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CFA Models with a General Factor and Multiple Sets of Secondary Factors

Author

Listed:
  • Minjeong Jeon

    (University of California, Los Angeles)

  • Frank Rijmen

    (American Institutes for Research)

  • Sophia Rabe-Hesketh

    (University of California, Berkeley)

Abstract

We propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor. The general factor accounts for the common variance among manifest variables, whereas multiple sets of secondary factors account for the remaining source-specific dependency among subsets of manifest variables. A special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings. This proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model. Furthermore, the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables, decomposition of the variances, and the inclusion of interactions, similar to generalizability theory. We provide two applications to illustrate the utility of the proposed class of models.

Suggested Citation

  • Minjeong Jeon & Frank Rijmen & Sophia Rabe-Hesketh, 2018. "CFA Models with a General Factor and Multiple Sets of Secondary Factors," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 785-808, December.
    • Handle: RePEc:spr:psycho:v:83:y:2018:i:4:d:10.1007_s11336-018-9633-x
    DOI: 10.1007/s11336-018-9633-x
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    References listed on IDEAS

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    1. Yiu-Fai Yung & David Thissen & Lori McLeod, 1999. "On the relationship between the higher-order factor model and the hierarchical factor model," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 113-128, June.
    2. Frank Rijmen & Minjeong Jeon & Matthias von Davier & Sophia Rabe-Hesketh, 2014. "A Third-Order Item Response Theory Model for Modeling the Effects of Domains and Subdomains in Large-Scale Educational Assessment Surveys," Journal of Educational and Behavioral Statistics, , vol. 39(4), pages 235-256, August.
    3. Kenneth A. Bollen & Shawn Bauldry, 2010. "Model Identification and Computer Algebra," Sociological Methods & Research, , vol. 39(2), pages 127-156, November.
    4. Li Cai, 2010. "A Two-Tier Full-Information Item Factor Analysis Model with Applications," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 581-612, December.
    5. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
    6. Roderick McDonald, 1982. "A note on the investigation of local and global identifiability," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 101-103, March.
    7. John Schmid & John Leiman, 1957. "The development of hierarchical factor solutions," Psychometrika, Springer;The Psychometric Society, vol. 22(1), pages 53-61, March.
    8. Michael Eid, 2000. "A multitrait-multimethod model with minimal assumptions," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 241-261, June.
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    Cited by:

    1. Minjeong Jeon & Paul Boeck & Xiangrui Li & Zhong-Lin Lu, 2020. "Trivariate Theory of Mind Data Analysis with a Conditional Joint Modeling Approach," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 398-436, June.
    2. Li Cai & Carrie R. Houts, 2021. "Longitudinal Analysis of Patient-Reported Outcomes in Clinical Trials: Applications of Multilevel and Multidimensional Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 754-777, September.

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