Psychometrika

, Volume 63, Issue 4, pp 359–367 | Cite as

Conditions for factor (in)determinacy in factor analysis

  • Wim P. Krijnen
  • Theo K. Dijkstra
  • Richard D. Gill
Article

Abstract

The subject of factor indeterminacy has a vast history in factor analysis (Guttman, 1955; Lederman, 1938; Wilson, 1928). It has lead to strong differences in opinion (Steiger, 1979). The current paper gives necessary and sufficient conditions for observability of factors in terms of the parameter matrices and a finite number of variables. Five conditions are given which rigorously define indeterminacy. It is shown that (un)observable factors are (in)determinate. Specifically, the indeterminacy proof by Guttman is extended to Heywood cases. The results are illustrated by two examples and implications for indeterminacy are discussed.

Key words

indeterminacy Heywood cases mean squared error factor score prediction 

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Copyright information

© The Psychometric Society 1998

Authors and Affiliations

  • Wim P. Krijnen
    • 1
  • Theo K. Dijkstra
    • 1
  • Richard D. Gill
    • 2
  1. 1.University of GroningenThe Netherlands
  2. 2.University of UtrechtThe Netherlands

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