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On the Relationship between the Higher-Order Factor Model and the Hierarchical Factor Model
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.
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Cites
The Development of Hierarchical Factor Solutions
Schmid, J., & Leiman, J. M. (1957) · Psychometrika · doi:10.1007/bf02289209 · Cited by 1,098
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The Rediscovery of Bifactor Measurement Models
Reise, S. P. (2012) · Multivariate Behavioral Research · doi:10.1080/00273171.2012.715555 · Cited by 2,112
A Comparison of Bifactor and Second-Order Models of Quality of Life
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Metadata
- Authors
- Yung, Y.-F., Thissen, D., & McLeod, L. D.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1999-06
- Volume
- 64
- Issue
- 2
- Pages
- 113-128
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2007404044
- Cited by
- 403
- References
- 1
- FWCI
- 2.35
- Type
- journal article
- Language
- en
- Open access
- closed
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