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J. Intell.
Volume 6
Issue 3
10.3390/jintelligence6030042
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Article

Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions

by
Michael Eid
1,*,
Stefan Krumm
1,
Tobias Koch
2 and
Julian Schulze
1
1
Department of Education and Psychology, Freie Universität Berlin, Habelschwerdter Allee 45, 14195 Berlin, Germany
2
Methodology Center, Leuphana Universität Lüneburg, 21335 Lüneburg, Germany
*
Author to whom correspondence should be addressed.
J. Intell. 2018, 6(3), 42; https://doi.org/10.3390/jintelligence6030042
Received: 21 March 2018 / Revised: 29 August 2018 / Accepted: 5 September 2018 / Published: 7 September 2018
(This article belongs to the Special Issue The Great Debate: General Ability and Specific Abilities in the Prediction of Important Outcomes)
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Abstract

The bifactor model is a widely applied model to analyze general and specific abilities. Extensions of bifactor models additionally include criterion variables. In such extended bifactor models, the general and specific factors can be correlated with criterion variables. Moreover, the influence of general and specific factors on criterion variables can be scrutinized in latent multiple regression models that are built on bifactor measurement models. This study employs an extended bifactor model to predict mathematics and English grades by three facets of intelligence (number series, verbal analogies, and unfolding). We show that, if the observed variables do not differ in their loadings, extended bifactor models are not identified and not applicable. Moreover, we reveal that standard errors of regression weights in extended bifactor models can be very large and, thus, lead to invalid conclusions. A formal proof of the nonidentification is presented. Subsequently, we suggest alternative approaches for predicting criterion variables by general and specific factors. In particular, we illustrate how (1) composite ability factors can be defined in extended first-order factor models and (2) how bifactor(S-1) models can be applied. The differences between first-order factor models and bifactor(S-1) models for predicting criterion variables are discussed in detail and illustrated with the empirical example. View Full-Text
Keywords: bifactor model; identification; bifactor(S-1) model; general factor; specific factors bifactor model; identification; bifactor(S-1) model; general factor; specific factors
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MDPI and ACS Style

Eid, M.; Krumm, S.; Koch, T.; Schulze, J. Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions. J. Intell. 2018, 6, 42. https://doi.org/10.3390/jintelligence6030042

AMA Style

Eid M, Krumm S, Koch T, Schulze J. Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions. Journal of Intelligence. 2018; 6(3):42. https://doi.org/10.3390/jintelligence6030042

Chicago/Turabian Style

Eid, Michael, Stefan Krumm, Tobias Koch, and Julian Schulze. 2018. "Bifactor Models for Predicting Criteria by General and Specific Factors: Problems of Nonidentifiability and Alternative Solutions" Journal of Intelligence 6, no. 3: 42. https://doi.org/10.3390/jintelligence6030042

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