublished - Dec 1 2005
Externally publishedYes


  • Functional data
  • Ill-defined components
  • Orthogonal rotation
  • Profile likelihood
  • Simplified component technique
  • Varimax

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty


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