Cited by 2,112Psychometric Methodologies and TestingMental Health Research TopicsPersonality Traits and Psychology

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The Rediscovery of Bifactor Measurement Models

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Reise, Steven P.·2012·Multivariate Behavioral Research

DOI 10.1080/00273171.2012.715555PMC PMC3773879

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Abstract

multidimensionality in a set of ordered categorical item responses. I begin by describing the Schmid-Leiman bifactor procedure (Schmid & Leiman, 1957), and highlight its relations with correlated-factors and second-order exploratory factor models. After describing limitations of the Schmid-Leiman, two newer methods of exploratory bifactor modeling are considered, namely, analytic bifactor (Jennrich & Bentler, 2011) and target bifactor rotations (Reise, Moore, & Maydeu-Olivares, 2011). In section two, I discuss limited and full-information estimation approaches to confirmatory bifactor models that have emerged from the item response theory and factor analysis traditions, respectively. Comparison of the confirmatory bifactor model to alternative nested confirmatory models and establishing parameter invariance for the general factor also are discussed. In the final section, important applications of bifactor models are reviewed. These applications demonstrate that bifactor modeling potentially provides a solid foundation for conceptualizing psychological constructs, constructing measures, and evaluating a measure's psychometric properties. However, some applications of the bifactor model may be limited due to its restrictive assumptions.

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BackgroundMethodInfluential
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Background
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Toland, M. D., Sulis, I., Giambona, F., Porcu, M., & Campbell, J. M. (2016) · Journal of School Psychology · doi:10.1016/j.jsp.2016.11.001 · Cited by 62
The development and psychometric properties of the Interpersonal Sexual Objectification Scale—Perpetration Version.
Gervais, S. J., Davidson, M. M., Styck, K. M., Canivez, G. L., & DiLillo, D. (2017) · Psychology of Violence · doi:10.1037/vio0000148 · Cited by 62
Positive maternal mental health during pregnancy associated with specific forms of adaptive development in early childhood: Evidence from a longitudinal study
Phua, D. Y., Kee, M. Z. L., Koh, D. X. P., Rifkin‐Graboi, A., Daniels, M., Chen, H., Chong, Y. S., Broekman, B. F. P., Magiati, I., Karnani, N., et al. (2017) · Development and Psychopathology · doi:10.1017/s0954579417001249 · Cited by 68
“4% were explained by the subfactors, which corroborated with the results that maternal mental health during pregnancy was multidimensional (Reise, 2012).”
ResultInfluential
General Psychopathology and Dysregulation Profile in a Longitudinal Community Sample: Stability, Antecedents and Outcomes
Deutz, M. H. F., Geeraerts, S. B., Belsky, J., Deković, M., van Baar, A. L., Prinzie, P., & Patalay, P. (2019) · Child Psychiatry & Human Development · doi:10.1007/s10578-019-00916-2 · Cited by 73
Multi-Faceted Constructs in Abnormal Psychology: Implications of the Bifactor S - 1 Model for Individual Clinical Assessment
Eid, M. (2020) · Research on Child and Adolescent Psychopathology · doi:10.1007/s10802-020-00624-9 · Cited by 67
“Although the model is more than 80 years old (Holzinger and Swineford 1937) it has been leading a niche existence for a long time and was rediscoverd only about ten years ago (Eid et al. 2017; Reise 2012).”
Method
The Dark Triad: Specific or general sources of variance? A bifactor exploratory structural equation modeling approach
McLarnon, M. J. W., & Tarraf, R. C. (2017) · Personality and Individual Differences · doi:10.1016/j.paid.2017.02.049 · Cited by 61
Using the Depression, Anxiety, Stress Scales–21 With U.S. Adolescents: An Alternate Models Analysis
Moore, S. A., Dowdy, E., & Furlong, M. J. (2017) · Journal of Psychoeducational Assessment · doi:10.1177/0734282916651537 · Cited by 61
“Omega coefficients and explained common variance (ECV) were calculated for the bifactor model with three specific factors to further assess the unidimensionality of the DASS–21 (Reise, 2012; Rodriguez, Reise, & Haviland, 2016).”
Method
Development and Initial Validation of a Multidimensional Scale Assessing Subjective Well-Being: The Well-Being Scale (WeBS)
Lui, P. P., & Fernando, G. A. (2017) · Psychological Reports · doi:10.1177/0033294117720696 · Cited by 79
Bifactor Models of Attention-Deficit/Hyperactivity Disorder (ADHD): An Evaluation of Three Necessary but Underused Psychometric Indexes
Arias, V. B., Ponce, F. P., & Núñez, D. (2016) · Assessment · doi:10.1177/1073191116679260 · Cited by 63
“, 2006) and the coefficient omega subscale (ω S ; Reise, 2012) of G ih , IN s , and HI s (B3F models), and impulsivity in the case of the models with three specific factors (B4F models).”
BackgroundMethodInfluential
Common mechanisms of executive attention underlie executive function and effortful control in children
Tiego, J., Bellgrove, M. A., Whittle, S., Pantelis, C., & Testa, R. (2019) · Developmental Science · doi:10.1111/desc.12918 · Cited by 68
“5%), and could therefore be collapsed into a unidimensional measure without introducing bias in the model (Reise, 2012; Reise et al., 2013; Rodriguez et al., 2016).”
BackgroundMethodInfluential
Psychometric properties of the Highly Sensitive Child scale across developmental stage, gender, and country
Weyn, S., Leeuwen, K. G. V., Pluess, M., Lionetti, F., Greven, C. U., Goossens, L., Colpin, H., Noortgate, W. V. D., Verschueren, K., Bastin, M., et al. (2019) · Current Psychology · doi:10.1007/s12144-019-00254-5 · Cited by 63
A longitudinal perspective on the associations between work engagement and workaholism
Tóth‐Király, I., Morin, A. J. S., & Salmela‐Aro, K. (2020) · Work & Stress · doi:10.1080/02678373.2020.1801888 · Cited by 59
The Interpersonal Shame Inventory for Asian Americans: Scale development and psychometric properties.
Wong, Y. J., Kim, B. S. K., Nguyen, C., Cheng, J. K. Y., & Saw, A. (2013) · Journal of Counseling Psychology · doi:10.1037/a0034681 · Cited by 59
“eral factor (Reise, 2012).”
Investigation of a bifactor model of the Strengths and Difficulties Questionnaire
Caci, H. M., Morin, A. J. S., & Tran, A. (2015) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-015-0679-3 · Cited by 73
“This could partly be related to the reliance on higher-order factor models over bifactor models [13, 15, 18].”
Background
University students' need satisfaction trajectories: A growth mixture analysis
Gillet, N., Morin, A. J. S., Huyghebaert, T., Burger, L., Maillot, A., Poulin, A., & Tricard, E. (2019) · Learning and Instruction · doi:10.1016/j.learninstruc.2017.11.003 · Cited by 57
“The measurement models for the need satisfaction variables were estimated using bifactor confirmatory factor analyses (Holzinger & Swineford, 1937; Reise, 2012).”
Method
Forgiveness takes place on an attitudinal continuum from hostility to friendliness: Toward a closer union of forgiveness theory and measurement
Forster, D. E., Billingsley, J., Russell, V. M., McCauley, T. G., Smith, A., Burnette, J. L., Ohtsubo, Y., Schug, J., Lieberman, D., & McCullough, M. E. (2020) · Journal of Personality and Social Psychology · doi:10.1037/pspi0000227 · Cited by 57
Double Barreled Questions: An Analysis of the Similarity of Elements and Effects on Measurement Quality
Menold, N. (2020) · Journal of Official Statistics · doi:10.2478/jos-2020-0041 · Cited by 43
“Because of the reversed formulation of the items for each sub-factor, Aichholzer and Zeglovits (2015) also modeled a latent “method” variable that claimed for potential acquiescence bias (the “bi-factor model”, Reise 2012).”
Method
Development of the PROMIS® Nicotine Dependence Item Banks
Shadel, W. G., Edelen, M. O., Tucker, J. S., Stucky, B. D., Hansen, M. H., & Cai, L. (2014) · Nicotine & Tobacco Research · doi:10.1093/ntr/ntu032 · Cited by 57
“Furthermore, in the exploratory subsample, the test-level explained common variance (ECV; Reise, 2012) associated with the nicotine dependence (general) factor increased substantially from 0.72 to 0.86 indicating a more strongly unidimensional model.”
Influential
Construct Validity of the WISC-V in Clinical Cases: Exploratory and Confirmatory Factor Analyses of the 10 Primary Subtests
Canivez, G. L., McGill, R. J., Dombrowski, S. C., Watkins, M. W., Pritchard, A. E., & Jacobson, L. A. (2020) · Assessment · doi:10.1177/1073191118811609 · Cited by 53
Exploratory and hierarchical factor analysis of the WJ-IV Cognitive at school age.
Dombrowski, S. C., McGill, R. J., & Canivez, G. L. (2016) · Psychological Assessment · doi:10.1037/pas0000350 · Cited by 56
The Psychometric Modeling of Scientific Reasoning: a Review and Recommendations for Future Avenues
Edelsbrunner, P. A., & Dablander, F. (2018) · Educational Psychology Review · doi:10.1007/s10648-018-9455-5 · Cited by 64
Screening for psychological distress using the Patient Health Questionnaire Anxiety and Depression Scale (PHQ-ADS): Initial validation of structural validity in dialysis patients
Chilcot, J., Hudson, J. L., Moss-Morris, R., Carroll, A., Game, D., Simpson, A., & Hotopf, M. (2018) · General Hospital Psychiatry · doi:10.1016/j.genhosppsych.2017.09.007 · Cited by 77
Validation of a Google Street View-Based Neighborhood Disorder Observational Scale
Marco, M., Enrique Gracia, A., Martín-Fernández, M., & López‐Quílez, A. (2017) · Journal of Urban Health · doi:10.1007/s11524-017-0134-5 · Cited by 55
“The model revealed also a general neighborhood disorder dimension that explained all the shared variance not captured by the specific dimensions [42].”
Background
The factor structure of the Hopkins Symptoms Checklist (HSCL-25) in a student population: A cautionary tale
Skogen, J. C., Øverland, S. N., Smith, O. R. F., & Aarø, L. E. (2017) · Scandinavian Journal of Public Health · doi:10.1177/1403494817700287 · Cited by 55
“Further, a bi-factor approach can also be used to determine whether the specific subscales are justified, and how reliable they are after taking the general factor into account [17], an opportunity missed by previous studies investigating the factor structure of HSCL-25.”
Influential
Explaining general and specific factors in longitudinal, multimethod, and bifactor models: Some caveats and recommendations.
Koch, T., Holtmann, J., Bohn, J., & Eid, M. (2017) · Psychological Methods · doi:10.1037/met0000146 · Cited by 63
“In applications of the bifactor models, it is typically assumed that the specific factors are “residualized factors” (Reise, 2012, p. 691).”
BackgroundMethodInfluential
Complementary variable- and person-centred approaches to the dimensionality of work engagement: a longitudinal investigation
Gillet, N., Caesens, G., Morin, A. J. S., & Stinglhamber, F. (2019) · European Journal of Work and Organizational Psychology · doi:10.1080/1359432x.2019.1575364 · Cited by 61
“…ratio of variance explained by the global factor (work engagement) relative to that explained by the specific factors (vigour, dedication, and absorption) is forced to be exactly the same for all items associated with a specific first-order factor (Gignac, 2016; Morin et al., 2016; Reise, 2012).”
BackgroundMethod
On the Meaning of the “ P Factor” in Symmetrical Bifactor Models of Psychopathology: Recommendations for Future Research From the Bifactor-( S −1) Perspective
Heinrich, M., Geiser, C., Zagorscak, P., Burns, G. L., Bohn, J., Becker, S. P., Eid, M., Beauchaine, T. P., & Knaevelsrud, C. (2021) · Assessment · doi:10.1177/10731911211060298 · Cited by 69
“Those correlations should, therefore, vanish when effects of the general factor are removed (Eid et al., 2017; Reise, 2012).”
BackgroundInfluential
The Structure and Measurement of Unusual Sensory Experiences in Different Modalities: The Multi-Modality Unusual Sensory Experiences Questionnaire (MUSEQ)
Mitchell, C. A. A., Maybery, M. T., Russell-Smith, S. N., Collerton, D., Gignac, G. E., & Waters, F. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.01363 · Cited by 61
“Modality Subscales and Group Differences Relating to this latter point is the issue of whether the modality factors are viable as subscales, as the presence of multidimensionality does not necessarily warrant the creation of subscores (Reise, 2012).”
Background
Community Collectivism: A social dynamic approach to conceptualizing culture
Akkuş, B., Postmes, T., & Stroebe, K. E. (2017) · PLoS ONE · doi:10.1371/journal.pone.0185725 · Cited by 54
“In order to do so we conducted bifactor analysis [62, 63] on Sample 1 using the Lavaan-package for R.”
Method
A multirater perspective on personality and performance: An empirical examination of the trait–reputation–identity model.
Connelly, B. S., McAbee, S. T., Oh, I., Jung, Y., & Jung, C.-W. (2021) · Journal of Applied Psychology · doi:10.1037/apl0000732 · Cited by 54
Psychometric Properties and Performance of the Patient Reported Outcomes Measurement Information System® (PROMIS®) Depression Short Forms in Ethnically Diverse Groups.
Teresi, J. A., Ocepek‐Welikson, K., Kleinman, M., Ramirez, M. M., & Kim, G. (2016) · PubMed · Cited by 54
Evaluation of the Strengths and Difficulties Questionnaire-Dysregulation Profile (SDQ-DP).
Deutz, M. H. F., Shi, Q., Vossen, H. G. M., Huijding, J., Prinzie, P., Deković, M., van Baar, A. L., & Woltering, S. (2018) · Psychological Assessment · doi:10.1037/pas0000564 · Cited by 56
“…ly fo r th e pe rs on al us e of th e in di vi du al us er an d is no t to be di ss em in at ed br oa dl y. recently been rediscovered as an effective approach to examine multidimensionality, that is, determining whether a set of items (symptoms) reflect a common underlying construct (Reise, 2012).”
Multidimensional Item Response Theory for Factor Structure Assessment in Educational Psychology Research
Immekus, J. C., Snyder, K. E., & Ralston, P. A. S. (2019) · Frontiers in Education · doi:10.3389/feduc.2019.00045 · Cited by 54
“In recent years, within educational Frontiers in Education | www.frontiersin.org 7 May 2019 | Volume 4 | Article 45 (Gibbons and Hedeker, 1992) and psychological (e.g., Gibbons et al., 2007) literature, the bifactor structure has garnered increased attention (see Model D; Reise, 2012).”
Background
Agreeableness and the common core of dark traits are functionally different constructs
Moshagen, M., Zettler, I., Horsten, L. K., & Hilbig, B. E. (2020) · Journal of Research in Personality · doi:10.1016/j.jrp.2020.103986 · Cited by 54
Assessment of Fear of COVID-19 in Older Adults: Validation of the Fear of COVID-19 Scale
Caycho‐Rodríguez, T., Tomás, J. M., Barboza-Palomino, M., Ventura‐León, J., Gallegos, M., Reyes-Bossio, M. A., & Vilca, L. W. (2021) · International Journal of Mental Health and Addiction · doi:10.1007/s11469-020-00438-2 · Cited by 53
“However, the two-factor model may have limitations to capture multidimensionality of fear of COVID-19, because the variance of every item may be associated to both a global factor and simultaneously to a specific factor (Reise 2012).”
BackgroundMethod
Factor structure, internal reliability, and construct validity of the Brief Resilience Scale (BRS) : A study on persons with serious mental illness living in the community
Sánchez, J., Estrada‐Hernández, N., Booth, J., & Pan, D. (2021) · Psychology and Psychotherapy Theory Research and Practice · doi:10.1111/papt.12336 · Cited by 66
Impulsivity is a stable, measurable, and predictive psychological trait
Huang, Y., Luan, S., Wu, B., Li, Y., Wu, J., Chen, W., & Hertwig, R. (2024) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2321758121 · Cited by 68
“A bifactor model encompasses both the broad and the narrow concepts of an underlying construct by establishing a general factor and several specific factors (46).”
A bifactor model of subjective well-being: A re-examination of the structure of subjective well-being
Jovanović, V. (2015) · Personality and Individual Differences · doi:10.1016/j.paid.2015.07.026 · Cited by 53
“The bifactor model consists of one general factor and a number of specific factors, allowing each item to load both on the general factor and specific factor (Reise, 2012).”
BackgroundMethod
Internal structure of the Community Assessment of Psychic Experiences—Positive (CAPE-P15) scale: Evidence for a general factor
Núñez, D., Arias, V. B., Vogel, E. H., & Gómez, L. E. (2015) · Schizophrenia Research · doi:10.1016/j.schres.2015.04.018 · Cited by 54
A General Approach for Fitting Pure Exploratory Bifactor Models
Lorenzo‐Seva, U., & Ferrando, P. J. (2018) · Multivariate Behavioral Research · doi:10.1080/00273171.2018.1484339 · Cited by 53
“Finally, there is the most general problem of the nonnegligible small cross-loadings that are forced to be zero, a restriction which is a potential source of misfit and biased parameter estimates in CFA applications (Ferrando & Lorenzo-Seva, 2000, Reise, 2012).”
BackgroundMethod
Unpacking eye movements during oral and silent reading and their relations to reading proficiency in beginning readers
Kim, Y. G., Petscher, Y., & Vorstius, C. (2019) · Contemporary Educational Psychology · doi:10.1016/j.cedpsych.2019.03.002 · Cited by 52
Modeling environment through a general exposome factor in two independent adolescent cohorts
Moore, T. M., Visoki, E., Argabright, S. T., DiDomenico, G. E., Sotelo, I., Wortzel, J. D., Naeem, A., Gur, R. C., Gur, R. E., Warrier, V., et al. (2022) · Exposome · doi:10.1093/exposome/osac010 · Cited by 60
Examining the Factor Structure and Structural Invariance of the PANAS Across Children, Adolescents, and Young Adults
Allan, N. P., Lonigan, C. J., & Phillips, B. M. (2015) · Journal of Personality Assessment · doi:10.1080/00223891.2015.1038388 · Cited by 52
“In contrast, bifactor models operate under the assumption that there is a general factor accounting for common variance among all items as well as factors that can be explained by common variance in item clusters, independent of the general factor (e.g., Chen, Hayes, Carver, Laurenceau, & Zhang, 2012; Reise, 2012).”
Background
Scale development and psychometric properties of internalizing symptoms: The interRAI Child and Youth Mental Health internalizing subscale
Lau, C., Stewart, S. L., Saklofske, D. H., & Hirdes, J. P. (2019) · Psychiatry Research · doi:10.1016/j.psychres.2019.06.013 · Cited by 54
Bifactor Models, Explained Common Variance (ECV), and the Usefulness of Scores from Unidimensional Item Response Theory Analyses
Quinn, H. (2019) · Carolina Digital Repository (University of North Carolina at Chapel Hill) · doi:10.17615/t6ff-a088 · Cited by 59
Development and Initial Validation Analyses of the Living with Idiopathic Pulmonary Fibrosis Questionnaire
Swigris, J. J., Andrae, D. A., Churney, T., Johnson, N., Scholand, M. B., White, E. S., Matsui, A., Raimundo, K., & Evans, C. J. (2020) · American Journal of Respiratory and Critical Care Medicine · doi:10.1164/rccm.202002-0415oc · Cited by 53
“Total scores for both symptoms and impact modules were calculated according to variations of the bifactor model (22, 23), in which items all contribute to a general factor but are then bundled into so-called “testlets” to account for residual variance in the data.”
Should We Be Looking at the Forest or the Trees? Overall Psychological Need Satisfaction and Individual Needs as Predictors of Physical Activity
Brunet, J., Gunnell, K. E., Teixeira, P., Sabiston, C. M., & Bélanger, M. (2016) · Journal of Sport and Exercise Psychology · doi:10.1123/jsep.2016-0256 · Cited by 50
“The bifactor model approach may offer a viable analytical alternative to account for the dilemmas inherent in the general-and specific-factor approaches (Reise, 2012).”
BackgroundMethodInfluential

Authors: Reise, S. P.
Affiliations: University of California, Los Angeles (US)
Corresponding author: Reise, Steven P.
ORCID: Reise, Steven P.
Venue: Multivariate Behavioral Research
Publisher: Informa UK Limited
Published: 2012-09
Volume: 47
Issue: 5
Pages: 667-696
ISSN: 0027-3171 (ISSN-L)
1532-7906
DOI: 10.1080/00273171.2012.715555
PMC: PMC3773879
OpenAlex: W2025929695
Cited by: 2,112
References: 70
Citations by year: 2026: 203 · 2025: 113 · 2024: 134 · 2023: 174 · 2022: 165 · 2021: 200 · 2020: 222 · 2019: 181 · 2018: 203 · 2017: 175 · 2016: 139 · 2015: 98 · 2014: 68 · 2013: 32 · 2012: 4
FWCI: 85.93
Type: journal article
Language: en
Open access: bronze
doi.org
Locations: Multivariate Behavioral Research (publishedVersion)
PubMed (publishedVersion)
Europe PMC (PubMed Central) (acceptedVersion)
PubMed Central (acceptedVersion)
Funders: National Institutes of Health
National Institute on Drug Abuse (RL1DA024853)
National Institute of Arthritis and Musculoskeletal and Skin Diseases (U01AR052177)
National Institute of Dental and Craniofacial Research (UL1DE019580)
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
Social Sciences › Psychology › Clinical Psychology › Personality Traits and Psychology
Keywords: bifactor model, multidimensionality, general factor, parameter invariance, nested models, construct measurement, psychometric properties

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The Rediscovery of Bifactor Measurement Models

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