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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Method
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Background
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Background
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Background
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BackgroundMethodInfluential
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Background
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Method
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Method
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“…the proportion of variance accounted for by both general and group factors, and the label omega hierarchical to represent the proportion accounted for by the general factor alone (McDonald, 1999; Reise, 2012; Reise et al., 2013; Rodriguez et al., 2016a, 2016b; Zinbarg, Revelle, Yovel, & Li, 2005).”
BackgroundMethod
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“A high ωh (> .70; Reise, 2012) is necessary to ensure adequate reliability of the substantive factor.”
BackgroundResultInfluential
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“The Bifactor model is suggested as an important analytical approach to examine construct-relevant psychometric multidimensionality (Reise, 2012; Myers et al., 2014).”
Method
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Background
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Method
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“Bifactor models (see Figure 1) are within the so-called hierarchical models (Canivez, 2016; Reise, 2012), also called nested factor models (Gustafsson & Balke, 1993), and direct hierarchical models (Gignac, 2008).”
BackgroundMethodInfluential
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“3 can be used to indicate good item fit [19].”
Method
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“Bifactor models have originally been invented in intelligence research (Holzinger & Swineford, 1937), but recently experienced a renaissance as an important structural representation of multidimensionality in various other fields (Reise, 2012; Reise et al., 2010).”
HOT and Attractive? The Hazardous Organization Tool as an Instrument to Avoid Attracting and Retaining People with Low Ethical Standards
Wang, B., Andrews, W., & de Vries, R. E. (2023) · Journal of Business and Psychology · doi:10.1007/s10869-023-09900-z · Cited by 12
Patients’ Needs for Care in Public Mental Health: Unity and Diversity of Self-Assessed Needs for Care
Bellier-Teichmann, T., Golay, P., Bonsack, C., & Pomini, V. (2016) · Frontiers in Public Health · doi:10.3389/fpubh.2016.00022 · Cited by 12
“When traditional methods for factor rotation fail to reveal clear and interpretable solutions, the exploration of more complex structures presenting both general and specific factors needs to be considered (15, 16).”
Background
Factor structure, factorial invariance, and validity of the Multidimensional Shame-Related Response Inventory-21 (MSRI-21).
García, A. F., Acosta, M., Pirani, S., Edwards, D. L., & Osman, A. (2017) · Journal of Counseling Psychology · doi:10.1037/cou0000192 · Cited by 12
“For the bifactor model, we computed bifactor-specific statistics, including the explained common variance (ECV; Bentler, 2009; Reise, Moore, & Haviland, 2010) and the percentage of uncontaminated correlations (PUC; Reise, 2012).”
Method
General and specific factors of working alliance in parent training: A bifactor exploratory structural equation modelling approach
Hukkelberg, S. S., & Ogden, T. (2017) · Psychotherapy Research · doi:10.1080/10503307.2017.1330574 · Cited by 12
“As such, these omegas represent indexes of the proportion of reliable variance accounted for by the general and specific factors (Reise, 2012; Zinbarg et al., 2005).”
BackgroundMethodInfluential
Using personality facets to understand the nature of personality-satisfaction relationships
Seltzer, B. K., Öneş, D. S., & Tatar, A. (2017) · Career Development International · doi:10.1108/cdi-08-2017-0141 · Cited by 12
Measuring Depression in a Non-Western War-Affected Displaced Population: Measurement Equivalence of the Beck Depression Inventory
Jayawickreme, N., Verkuilen, J., Jayawickreme, E., Acosta, K., & Foa, E. B. (2017) · Frontiers in Psychology · doi:10.3389/fpsyg.2017.01670 · Cited by 12
“For this, we used exploratory bifactor analysis (Reise, 2012; Mansolf and Reise, 2016).”
Test-Retest Measurement Invariance of Clinic Referred Children’s ADHD Symptoms
Gomez, R., Vance, A. L. A., & Stavropoulos, V. (2017) · Journal of Psychopathology and Behavioral Assessment · doi:10.1007/s10862-017-9636-4 · Cited by 11
A Mokken scale analysis of the peer physical examination questionnaire
Vaughan, B., & Grace, S. (2018) · Chiropractic & Manual Therapies · doi:10.1186/s12998-018-0176-0 · Cited by 12
“High ωh values suggest that the general factor accounts for the total score variance, and supports unidimensionality [37].”
Assessing the Big Five with bifactor computerized adaptive testing.
Nieto, M. D., Abad, F. J., & Olea, J. (2018) · Psychological Assessment · doi:10.1037/pas0000631 · Cited by 12
Establishing norms for mental well‐being in young people (7–19 years) using the General Health Questionnaire‐12
Centofanti, S. A., Lushington, K., Wicking, A., Wicking, P., Fuller, A., Janz, P., & Dorrian, J. (2018) · Australian Journal of Psychology · doi:10.1111/ajpy.12227 · Cited by 12
“…in combination with different ways of quantifying consistency (such as omega as an alternative to Cronbach's alpha), are (re)emerging in recent literature as informative techniques for understanding factor structure (Dunn, Baguley, & Brunsden, 2014; Gignac, 2014; McNeish, 2018; Reise, 2012).”
Method
Initial Validation of the Psychobiosocial States in Physical Education (PBS-SPE) Scale
Bortoli, L., Vitali, F., Battista, R. D., Ruiz, M. C., & Robazza, C. (2018) · Frontiers in Psychology · doi:10.3389/fpsyg.2018.02446 · Cited by 12
“The bifactor model, in particular, is contended to offer a number of key advantages including an easy interpretation of the general factor (which we named “affect/functionality” on the PBS-SPE scale) with direct influences on indicators, simultaneous examination of both general and specific influences on indicators, a…”
Background
Using Exploratory Structural Equation Modeling (ESEM) to Examine the Internal Structure of Posttraumatic Stress Disorder Symptoms
Fresno, A., Arias, V. B., Núñez, D., Spencer, R., Ramos, N., Espinoza, C., Bravo, P., Arriagada, J., & Brunet, A. (2020) · The Spanish Journal of Psychology · doi:10.1017/sjp.2020.46 · Cited by 13
“, 2006) and the omega sub-scale were estimated in the case of the bifactor model (Reise, 2012).”
Method
EDAS-18: validación de la versión corta de la escala de dependencia y adicción al smartphone
García‐Domingo, M., Gutiérrez, V. F., Padilla, J. P., & Aranda, M. (2020) · Terapia psicológica · doi:10.4067/s0718-48082020000300339 · Cited by 12
A mixture modeling perspective of relational turbulence theory in marriage
Goodboy, A. K., Bolkan, S., & Shin, M. (2021) · Communication Monographs · doi:10.1080/03637751.2021.1951785 · Cited by 12
A New Story on the Multidimensionality of the MSPSS: Validity of the Internal Structure through Bifactor ESEM
Merino‐Soto, C., Carbajal, A. B., Toledano‐Toledano, F., Nabors, L., & Núñez-Benítez, M. Á. (2022) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph19020935 · Cited by 12
Bifactor Approach to Modeling Multidimensionality of Physical Self-Perception Profile
Chung, C., Liao, X., Song, H., & Lee, T. (2015) · Measurement in Physical Education and Exercise Science · doi:10.1080/1091367x.2015.1081594 · Cited by 15
“The ECV is the ratio of variance explained by the general factor to the variance explained by the general plus the group factors.”
BackgroundMethodInfluential
Evidence for the Trait-Impulsivity Etiological Model in a Clinical Sample: Bifactor Structure and Its Relation to Impairment and Environmental Risk
Rodenacker, K., Hautmann, C., Görtz‐Dorten, A., & Döpfner, M. (2017) · Research on Child and Adolescent Psychopathology · doi:10.1007/s10802-017-0329-y · Cited by 15
Factor analysis of the Clinical Outcomes in Routine Evaluation – Outcome Measures (CORE-OM) in a Kenyan sample
Falkenström, F., Kumar, M., Zahid, A., Kuria, M. W., & Othieno, C. J. (2018) · BMC Psychology · doi:10.1186/s40359-018-0260-1 · Cited by 13
Measuring Quality of Classroom Interactions in Italian Primary School: Structural Validity of the CLASS K–3
Longobardi, C., Pasta, T., Marengo, D., Prino, L. E., & Settanni, M. (2018) · The Journal of Experimental Education · doi:10.1080/00220973.2018.1533795 · Cited by 15
“With respect to the bifactor model, reliability of general and specific factors was studied by computing the following indicators, as suggested by Reise (2012) and Rodriguez, Reise, & Haviland (2016): coefficients of omega (ω) and coefficients of omega hierarchical for both general (ωh) and…”
BackgroundMethodInfluential
Putting behaviour back into brain-behaviour correlation analysesPreprint
Tiego, J., & Fornito, A. (2022) · OSF Preprints (OSF Preprints) · doi:10.31219/osf.io/g84j2 · Cited by 12
Measurement Invariance of the WISC-V across a Clinical Sample of Children and Adolescents with ADHD and a Matched Control Group
Becker, A. B. C., Maurer, J., Daseking, M., & Pauls, F. (2024) · Journal of Intelligence · doi:10.3390/jintelligence12010006 · Cited by 11
“…primary subtests of the German WISC-V (Wechsler 2017a), omega-hierarchical and omega-hierarchical subscale coefficients have been frequently recommended as more appropriate reliability measures for hierarchical model structures (Brunner et al. 2012; Reise 2012; Sijtsma 2009; Yang and Green 2011).”
BackgroundMethod
Subject and time specificity of students' cognitive, behavioral, and emotional engagement at school
Weich, M., Göllner, R., & Stalder, B. E. (2024) · Learning and Individual Differences · doi:10.1016/j.lindif.2024.102511 · Cited by 15
Cross-national measurement invariance of the Purpose in Life Test in seven Latin American countries
Caycho‐Rodríguez, T., Vilca, L. W., Cervigni, M., Gallegos, M., Martino, P., Calandra, M., Anacona, C. A. R., López-Calle, C., Moreta‐Herrera, R., Chacón-Andrade, E. R., et al. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2022.974133 · Cited by 12
“Thus, the second-order and bifactor models would allow for evaluating the effects of the multidimensionality of the PIL on the total score and on each factor (Reise, 2012).”
Background
The overlap between burnout and depression through a different lens: A multi-method study
Baptista, M. N., Filho, N. H., & Cardoso, H. F. (2022) · Journal of Affective Disorders Reports · doi:10.1016/j.jadr.2022.100437 · Cited by 11
Unraveling the complexity of the associations between students’ science achievement, motivation, and teachers’ feedback
Katsantonis, I., McLellan, R., & Torres, P. E. (2023) · Frontiers in Psychology · doi:10.3389/fpsyg.2023.1124189 · Cited by 14
“…of common method bias was also examined through the Explained Common Variance (ECV) coefficient (Sijtsma, 2009; Rodriguez et al., 2016), which indexes variance explained by a common general latent factor divided by the total variance explained by the group and the general factors (Reise, 2012).”
BackgroundMethod
Validation of the Opening Minds Scale for Health Care Providers (OMS-HC): Factor Structure and Psychometric Properties of the Brazilian Version
Carrara, B. S., Sanches, M., Bobbili, S. J., de Godoy, S., de Sousa, Á. F. L., de Souza, J., & Ventura, C. A. A. (2023) · Healthcare · doi:10.3390/healthcare11071049 · Cited by 11
“The use of the bifactor model for the psychometric evaluation of scales has increased in the literature, particularly regarding the dimensionality of the scale and the relevance of subscales [41].”
Method
Conceptualising and Measuring Adolescents’ Hedonic and Eudemonic Wellbeing: Discriminant Validity and Dimensionality Concerns
Khanna, D., Black, L., Panayiotou, M., Humphrey, N., & Demkowicz, O. (2024) · Child Indicators Research · doi:10.1007/s12187-024-10106-9 · Cited by 12
“Moreover, just as caution must be taken in applying thresholds to other goodness-of-fit indices, Reise (2012) argues that no specific benchmark values for ECV can be proposed as inherently high enough to apply unidimensional models to multidimensional data.”
Computational Concepts and their Assessment in Preschool Students: An Empirical Study
Jiménez, M., Zapata-Cáceres, M., Román-González‬, ‪., Robles, G., Moreno-León, J., & Martín, E. (2024) · Journal of Science Education and Technology · doi:10.1007/s10956-024-10142-8 · Cited by 11
“…were allowed to correlate, and a bi-factor model, a popular method to address within-item multidimensionality by decomposing systematic item variance in a general factor that explains the commonalities between all the items and speciﬁc factors that only affect a subset of the items (Reise, 2012).”
Development and validation of the persistent academic possible selves scale for adolescents (PAPSS)
Lee, J., Husman, J. E., Green, S. B., & Brem, S. K. (2016) · Learning and Individual Differences · doi:10.1016/j.lindif.2016.09.005 · Cited by 11
Factor Structure and Invariance of an Adolescent Risks and Needs Assessment
Strand, P. S., Gotch, C. M., French, B. F., & Beaver, J. L. (2017) · Assessment · doi:10.1177/1073191117706021 · Cited by 11
“As discussed by Reise (2012) and Rodriguez, Reise, and Haviland (2016), the ω coefficient is a latent-variable analogue to Cronbach’s alpha coefficient, capturing all sources of common variance.”
BackgroundMethod
Fathering quality in early childhood and kindergarten achievement in low-income racial–ethnic minority children.
Caughy, M. O., Brinkley, D. Y., Smith, E. P., & Owen, M. T. (2019) · Journal of Family Psychology · doi:10.1037/fam0000611 · Cited by 11
“Bi-factor models are an example of complex factor structure models, as contrasted to more common “simple structure” models, which emphasize a 1:1 correspondence between indicators and factors (Reise, 2012).”
Background
Slow drift rate predicts ADHD symptomology over and above executive dysfunction
Feldman, J. S., & Huang‐Pollock, C. L. (2021) · Child Neuropsychology · doi:10.1080/09297049.2021.1902490 · Cited by 12
“…conjunction with ECV to evaluate potential parameter bias; (3) coefficient omega hierarchical (ωH; McDonald, 1999) and coefficient omega subscale (ωS; Reise, 2012), indices of factor interpretability for the general and specific factors, respectively; and (4) H-index (Hancock & Mueller, 2001),…”
Method
Genetic influences on externalizing psychopathology overlap with cognitive functioning and show developmental variation
Mollon, J., Knowles, E. E. M., Mathias, S. R., Rodrigue, A., Moore, T. M., Calkins, M. E., Gur, R. C., Peralta, J. M., Weiner, D. J., Robinson, E., et al. (2021) · European Psychiatry · doi:10.1192/j.eurpsy.2021.21 · Cited by 11
Validity of the Patient Health Questionnaire Anxiety and Depression Scale (PHQ-ADS) in Patients With Dizziness
Herdman, D., Picariello, F., & Moss-Morris, R. E. (2022) · Otology & Neurotology · doi:10.1097/mao.0000000000003460 · Cited by 11
Adaptation and validation of the self-compassion scale (SCS) in an argentine context
Cababie, M., & Etchezahar, E. D. (2022) · Current Psychology · doi:10.1007/s12144-021-02505-w · Cited by 12
“…complex constructs, as she argues that bifactor models can both grasp the global and the smaller group factors, allowing for all of them to possibly explain the commonality of the items (Brenner et al., 2017; Chen et al., 2011; Neff, 2016; Neff et al., 2017; Reise, 2012; Tóth-Király et al., 2017).”
Background
The factor structure of attention-deficit/hyperactivity disorder in schoolchildren
Arildskov, T. W., Virring, A., Lambek, R., Carlsen, A. H., Sonuga-Barke, E. J. S., Østergaard, S. D., & Thomsen, P. H. (2022) · Research in Developmental Disabilities · doi:10.1016/j.ridd.2022.104220 · Cited by 11
Examining the Factor Structure and Incremental Utility of the Contrast Avoidance Questionnaires via Bifactor Analysis
Rogers, T. A., Gorday, J. Y., Bardeen, J. R., & Benfer, N. (2022) · Journal of Personality Assessment · doi:10.1080/00223891.2022.2081921 · Cited by 11
“Measures that have previously been confirmed with either correlated factors or hierarchical modeling approaches, such as the CAQs, are good candidates for bifactor modeling (Reise, 2012).”
Factor structure and measurement invariance of post-concussion symptom ratings on the Health and Behaviour Inventory across time, raters, and groups: An A-CAP study
Zhang, C., Tang, K., Zemek, R. L., Beauchamp, M. H., Craig, W. R., Doan, Q. H., & Yeates, K. O. (2022) · Journal of the International Neuropsychological Society · doi:10.1017/s1355617722000340 · Cited by 12
“Model-based reliability measures of omega, omega hierarchical (omegaH), and relative omega were computed, with a particular focus on omegaH, to estimate the proportion of observed variance in total and subscale scores that could be attributed to the underlying general and subfactors (Reise, 2012).”
An Evaluation of Item Harmonization Strategies Between Assessment Tools of Psychopathology in Children and Adolescents
Hoffmann, M. S., Moore, T. M., Axelrud, L. K., Tottenham, N., Pan, P. M., Miguel, E. C., Rohde, L. A., Milham, M. P., Satterthwaite, T. D., & Salum, G. A. (2023) · Assessment · doi:10.1177/10731911231163136 · Cited by 11
“In a bifactor structure, the shared variance among all symptoms is explained by a general factor, and covariance not explained by this general factor can be explained by uncorrelated specific factors (Reise, 2012).”
Background
Estudos de validade e confiabilidade da Escala de Avaliação dos Efeitos da Musicoterapia em Grupo na Dependência Química (MTDQ)
Pedrosa, F. G., Garcia, F. D., Gomes, C. M. A., & Loureiro, C. M. V. (2023) · Per Musi · doi:10.35699/2317-6377.2023.45027 · Cited by 11
Teacher personality domains and facets: Their unique associations with student-ratings of teaching quality and teacher enthusiasm
Burić, I., Butković, A., & Kim, L. E. (2023) · Learning and Instruction · doi:10.1016/j.learninstruc.2023.101827 · Cited by 20
The Coexistence of Coping Resources and Specific Coping Styles in Stress: Evidence from Full Information Item Bifactor Analysis
Zhang, J., Cui, M., Wang, W., Lu, H., Wu, Q., Zhu, X., Miao, D., Zhang, Y., Feng, X., & Xiao, W. (2014) · PLoS ONE · doi:10.1371/journal.pone.0096451 · Cited by 13
“Such a model would therefore (a) provide a way to account for the general factor underlying an entire item pool in addition to the domain factors underlying item subsets [42]; and (b) account for the conditional independence of items between domains and the conditional dependence within domains [44].”
Background
Factor analytic replication and model comparison of the BASC-2 Behavioral and Emotional Screening System.
Splett, J. W., Raborn, A., Lane, K. L., Binney, A. J., & Chafouleas, S. M. (2017) · Psychological Assessment · doi:10.1037/pas0000458 · Cited by 11
“Reise (2012) and Reise et al., (2013) suggest that if a proposed bifactor model has a PUC lower than 80%, ECV lower than 60%, and k lower than .70, then the multidimensionality suggested by the bifactor model cannot be ignored and a single score does not adequately explain the variance in the…”
BackgroundResultInfluential
Temperament, Repetitive Negative Thinking, and Depressive Symptoms in Early Adolescence: a Prospective Study
Bijttebier, P., Bastin, M., Nelis, S., Weyn, S., Luyckx, K., Vasey, M. W., & Raes, F. (2017) · Journal of Psychopathology and Behavioral Assessment · doi:10.1007/s10862-017-9624-8 · Cited by 11

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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