  Beginning with a discussion of R. A. Fisher's early written remarks that
relate to dimension reduction, this article revisits principal components as a
reductive method in regression, develops several model-based extensions and
ends with descriptions of general approaches to model-based and model-free
dimension reduction in regression. It is argued that the role for principal
components and related methodology may be broader than previously seen and that
the common practice of conditioning on observed values of the predictors may
unnecessarily limit the choice of regression methodology.
