Psychometrika

, Volume 64, Issue 2, pp 113–128

On the relationship between the higher-order factor model and the hierarchical factor model

  • Yiu-Fai Yung
  • David Thissen
  • Lori D. McLeod
Article

DOI: 10.1007/BF02294531

Cite this article as:
Yung, YF., Thissen, D. & McLeod, L.D. Psychometrika (1999) 64: 113. doi:10.1007/BF02294531

Abstract

The relationship between the higher-order factor model and the hierarchical factor model is explored formally. We show that the Schmid-Leiman transformation produces constrained hierarchical factor solutions. Using a generalized Schmid-Leiman transformation and its inverse, we show that for any unconstrained hierarchical factor model there is an equivalent higher-order factor model with direct effects (loadings) on the manifest variables from the higher-order factors. Therefore, the class of higher-order factor models (without direct effects of higher-order factors) is nested within the class of unconstrained hierarchical factor models. In light of these formal results, we discuss some implications for testing the higher-order factor model and the issue of general factor. An interesting aspect concerning the efficient fitting of the higher-order factor model with direct effects is noted.

Key words

factor analysis higher-order factor models hierarchical factor models bi-factor solutions general factor model equivalence 

Copyright information

© The Psychometric Society 1999

Authors and Affiliations

  • Yiu-Fai Yung
    • 1
  • David Thissen
    • 1
  • Lori D. McLeod
    • 1
  1. 1.L. L. Thurstone Psychometric LaboratoryUniversity of North Carolina at Chapel HillUSA
  2. 2.SAS Institute, Inc.Cary

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