Principal fitted components for dimension reduction in regression

R. Dennis Cook, Liliana Forzani

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components [Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression (with discussion). Statist. Sci. 22 1-26] and uses normal models for the inverse regression of the predictors on the response to gain reductive information for the forward regression of interest. This approach includes methodology for testing hypotheses about the number of components and about conditional independencies among the predictors.

Original languageEnglish (US)
Pages (from-to)485-501
Number of pages17
JournalStatistical Science
Issue number4
StatePublished - Nov 2008


  • Central subspace
  • Dimension reduction
  • Inverse regression
  • Principal components

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