Principal Fitted Components for Dimension Reduction in Regression

COOK, R. D. AND FORZANI, L.

Statistical Science

Año: 2009

We extend principal fitted components (Cook, 2007) to allow for a more general error. This provide remedies 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 hinges on using 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.