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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Modelos factoriales de la Escala de Autoestima de Rosenberg en adolescentes peruanos
Sánchez‐Villena, A. R., Fuente-Figuerola, V. D. L., & Ventura‐León, J. (2021) · Revista de Psicopatología y Psicología Clínica · doi:10.5944/rppc.26631 · Cited by 26
“59, un valor nada despreciable que sugeriría unidimensionalidad (Reise, 2012); b) si bien los modelos bifactor de la RSE han demostrado resultados óptimos (Alessandri et al.”
Background
Development and validation of the Perceived Online Racism Scale short form (15 items) and very brief (six items)
Keum, B. T. (2021) · Computers in Human Behavior Reports · doi:10.1016/j.chbr.2021.100082 · Cited by 26
Impact of COVID-19 on psychological wellbeing
Zhao, Q., Sun, X.-X., Xie, F., Chen, B.-J., Wang, L., Hu, L., & Dai, Q. (2021) · International Journal of Clinical and Health Psychology · doi:10.1016/j.ijchp.2021.100252 · Cited by 22
Cross-cultural adaptation and psychometric properties of the Kessler Distress Scale (K10): an application of the rating scale model
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“According to Reise (2012), in the case of a second-order factor model, the general factor is responsible for explaining the variance of first-order factors, which in turn mirrors the variance of the items.”
BackgroundMethod
Assessing Alexithymia: Psychometric Properties of the Perth Alexithymia Questionnaire in a Spanish-Speaking Sample
Becerra, R., Baeza, C. G., Fernández, A. M., & Preece, D. A. (2021) · Frontiers in Psychiatry · doi:10.3389/fpsyt.2021.710398 · Cited by 26
A psychometric investigation of harmonious and obsessive work passion
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Development of the Japanese Version of the State Self-Compassion Scale (SSCS-J)
Miyagawa, Y., Tóth‐Király, I., Knox, M. C., Taniguchi, J., & Niiya, Y. (2022) · Frontiers in Psychology · doi:10.3389/fpsyg.2021.779318 · Cited by 27
“First, this framework accounts for the co-existence of hierarchically ordered constructs by providing a direct and explicit estimate of global self-compassion (i.e., G-factors; Reise, 2012) in conjunction with specific factors (i.e., S-factors) depicting the unique quality associated with each subscale and left unexpl…”
Background
Can hypnotic susceptibility be explained by bifactor models? Structural equation modeling of the Harvard group scale of hypnotic susceptibility – Form A
Zahedi, A., & Sommer, W. (2022) · Consciousness and Cognition · doi:10.1016/j.concog.2022.103289 · Cited by 29
The general psychopathology factor (p) from adolescence to adulthood: Exploring the developmental trajectories ofpusing a multi-method approach
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“…was quantified by calculating the explained common variance (ECV), Omega total ( ω ), Omega Subscale ( ω S ), Omega Hierarchical/Hierarchical Subscale ( ω HS / ω HS ), Relative ω , and Hancock and Mueller’s (2001) H construct replicability index (Reise, 2012; Rodriguez et al., 2016a, 2016b).”
Model fit is a fallible indicator of model quality in quantitative psychopathology research: A reply to Bader and Moshagen.
Greene, A. L., Eaton, N. R., Forbes, M. K., Fried, E. I., Watts, A. L., Kotov, R., & Krueger, R. F. (2022) · Journal of Psychopathology and Clinical Science · doi:10.1037/abn0000770 · Cited by 29
“If so, they should be indifferent to their indicators, or consistently de ﬁ ned no matter which subset of indicators are included in the model (i.e., indicator invariance; Reise, 2012).”
Background
Measurement properties of the Client-centered Care Questionnaire (CCCQ): factor structure, reliability and validity of a questionnaire to assess self-reported client-centeredness of home care services in a population of frail, older people
Muntinga, M. E., Mokkink, L. B., Knol, D. L., Nijpels, G., & Jansen, A. P. D. (2014) · Quality of Life Research · doi:10.1007/s11136-014-0650-7 · Cited by 25
“However, since so far there is no standard approach to determine whether a scale is sufficiently unidimensional, this conclusion is tentative [29, 38].”
BackgroundMethodInfluential
Development, Administration, and Structural Validity of a Brief, Computerized Neurocognitive Battery: Results From the Army Study to Assess Risk and Resilience in Servicemembers
Moore, T. M., Gur, R. C., Thomas, M. L., Brown, G. G., Nock, M. K., Savitt, A. P., Keilp, J. G., Heeringa, S. G., Ursano, R. J., Stein, M. B., et al. (2017) · Assessment · doi:10.1177/1073191116689820 · Cited by 27
“For more information on strengths and weaknesses of bifac-tor modeling, see Reise (2012) and Reise, Moore, and Haviland (2010).”
Method
Comparing set-to-number and number-to-set measures of cardinal number knowledge in preschool children using latent variable modeling
Mou, Y., Zhang, B., Manuela Piazza, A., & Hyde, D. C. (2020) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2020.05.016 · Cited by 28
Selection, optimization, and compensation
Geldhof, G. J., Gestsdóttir, S., Stefánsson, K. K., Johnson, S. K., Bowers, E. P., & Lerner, R. M. (2014) · International Journal of Behavioral Development · doi:10.1177/0165025414560447 · Cited by 26
“A bifactor model instead suggests that each item has two sources of true-score variance: global PYD and C-specific variance (see Reise, 2012, for further information about bifactor models).”
Background
Confirmatory factor analysis: foundations and extensions
Price, L. R. (2022) · Elsevier eBooks · doi:10.1016/b978-0-12-818630-5.10016-8 · Cited by 35
Factor structure, psychometric properties, and validity of the Big Five Inventory-2 facets: evidence from the French adaptation (BFI-2-Fr)
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The development and validation of the Microaggressions Against Non-religious Individuals Scale (MANRIS).
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Modeling the Structure of Acute Sport-Related Concussion Symptoms: A Bifactor Approach
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“, 2011; Gignac & Watkins, 2013; Patrick, Hicks, Nichol, & Krueger, 2007; Thomas, 2012) due to the practical and theoretical advantages of modeling broad traits of interest in these research domains (Reise, 2012; Reise, Morizot, & Hays, 2007; Thomas, 2012).”
Negative Keying Effects in the Factor Structure of TIMSS 2011 Motivation Scales and Associations with Reading Achievement
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“Omega indices were calculated on the unstandardized estimates of the model (Reise, 2012) with a latent factor for negative items (model M4) to estimate the proportion of variance attributable to the negative method factor vis-à-vis the three substantive factors.”
Method
The Internal Structure of the Aberrant Behavior Checklist Irritability Subscale: Implications for Studies of Irritability in Treatment-Seeking Youth With Autism Spectrum Disorders
Stoddard, J., Zik, J. B., Mazefsky, C. A., Dechant, B., & Gabriels, R. L. (2019) · Behavior Therapy · doi:10.1016/j.beth.2019.09.006 · Cited by 25
“For a single scale, like the ABC-I subscale, an ECV > 0.5 suggests that a scale acceptably measures a unitary construct of interest as represented by the general factor (an example provided by Reise, 2012).”
BackgroundInfluential
Psychometric properties of the UWES-9S in Peruvian college students
Domínguez-Lara, S., Sánchez‐Villena, A. R., & Fernández-Arata, M. (2020) · Acta Colombiana de Psicología · doi:10.14718/acp.2020.23.2.2 · Cited by 28
“In situations like this, the incorporation of bifactor models (Reise, 2012) can be methodologically useful.”
Background
Fidedignidade Dos Escores Do Exame Nacional Do Ensino Médio (ENEM)
Gomes, C. M. A., Golino, H. F., & Peres, A. J. D. S. (2020) · Psico · doi:10.15448/1980-8623.2020.2.31145 · Cited by 25
Confirmatory factor analysis of the Evidence-Based Practice Attitude Scale (EBPAS) in a large and representative Swedish sample: is the use of the total scale and subscale scores justified?
Santesson, A. H. E., Bäckström, M., Holmberg, R. G., Perrin, S. G., & Jarbin, H. (2020) · BMC Medical Research Methodology · doi:10.1186/s12874-020-01126-4 · Cited by 26
“there is unique systematic variance in the subscales [38].”
Background
Psychometric Properties of the German Brief Experiential Avoidance Questionnaire (BEAQ)
Schaeuffele, C., Knaevelsrud, C., Renneberg, B., & Boettcher, J. (2021) · Assessment · doi:10.1177/10731911211010955 · Cited by 28
“For the bifactor model, Omega Hierarchical (ωH) was calculated as a reliability measure and explained common variance (ECV) and percentage of uncontaminated correlations (PUC), were calculated to evaluate the unidimensionality of the scale (Dueber, 2017; Reise, 2012; Rodriguez et al., 2016).”
Method
Validity and reliability of the Polish version of the Self-Compassion Scale and its correlates
Kocur, D. J., Flakus, M., & Fopka-Kowalczyk, M. J. (2022) · PLoS ONE · doi:10.1371/journal.pone.0267637 · Cited by 32
“Hence, within a bifactor model, a group of specific factors do not correlate [22, 23].”
Background
Revisiting after-class boredom via exploratory structural equation modeling
Pawlak, M., Solhi, M., Shirvan, M. E., Kruk, M., & Taherian, T. (2023) · IRAL - International Review of Applied Linguistics in Language Teaching · doi:10.1515/iral-2022-0151 · Cited by 25
Investigating the Properties of the General Factor (M) in Bifactor Models Applied to Big Five or HEXACO Data in Terms of Method or Meaning
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“(Reise, 2012, p. 668) In the bifactor approach, a general factor, therefore, accounts for common variance among items.”
Background
Using Bifactor EFA, Bifactor CFA and Exploratory Structural Equation Modeling to Validate Factor Structure of the Meaning in Life Questionnaire, Greek Version
Stalikas, A., Kyriazos, T. A., Yotsidi, V., & Prassa, K. (2018) · Psychology · doi:10.4236/psych.2018.93022 · Cited by 29
“Each item is specified to load on the general factor and also its target group factor (Reise, 2012), here “Presence of meaning” and “Search for meaning”.”
BackgroundMethod
Re-evaluation of the Latent Structure of Common Childhood Disorders: Is There a General Psychopathology Factor (P-Factor)?
Gomez, R., Stavropoulos, V., Vance, A. L. A., & Griffiths, M. D. (2018) · International Journal of Mental Health and Addiction · doi:10.1007/s11469-018-0017-3 · Cited by 28
“Since 2012, a growing number of studies have examined this possibility using a type of confirmatory factor analysis (CFA) model called the bifactor model (Reise 2012).”
Background
Evaluating the Psychometric Properties of the Short Dark Triad (SD3) in Italian Adults and Adolescents
Somma, A., Paulhus, D. L., Borroni, S., & Fossati, A. (2019) · European Journal of Psychological Assessment · doi:10.1027/1015-5759/a000499 · Cited by 25
The relationships between WAIS-IV factor index scores and educational level: A bifactor model approach.
Abad, F. J., Sorrel, M. A., Román, F. J., & Colom, R. (2016) · Psychological Assessment · doi:10.1037/pas0000228 · Cited by 24
Social-Scientific Research Competency
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Evidence regarding the domains of the CLASS PreK in Head Start classrooms
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Evaluation of the measurement properties of the Perceived Stress Scale (PSS) in Hispanic caregivers to patients with Alzheimer’s disease and related disorders
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“In the bifactor model, a general factor is specified and two additional group factors are used to model the residual covariation among the items that is not captured by the general factor (Reise, 2012; Reise et al., 2007).”
BackgroundMethod
Early childhood Special education teachers' self-efficacy in relation to individual children: Links to children's literacy learning
Guo, Y. J., Dynia, J. M., & Lai, M. H. C. (2020) · Early Childhood Research Quarterly · doi:10.1016/j.ecresq.2020.09.002 · Cited by 24
Validation of the French Psychological Capital Questionnaire (F-PCQ-24) and its measurement invariance using bifactor exploratory structural equation modeling framework
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Consistent g- as well as consistent verbal-, numerical- and figural-factors in nested factor models? Confirmatory factor analyses using three test batteries
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“As shown in prior studies (e.g., Brunner et al., 2012; Reise, 2012), the model-based reliability estimates of the domain-specific factors in the NF-model as operationalized by omega hierarchical [ωh] using factor loadings were rather low.”
BackgroundMethodResultInfluential
Higher-Order and Bifactor Models of the Drinking Motives Questionnaire
Lac, A., & Donaldson, C. D. (2015) · Assessment · doi:10.1177/1073191115603503 · Cited by 26
“In bifactor models, factors are presumed to be orthogonal (Brunner et al., 2012; Chen et al., 2012; Chen, West, & Sousa, 2006; Reise, 2012; Reise, Moore, & Haviland, 2010).”
Background
Examining the unique relations between anxiety sensitivity factors and suicidal ideation and past suicide attempts
Allan, N. P., Norr, A. M., Boffa, J. W., Durmaz, D. A., Raines, A. M., & Schmidt, N. B. (2015) · Psychiatry Research · doi:10.1016/j.psychres.2015.05.066 · Cited by 24
“One approach that can clarify the true relation between global AS, specific AS dimensions, and suicidality is bifactor modeling (Chen et al., 2012; Reise, 2012).”
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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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