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Cited by 766Psychometric Methodologies and TestingMental Health Research TopicsStatistical Methods and Bayesian Inference

Multidimensionality and Structural Coefficient Bias in Structural Equation Modeling: A Bifactor Perspective

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Reise, Steven P., Scheines, Richard, Widaman, Keith F., Haviland, Mark G.·2013·Educational and Psychological Measurement
DOI 10.1177/0013164412449831
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Abstract

In this study, the authors consider several indices to indicate whether multidimensional data are “unidimensional enough” to fit with a unidimensional measurement model, especially when the goal is to avoid excessive bias in structural parameter estimates. They examine two factor strength indices (the explained common variance and omega hierarchical) and several model fit indices (root mean square error of approximation, comparative fit index, and standardized root mean square residual). These statistics are compared in population correlation matrices determined by known bifactor structures that vary on the (a) relative strength of general and group factor loadings, (b) number of group factors, and (c) number of items or indicators. When fit with a unidimensional measurement model, the degree of structural coefficient bias depends strongly and inversely on explained common variance, but its effects are moderated by the percentage of correlations uncontaminated by multidimensionality, a statistic that rises combinatorially with the number of group factors. When the percentage of uncontaminated correlations is high, structural coefficients are relatively unbiased even when general factor strength is low relative to group factor strength. On the other hand, popular structural equation modeling fit indices such as comparative fit index or standardized root mean square residual routinely reject unidimensional measurement models even in contexts in which the structural coefficient bias is low. In general, such statistics cannot be used to predict the magnitude of structural coefficient bias.

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  • As the ECV and ωh values of the general factor were ≥0.60 and ≥0.70, respectively, in both the WISC/bifactor and CHC/higher order factor models, it follows that the FSIQ score will not be biased.

    “As this was the case for the general factors in both the WISC/bifactor and CHC/higher order factor models, it follows that the FSIQ score will not be biased.”

    From Structure of the Wechsler Intelligence Scale for Children – Fourth Edition in a Group of Children with ADHD (2016) · cites this paper as Reise et al. (2013b)

    The Discussion (page unavailable) gives ECV >.60 and ωh >.70 as tentative benchmarks for predicting bias in structural coefficient estimates when PUC is below .80. It does not establish that meeting those thresholds guarantees an unbiased FSIQ score in either the WISC/bifactor or CHC/higher-order model; it cautions that the findings need further generalization. (LLM, conf=0.88)

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  • There is no cut-off point for omega to evaluate acceptable reliability; a minimum of .50 and values closer to .75 are recommended for satisfactory and good reliability.

    “There is no cut-off point for omega to evaluate acceptable reliability, a minimum of .50 and values closer to .75 are recommended for satisfactory and good reliability [40].”

    From Dimensionality of the system usability scale among professionals using internet-based interventions for depression: a confirmatory factor analysis (2020) · cites this paper as [40]

  • When PUC is lower than .80, general ECV is greater than .60 and omega hierarchical is greater than .70, multidimensionality is not severe enough to disqualify the interpretation of the instrument as primarily unidimensional.

    “When a PUC value is lower than .80, the general ECV value greater than .60 and omega hierarchical (of the general factor) is greater than .70 it is suggested that the presence of multidimensionality is not severe enough to disqualify the interpretation of the instrument as primarily unidimensional [40].”

    From Dimensionality of the system usability scale among professionals using internet-based interventions for depression: a confirmatory factor analysis (2020) · cites this paper as [40]

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Research works printed but not linked: 11

  1. Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
  2. Chen, F. F., Hayes, A., Carver, C. S., Laurenceau, J.-P., & Zhang, Z. (2012). Modeling general and specific variance in multifaceted constructs: A comparison of the bifactor model to other approaches. Journal of Personality, 80, 219-251.
  3. Gustafsson, J. E., & Aberg-Bengtsson, L. (2010). Unidimensionality and the interpretability of psychological instruments. In S. E. Embretson (Ed.), Measuring psychological constructs (pp. 97-121). Washington, DC: American Psychological Association.
  4. Hattie, J. (1985). Methodology review: Assessing unidimensionality of tests and items. Applied Psychological Measurement, 9, 139-164.
  5. Ip, E. H. (2010). Empirically indistinguishable multidimensional IRT and locally dependent unidimensional item response models. British Journal of Mathematical and Statistical Psychology, 63, 395-416.
  6. MacCallum, R. C., & Tucker, L. R. (1991). Representing sources of error in the common factor model: Implications for theory and practice. Psychological Bulletin, 109, 502-511.
  7. Reise, S. P., Cook, K. F., & Moore, T. M. (in press). A direct modeling approach for evaluating the impact of multidimensionality on unidimensional item response theory model parameters. In S. Reise & D. Revicki (Eds.), Handbook of applied item response theory in typical performance assessment. New York, NY: Taylor & Francis.
  8. Reise, S. P., Moore, T. M., & Haviland, M. G. (2010). Bifactor models and rotations: Exploring the extent to which multidimensional data yield univocal scale scores. Journal of Personality Assessment, 92, 544-559.
  9. Reise, S. P., Moore, T. M., & Haviland, M. G. (in press). Applying unidimensional item response theory models to psychological data. In K. Geisinger (Ed.), APA handbook of testing and assessment in psychology. Washington, DC: American Psychological Association.
  10. Wainer, H., Bradlow, E., & Wang, X. (2007). Testlet response theory and its applications. New York, NY: Cambridge University Press.
  11. West, S. G., Taylor, A. B., & Wu, W. (in press). Model fit and model selection in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling. New York, NY: Guilford Press.

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Authors
Reise, S. P., Scheines, R., Widaman, K. F., & Haviland, M. G.
Affiliations
  • University of California, Los Angeles (US)
  • Carnegie Mellon University (US)
  • University of California, Davis (US)
  • Loma Linda University (US)
ORCID
Venue
Educational and Psychological Measurement
Publisher
SAGE Publications
Published
2012-07-17
Volume
73
Issue
1
Pages
5-26
ISSN
  • 0013-1644 (ISSN-L)
  • 1552-3888
DOI
10.1177/0013164412449831
OpenAlex
W1981882373
Cited by
766
References
5
Citations by year
2026: 72 · 2025: 62 · 2024: 58 · 2023: 97 · 2022: 95 · 2021: 88 · 2020: 63 · 2019: 70 · 2018: 50 · 2017: 41 · 2016: 32 · 2015: 15 · 2014: 9 · 2013: 11 · 2012: 2
FWCI
15.66
Type
journal article
Language
en
Open access
Licence
journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
Locations
  • Educational and Psychological Measurement (publishedVersion)
  • eScholarship (California Digital Library) (submittedVersion)
Topics
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
  • Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords
multidimensionality, bifactor model, omega hierarchical, model fit indices, comparative fit index, RMSEA

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