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Structural Equation Modeling: Basic Concepts and Applications in Personality Assessment Research
Abstract
Structural equation modeling (SEM) has become an increasingly used methodological strategy in psychology. Nevertheless, many psychologists continue to be unclear about how to apply this analytic tool in their research. This article reviews SEM from a conceptual perspective, particularly focusing on confirmatory factor analysis. Additionally, the relation between SEM and other analytic techniques (e.g., exploratory factor analysis) are addressed. A confirmatory factor analytic example is presented and reviewed in detail. Finally, limitations of SEM and other considerations are discussed.
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“When reporting the assessment of model fit in SEM, it is important to use several different indices, as there are no consensus rules within the literature that researchers can follow (Crowley & Fan, 1997; Hooper et al., 2008).”
From Testing Mindfulness Mechanisms of Action on the Stress and Burnout of Social Workers (2024) · cites this paper as Crowley & Fan, 1997
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“…(CFI), Tucker Lewis Index (TLI), Root Mean Square of Approximation (RMSEA) and Standardized Root Mean Square Residual (SRMR), as recommended by Crowley and Fan (1997) and Salisbury et al. (2002 showed that all the indicators met the recommended criteria for a large sample size, with values of…”
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“An acceptable fit for the CFI is between .90 and 1.0 (Crowley and Fan 1997).”
BackgroundInfluentialThe Structure of the School Social Behavior Scales: A Confirmatory Factor Analysis
Crowley, S. L., & Merrell, K. W. (2003) · Assessment for Effective Intervention · doi:10.1177/073724770302800205 · Cited by 21
Self-citationHan, C.-W., Yajima, Y., Lee, E. J., et al. (2005) · The Tohoku Journal of Experimental Medicine · doi:10.1620/tjem.206.41 · Cited by 21
“This may be attributed to differences in the statistical approach, because the SEM enables us to correct for attenuation due to measurement error (Bentler 1980; Crowley and Fan 1997; Peek 2000).”
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“CFA result provides multiple indices for analysis of model fit (Crowley & Fan, 1997).”
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“3 For more details regarding Structure Equation Modeling the reader is referred to Crowley and Fan (1997), Boomsma (2000), Kaplan (2000), Barrett (2007), Hooper, Coughlan and Mullen (2008), Asparohov and Muthén (2009) and Byrne (2009).”
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“90 indicate good fit) [94,95], and the root-mean-square error of approximation.”
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“Although there is no golden rule for the assessment of model fit, reporting a variety of indexes is advisable (Crowley & Fan, 1997) because different indexes reflect different aspects of model fit.”
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“…be explicit about their theory, and to specify, estimate, and test the hypothesized interrelations among manifest variables based on latent variables (Crowley & Fan, 1997; Kline, 2011; Nachtigall, Kroehne, Funke, & Steyer, 2003; Raykov & Marcoulides, 2006; Ullman, 2006; Widaman & Thompson, 2003).”
BackgroundKanapeckaitė, R., & Bagdžiūnienė, D. (2024) · Frontiers in Psychology · doi:10.3389/fpsyg.2024.1353793 · Cited by 20
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“In this regard, an assortment of indices is important since all represent different aspects of model fitness (Crowley & Fan, 1997).”
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MethodCORWYN, R. F., & Bradley, R. H. (2005) · Parenting · doi:10.1207/s15327922par0501_1 · Cited by 8
“Although it is only a crude approximation, a χ2/degrees of freedom (df) ratio of less than 2.0 is often considered an indication of good fit (Crowley & Fan, 1997).”
BackgroundInfluentialAsgari, H. (2015) · doi:10.25148/etd.fidc000118 · Cited by 8
“This will results in a less rigorous theoretical model that paradoxically produces better fit indices (Mulaik et al., 1989; Crowley and Fan, 1997).”
BackgroundTesting Mindfulness Mechanisms of Action on the Stress and Burnout of Social Workers
Maddock, A. (2024) · Mindfulness · doi:10.1007/s12671-024-02353-2 · Cited by 8
“When reporting the assessment of model fit in SEM, it is important to use several different indices, as there are no consensus rules within the literature that researchers can follow (Crowley & Fan, 1997; Hooper et al., 2008).”
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“(3) Parsimony Fit indices (PGFI) are based upon the GFI by adjusting for loss of degrees of freedom (Crowley & Fan, 1997).”
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“Various indices are important individually since all represent different aspects of model fitness (Crowley and Fan, 1997).”
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“With the confirmatory factor analysis (CFA) technique, the SEM model allows the flexibility to find the most suitable model in the proposed models (Crowley & Fan, 1997; Kline, 2015; Nachtigall et al., 2003; Raykov & Marcoulides, 2006; Ullman, 2006; Widaman & Reise, 1997).”
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“As in regression, the significance levels of parameter estimates, that is, path coefficients or beta weights, indicate whether the variables significantly influence or predict each other in the hypothesized directions (Crowley & Fan, 1997; Kelloway, 1998).”
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“There are no required indices to be included in decision-making for structural models; however, it is necessary to report a variety of indices to capture different parts of the model fit and make reasonable determinations (Crowley & Fan, 1997).”
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“The literature for that purpose supports on not to rely on reporting any single index, a combination of indices for measuring the fitness of the model shall be reported (Crowley & Fan, 1997).”
BackgroundWeiner, M. D., Pentz, M. A., Skara, S. N., Li, C., Chou, C., & Dwyer, J. H. (2003) · Journal of Child & Adolescent Substance Abuse · doi:10.1300/j029v13n02_03 · Cited by 5
“For the chi-square test, fit is considered acceptable with a p-value greater than .05, which indicates that there is no significant difference between the data and the model imposed upon them (Crowley & Fan, 1997).”
BackgroundMethodInfluentialMODELING PRECOGNITIVE DREAMS AS MEANINGFUL COINCIDENCES
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“For instance, in psychology, SEM uses confirmatory factor analysis (CFA) to examine individual psychological changes (51); in sociology, it clarifies the relationships between different social variables (52); and in medical science, it investigates the causal links between causes of diseases and…”
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How do the cost bias and probability bias influence social anxiety symptoms?
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“Model uyumunun değerlendirilebilmesi için literatürde fikir birliği olmamakla beraber farklı uyum değerlerinin modele yönelik farklı yönleri vurgulaması bakımından çeşitli uyum değerlerinin raporlanması gerektiği belirtilmektedir (Crowley & Fan, 1997).”
Maddock, A. (2025) · Current Psychology · doi:10.1007/s12144-025-07801-3 · Cited by 1
“When assessing model fit, as there are no consensus rules within the literature, several fit indices are required to establish model fit (Crowley & Fan, 1997; Hooper et al. 2008 ).”
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“95 set for good model fit.[22,23] Cronbach’s alpha was used as an estimation of the reliability of the estimation of the underlying categories.”
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“Finally, in this study, multiple goodness of fit measures were estimated instead of just one as has been strongly recommended (Crowley and Fan 1997; Hu and Bentler 1999; Mueller 1999).”
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Metadata
- Authors
- Crowley, S. L., & Fan, X.
- Affiliations
- Utah State University (US)
- Venue
- Journal of Personality Assessment
- Publisher
- Informa UK Limited
- Published
- 1997-06
- Volume
- 68
- Issue
- 3
- Pages
- 508-531
- ISSN
- 0022-3891 (ISSN-L)
- 1532-7752
- OpenAlex
- W1971726054
- Cited by
- 311
- References
- 4
- Citations by year
- 2026: 3 · 2025: 9 · 2024: 11 · 2023: 13 · 2022: 14 · 2021: 40 · 2020: 12 · 2019: 23 · 2018: 12 · 2017: 14 · 2016: 17 · 2015: 16 · 2014: 10 · 2013: 13 · 2012: 7
- FWCI
- 10.37
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Personality Assessment (publishedVersion)
- PubMed (publishedVersion)
- Digital Commons - USU (Utah State University) (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Social Sciences › Psychology › Clinical Psychology › Personality Traits and Psychology
- Social Sciences › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- structural equation modeling, confirmatory factor analysis, exploratory factor analysis, personality assessment
- MeSH terms
- Humans, Personality Assessment, Psychometrics, Research, Models, Statistical
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