Psychometrika

, Volume 52, Issue 1, pp 125–135 | Cite as

The rank of reduced dispersion matrices

  • Paul A. Bekker
  • Jan de Leeuw
Article

Abstract

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historial discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.

Key words

factor analysis errors of measurement structural regression functional models communalities errors in variables 

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Copyright information

© The Psychometric Society 1987

Authors and Affiliations

  • Paul A. Bekker
    • 1
  • Jan de Leeuw
    • 2
  1. 1.Department of EconometricsTilburg UniversityThe Netherlands
  2. 2.Department of Data Theory FSW/RULLeidenThe Netherlands

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