, Volume 48, Issue 4, pp 575–595 | Cite as

Monotone spline transformations for dimension reduction

  • S. Winsberg
  • J. O. Ramsay


Consider a set of data consisting of measurements ofn objects with respect top variables displayed in ann ×p matrix. A monotone transformation of the values in each column, represented as a linear combination of integrated basis splines, is assumed determined by a linear combination of a new set of values characterizing each row object. Two different models are used: one, an Eckart-Young decomposition model, and the other, a multivariate normal model. Examples for artificial and real data are presented. The results indicate that both methods are helpful in choosing dimensionality and that the Eckart-Young model is also helpful in displaying the relationships among the objects and the variables. Also, results suggest that the resulting transformations are themselves illuminating.

Key words

I-splines Eckart-Young decomposition transformation to normality multivariate normal covariance structure maximum likelihood estimation 


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Copyright information

© The Psychometric Society 1983

Authors and Affiliations

  • S. Winsberg
    • 1
  • J. O. Ramsay
    • 2
  1. 1.Université de MontréalCanada
  2. 2.Mcgill UniversityUSA

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