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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“Specifically, Reise concluded that B(…) bi-factor modeling potentially provides a solid foundation for conceptualizing psychological constructs, constructing measures, and evaluating a measure’s psychometric properties^ (Reise 2012: 667).”
Background
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Method
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“acceptably well and thus could be empirically justified, which is common across studies of multidimensional constructs (Brunner et al., 2012; Reise, 2012).”
BackgroundMethodInfluential
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Background
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Method
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“This procedure transforms the oblique EFA solution with m correlated factors into an orthogonal m + 1 factor solution represented by one “general factor” common to all items and p orthogonal “group factors” with salient loadings on only a subset of the items (Reise 2012).”
Method
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“A contemporary trend in psychometrics is the rising popularity of bifactor modeling applications (Chen et al., 2006; Reise, 2012).”
BackgroundSelf-citation
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“Yet another example is the use of bifactor models, which have increased in popularity in recent years (Reise, 2012).”
John Carroll’s Views on Intelligence: Bi-Factor vs. Higher-Order Models
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“As the SLT just re-expresses the factor loadings from a higher-order factor model in a form that highlights the relation of the MVs to g and R, the resulting loadings from the SLT are still estimates derived from a higher-order model [53].”
BackgroundMethod
The German Version of the PERMA-Profiler: Evidence for Construct and Convergent Validity of the PERMA Theory of Well-Being in German Speaking Countries
Wammerl, M., Jaunig, J., Mairunteregger, T., & Streit, P. (2019) · Journal of Well-Being Assessment · doi:10.1007/s41543-019-00021-0 · Cited by 109
“Bi-Factor Models are more and more on the rise in personality and particularly in well-being research (Reise 2012).”
Background
Three recommendations based on a comparison of the reliability and validity of the predominant models used in research on the empirical structure of psychopathology.
Forbes, M. K., Greene, A. L., Levin-Aspenson, H. F., Watts, A. L., Hallquist, M. N., Lahey, B. B., Markon, K. E., Patrick, C. J., Tackett, J. L., Waldman, I. D., et al. (2021) · Journal of Abnormal Psychology · doi:10.1037/abn0000533 · Cited by 91
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Schlaegel, C., Richter, N., & Taras, V. (2021) · Journal of World Business · doi:10.1016/j.jwb.2021.101209 · Cited by 113
“Bi-factor models provide information on the common effect of a general factor and the individual effects of its sub-domains (Reise, 2012).”
Background
Construct Validity of the WISC-IV with a Referred Sample: Direct versus Indirect Hierarchical Structures
Canivez, G. L. (2014) · School Psychology Quarterly · doi:10.1037/spq0000032 · Cited by 87
“Reise (2012) noted several advantages of the direct hierarchical (bifactor) model, including: the general factor having direct influences is easy to interpret, both general and specific influences on indicators (subtests) can be examined simultaneously, and examining the psychometric properties is…”
BackgroundMethodInfluential
Association of allostatic load with brain structure and cognitive ability in later life
Booth, T., Royle, N. A., Corley, J., Gow, A. J., Valdés Hernández, M. D. C., Muñoz Maniega, S., Ritchie, S. J., Bastin, M. E., Starr, J. M., Wardlaw, J. M., et al. (2015) · Neurobiology of Aging · doi:10.1016/j.neurobiolaging.2014.12.020 · Cited by 88
Cognitive profile analysis in school psychology: history, issues, and continued concerns
McGill, R. J., Dombrowski, S. C., & Canivez, G. L. (2018) · Journal of School Psychology · doi:10.1016/j.jsp.2018.10.007 · Cited by 91
Applied Psychometrics: The 3-Faced Construct Validation Method, a Routine for Evaluating a Factor Structure
Kyriazos, T. A. (2018) · Psychology · doi:10.4236/psych.2018.98117 · Cited by 90
“In Bifactor ESEM (c.f. Reise, 2012; Marsh et al., 2014) direct effects of the higher-order dimension are specified and additionally because ESEM (Asparouhov & Muthén, 2009) can potentially resolve misspecifications and inflated factor loadings, inherent in CFA method as a result of forcing…”
Method
Don’t Forget the Model in Your Model-based Reliability Coefficients: A Reply to McNeish ()
Savalei, V., & Reise, S. P. (2019) · Collabra Psychology · doi:10.1525/collabra.247 · Cited by 88
Self-citation
The Rosenberg Self-Esteem Scale: A Bifactor Answer to a Two-Factor Question?
McKay, M., Boduszek, D., & Harvey, S. A. (2014) · Journal of Personality Assessment · doi:10.1080/00223891.2014.923436 · Cited by 98
“In this context, the bifactor model can resolve these potentially problematic dimensionality issues (Reise, 2012) as observed in this study.”
TAM: Test Analysis Modules
Robitzsch, A., Kiefer, T., & Wu, M. (2013) · doi:10.32614/cran.package.tam · Cited by 97
Development and testing of a scale to evaluate diet according to the recommendations of the Dietary Guidelines for the Brazilian Population
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The Structure of Academic Self-Concept: A Methodological Review and Empirical Illustration of Central Models
Arens, A. K., Jansen, M., Preckel, F., Schmidt, I., & Brunner, M. (2020) · Review of Educational Research · doi:10.3102/0034654320972186 · Cited by 94
“2016; Reise, 2012; Reise et al., 2011).”
On the Inappropriateness of Using Items to Calculate Total Scale Score Reliability via Coefficient Alpha for Multidimensional Scales
Gignac, G. E. (2013) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000181 · Cited by 86
“Although multifactor models such as the oblique factor model and the higher-order model are much more popular, the bifactor model may be suggested to be gaining some attention (Reise, 2012; Schweizer, Altmeyer, Reiß, & Schreiner, 2010).”
Method
Structural and incremental validity of the Wechsler Adult Intelligence Scale–Fourth Edition with a clinical sample.
Nelson, J. M., Canivez, G. L., & Watkins, M. W. (2013) · Psychological Assessment · doi:10.1037/a0032086 · Cited by 86
“Omega estimated the reliability of the latent factor combining general and specific factor variance, whereas h (what Reise, 2012, termed omega subscale) estimated the reliability of each latent factor with variance from other factors removed (Brunner, Nagy, & Wilhelm, 2012).”
Background
Temperament and brain networks of attention
Posner, M. I., & Rothbart, M. K. (2018) · Philosophical Transactions of the Royal Society B Biological Sciences · doi:10.1098/rstb.2017.0254 · Cited by 95
Transcultural Adaptation of the Oldenburg Burnout Inventory (OLBI) for Brazil and Portugal
Sinval, J., Queirós, C. M. L., Pasian, S. R., & Marôco, J. P. (2019) · Frontiers in Psychology · doi:10.3389/fpsyg.2019.00338 · Cited by 119
Bifactor Models of Personality and College Student Performance: A Broad versus Narrow View
McAbee, S. T., Oswald, F. L., & Connelly, B. S. (2014) · European Journal of Personality · doi:10.1002/per.1975 · Cited by 86
“However, personality inventories are also often designed to measure narrow personality facets that underlie a broader factor (Markon, 2009; Reise, 2012).”
BackgroundMethodInfluential
Internal structure and reliability of the Internalized Stigma of Mental Illness Scale (ISMI-29) and Brief Versions (ISMI-10, ISMI-9) among Americans with depression.
Hammer, J. H., & Toland, M. D. (2016) · Stigma and Health · doi:10.1037/sah0000049 · Cited by 91
“…be best accounted for by (a) a single general internalized stigma of mental illness factor that reflects the common variance across all items plus (b) group factors (i.e., the five subscales) that capture some additional (i.e., unique) common variance among clusters of items (Reise, 2012, p. 688).”
Background
Measuring Disability: Comparing the Impact of Two Data Collection Approaches on Disability Rates
Sabariego, C., Oberhauser, C., Posarac, A., Bickenbach, J. E., Kostanjsek, N. F. I., Chatterji, S., Officer, A., Coenen, M., Chhan, L., & Cieza, A. (2015) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph120910329 · Cited by 85
“Unidimensionality [10] was tested with bifactor analysis [11–13], which assumes the presence of a single general factor and multiple independent group factors.”
Method
Examining the integrity of measurement of cognitive abilities in the prediction of achievement: Comparisons and contrasts across variables from higher-order and bifactor models
Benson, N. F., Kranzler, J. H., & Floyd, R. G. (2016) · Journal of School Psychology · doi:10.1016/j.jsp.2016.06.001 · Cited by 84
Important Goals, Meanings, and Relationships in Flourishing and Languishing States: Towards Patterns of Well-being
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“For this particular study, a three-factor bifactor confirmatory factor analysis model (Reise 2012) applied to the total combined sample (N = 1226) displayed adequate fit with the comparative fit index (CFI) obtaining a value of .”
Envisioning innovation: Does visionary leadership engender team innovative performance through goal alignment?
Mascareño, J., Rietzschel, E. F., & Wisse, B. M. (2019) · Creativity and Innovation Management · doi:10.1111/caim.12341 · Cited by 89
“…our outcome variable by assessing a bi-factor model—a multidimensional structural model specifying that each item on a measure is an indicator of a single factor (labelled the ‘target’ dimension), and each item also is an indicator of one (or more) orthogonal group factors (see Reise, 2012).”
Perceived Demands of Schooling, Stress and Mental Health: Changes from Grade 6 to Grade 9 as a Function of Gender and Cognitive Ability
Giota, J., & Gustafsson, J. (2016) · Stress and Health · doi:10.1002/smi.2693 · Cited by 96
Evaluating dimensional distinctness with correlated-factor models: Limitations and suggestions
Gignac, G. E., & Kretzschmar, A. (2017) · Intelligence · doi:10.1016/j.intell.2017.04.001 · Cited by 91
Assessing student-writers’ self-efficacy beliefs about text revision in EFL writing
Chen, J., & Zhang, L. J. (2019) · Assessing Writing · doi:10.1016/j.asw.2019.03.002 · Cited by 91
Student assessment of teaching as a source of information about aspects of teaching quality in multiple subject domains: an application of multilevel bifactor structural equation modeling
Scherer, R., & Gustafsson, J. (2015) · Frontiers in Psychology · doi:10.3389/fpsyg.2015.01550 · Cited by 81
Building Theories on Top of, and Not Independent of, Statistical Models: The Case of the p-factor
Watts, A. L., Lane, S. P., Bonifay, W. E., Steinley, D., & Meyer, F. A. C. (2020) · Psychological Inquiry · doi:10.1080/1047840x.2020.1853476 · Cited by 89
Dark triads, tetrads, tents, and cores: Why navigate (research) the jungle of dark personality models without a compass (criterion)?
Kowalski, C. M., Rogoza, R., Saklofske, D. H., & Schermer, J. A. (2021) · Acta Psychologica · doi:10.1016/j.actpsy.2021.103455 · Cited by 81
Bifactor Analysis of the Mental Health Continuum—Short Form (MHC—SF)
de Bruin, G. P., & du Plessis, G. A. (2015) · Psychological Reports · doi:10.2466/03.02.pr0.116k20w6 · Cited by 80
Multi-group and hierarchical confirmatory factor analysis of the Wechsler Intelligence Scale for Children—Fifth Edition: What does it measure?
Reynolds, M. R., & Keith, T. Z. (2017) · Intelligence · doi:10.1016/j.intell.2017.02.005 · Cited by 80
The Existential Concerns Questionnaire (ECQ)–Development and Initial Validation of a New Existential Anxiety Scale in a Nonclinical and Clinical Sample
van Bruggen, V., ten Klooster, P. M., Westerhof, G. J., Vos, J., de Kleine, E., Bohlmeijer, E. T., & Glas, G. G. (2017) · Journal of Clinical Psychology · doi:10.1002/jclp.22474 · Cited by 92
The Positive Valence Systems Scale: Development and Validation
Khazanov, G. K., Ruscio, A. M., & Forbes, C. N. (2019) · Assessment · doi:10.1177/1073191119869836 · Cited by 83
“This is in contrast to a scale in which the subscales account for substantial additional variance over and above the general factor (as represented by a bifactor model; Chen, West, & Sousa, 2006; Reise, 2012).”
Psychometric evaluation of two short versions of the Revised Child Anxiety and Depression Scale
Klaufus, L. H., Verlinden, E., van der Wal, M. F., Kösters, M. P., Cuijpers, P. J., & Chinapaw, M. J. M. (2020) · BMC Psychiatry · doi:10.1186/s12888-020-2444-5 · Cited by 87
What is text reading fluency and is it a predictor or an outcome of reading comprehension? A longitudinal investigation.
Kim, Y. G., Quinn, J. M., & Petscher, Y. (2021) · Developmental Psychology · doi:10.1037/dev0001167 · Cited by 79
From inspection to quality: Ways in which school inspection influences change in schools
Gustafsson, J., Ehren, M., Conyngham, G., McNamara, G., Altrichter, H., & O’Hara, J. (2015) · Studies In Educational Evaluation · doi:10.1016/j.stueduc.2015.07.002 · Cited by 79
Investigating the combined effects of workaholism and work engagement: A substantive-methodological synergy of variable-centered and person-centered methodologies
Gillet, N., Morin, A. J. S., Sandrin, É., & Houle, S. A. (2018) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2018.09.006 · Cited by 91
Application of the Bifactor S – 1 Model to Multisource Ratings of ADHD/ODD Symptoms: an Appropriate Bifactor Model for Symptom Ratings
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“Trait impulsivity theory Bifactor statistical models (Holzinger and Swineford 1937; Reise 2012) are frequently used to study the hierarchical nature of psychological constructs.”
Background
Ethnic differences in the mother-son relationship of incarcerated and non-incarcerated male adolescents.
Veen, V. C., Stevens, G. W. J. M., DORELEIJERS, T. A. H., Pels, T. V. M., & Vollebergh, W. (2011) · Pure Amsterdam UMC · doi:10.1186/s13034-016-0111-x · Cited by 31
“Reise SP, Moore TM, Haviland MG. Bifactor models and rotations: explor‑ ing the extent to which multidimensional data yield univocal scale scores.”
BackgroundMethodInfluential
Physical Literacy in Children and Youth—A Construct Validation Study
Cairney, J., Clark, H. J., Dudley, D. A., & Kriellaars, D. J. (2019) · Journal of Teaching in Physical Education · doi:10.1123/jtpe.2018-0270 · Cited by 89
Effect of Foster Care Intervention on Trajectories of General and Specific Psychopathology Among Children With Histories of Institutional Rearing: A Randomized Clinical Trial
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Exploratory Structural Equation Modeling Analysis of the Self-Compassion Scale
Tóth‐Király, I., Bőthe, B., & Orosz, G. (2016) · Mindfulness · doi:10.1007/s12671-016-0662-1 · Cited by 86
“…because bifactor models can grasp a global construct (in the present case, self-compassion) as well as the smaller, more specific constructs (in the present case, the six dimensions) and all can possibly account for the commonality of the items (Brunner et al. 2012; Chen et al. 2012; Reise 2012).”
Background

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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