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Monotone Spline Transformations for Dimension Reduction

Published online by Cambridge University Press:  01 January 2025

S. Winsberg  and
J. O. Ramsay
S. Winsberg
Affiliation:
Université de Montréal
J. O. Ramsay*
Affiliation:
McGill University
*
Requests for reprints should be sent to J. O. Ramsay, Department of Psychology, 1205 Dr. Penfield Ave., Montréal, Québec, Canada H3A 1B1.
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Abstract

Consider a set of data consisting of measurements of n objects with respect to p variables displayed in an n × 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.

Keywords

I-splinesEckart-Young decompositiontransformation to normalitymultivariate normalcovariance structuremaximum likelihood estimation
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 4 , December 1983 , pp. 575 - 595
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

This investigation was supported in part by research grants A4035 and APA0320 from the Natural Sciences and Engineering Research Council of Canada to the first and second authors, respectively. We wish to thank the referees for their helpful comments.

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