, Volume 42, Issue 1, pp 127–140 | Cite as

On rotating to smooth functions

  • James Arbuckle
  • Michael L. Friendly


Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. “Simple structure” is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.

Key words

factor analysis principal components rotation factor transformation 


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Reference note

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Copyright information

© Psychometric Society 1977

Authors and Affiliations

  • James Arbuckle
    • 2
  • Michael L. Friendly
    • 1
  1. 1.York UniversityCanada
  2. 2.Department of PsychologyTemple UniversityPhiladelphia

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