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Psychometrika

, Volume 49, Issue 1, pp 79–94 | Cite as

Linear relations amongk sets of variables

  • John P. Van de Geer
Article

Abstract

A family of solutions for linear relations amongk sets of variables is proposed. It is shown how these solutions apply fork=2, and how they can be generalized from there tok≥3.

The family of solutions depends on three independent choices: (i) to what extent a solution may be influenced by differences in variances of components within each set; (ii) to what extent the sets may be differentially weighted with respect to their contribution to the solution—including orthogonality constraints; (iii) whether or not individual sets of variables may be replaced by an orthogonal and unit normalized basis.

Solutions are compared with respect to their optimality properties. For each solution the appropriate stationary equations are given. For one example it is shown how the determinantal equation of the stationary equations can be interpreted.

Key words

canonical correlation linear relations between sets multiple regression redundancy analysis ridge regression 

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Reference notes

  1. Dauxois, J., and Pousse, A. (1976).Les analyses factorielles en calcul des probabilités et en statistique: essai d'étude synthétique. Toulouse; Ph.D. Thesis, Université de Toulouse.Google Scholar
  2. Ten Berge, J. M. F. (1977).Optimizing factorial invariance. Groningen; Ph.D. Thesis, University of Groningen.Google Scholar

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Copyright information

© The Psychometric Society 1984

Authors and Affiliations

  • John P. Van de Geer
    • 1
  1. 1.Department of Data TheoryUniversity of LeidenLeidenThe Netherlands

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