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 assessment of model fit in SEM, it is important to use several different indices, as there are no consensus rules within the literature.
“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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“While there are no golden rules for assessment of model fit, reporting a variety of indices is necessary ( Crowley and Fan 1997 ) because different indices reflect a different aspect of model fit.”
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“…categorical leastsquares, robust statistics Supplemental materials: http://dx.doi.org/10.1037/a0029315.supp Confirmatory factor analysis (CFA) models are among the most popular types of structural equation models (SEMs) in psychology (Crowley & Fan, 1997; Marsh & Hau, 2007; Martens, 2005).”
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“90 was considered an adequate fit (Bentler, 1992; Crowley and Fan, 1997; Musil et al., 1998).”
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“3), implying that they are poor indicators of the latent construct [56].”
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“Crowley and Fan (1997) noted that acceptable GFI and AGFI values are typically higher than the .”
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“applied [ 36 ]. In the first step, we assessed the measurement model, which consisted of correlated latent variables (i.e., unobserved variables).”
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“In contrast to 726 Journal of Interpersonal Violence 26(4) EFA, which usually explores the possible underlying factor structure, CFA aims to test the proposed relationship between variables and their underlying latent constructs.”
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“The analysis includes checking if the assumptions are matched (i.e. confirmed) or not by empirical data (Crowley & Fan, 1997).”
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“Generally, GFI and None of the models could be accepted based upon the population X2 because the X2 measure is extremely sensitive to large sample sizes (Crowley & Fan, 1997).”
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“The chi-square index is considered to be a conservative and overly sensitive index ( Crowley and Fan, 1997 ).”
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“To assess model goodness-of-fit, we used the Comparative Fit Index (CFI; Bentler, 1990), the Tucker-Lewis Incremental fit index (TLI; Tucker & Lewis, 1973), RMSEA, and the v2/df ratio (Crowley & Fan, 1997).”
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“Others have taken a more nuanced perspective and recognize the merit in reporting a number of fit indices (Crowley and Fan 1997; Hooper, Coughlan, and Mullen 2008) because different indices reflect a different aspect of model fit.”
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“With a substantial sample size for the confirmatory factor analysis [50], this study demonstrates that the WHOQOL-BREF (TW) is a suitable scale for IDUs even though a few modifications are needed.”
MethodThe Learning Transfer System Inventory (LTSI) in Ukraine
Yamkovenko, B., Holton, E. F., & Bates, R. A. (2007) · Journal of European Industrial Training · doi:10.1108/03090590710756819 · Cited by 34 · see citing works
Structural Equation Modeling in Pediatric Psychology: Overview and Review of Applications
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“Consistent with the movement toward more sophisticated analytic strategies in the broader social science literature, increases in the use of SEM have been noted in both psychological (Crowley & Fan, 1997) and medical research (Bentler & Stein, 1992).”
BackgroundMarital Quality for Men and Women in Stepfamilies
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“An acceptable fit for the CFI is higher than .90 (Crowley & Fan, 1997).”
BackgroundJain, R. K., & Jain, S. (2013) · Vision The Journal of Business Perspective · doi:10.1177/0972262912483528 · Cited by 30 · see citing works
“It is to be noted here that there are no golden rules for assessment of model fit, reporting a variety of indices is necessary (Crowley and Fan, 1997) because different indices reflect a different aspect of model fit.”
BackgroundGregg, N., & Scott, S. S. (2000) · Journal of Learning Disabilities · doi:10.1177/002221940003300104 · Cited by 32 · see citing works
“Such capability has led to a significant interest in SEM’s applications across fields, such as across special education, general education, and counseling (Crowley & Fan, 1997; Fassinger, 1987; Hoyle & Smith, 1994; Willson & Rupley, 1997).”
BackgroundArroyo, J. C., & Orozco, F. C. E. (2016) · Estudios Gerenciales · doi:10.1016/j.estger.2016.07.001 · Cited by 32 · see citing works
Modeling Maher's Attribution Theory of Delusions as a Cusp Catastrophe
Lange, R., & Houran, J. (2000) · Nonlinear Dynamics Psychology and Life Sciences · doi:10.1023/a:1009584528352 · Cited by 31 · see citing works
“Tegano, 1990). Note however that while Maher (1974, 1988) described delusion formation in terms of two types of effects (i.e., an initial increase in fear, followed by a decrease), path analysis allows just one type of relation (i.e., either a negative or a positive correlation; see e.g., Crowley & Fan, 1997 ).”
BackgroundCollett, B. R., Crowley, S. L., Gimpel, G. A., et al. (2000) · Journal of Psychoeducational Assessment · doi:10.1177/073428290001800406 · Cited by 31 · see citing works
Self-citationChien, C., Wang, J., Yao, G., et al. (2007) · Quality of Life Research · doi:10.1007/s11136-007-9236-y · Cited by 30 · see citing works
“In addition, this study had a substantial sample size for the CFA operation (more than 200 subjects) according to suggestions from previous studies [25, 26].”
ResultA New Compassion Scale for Children and Its Psychometric Properties
Eşref, N. A. S., & Sak, R. (2020) · Child Psychiatry & Human Development · doi:10.1007/s10578-020-01034-0 · Cited by 30 · see citing works
Wang, J., Li, Y.-S., Chen, J.-D., et al. (2015) · PLoS ONE · doi:10.1371/journal.pone.0140581 · Cited by 26 · see citing works
“Regarding stress reactions, previous study suggested that depression and anxiety might display an asymmetric relationship [24], the unidirectional effect from depression to anxiety.”
BackgroundZhang, Y., Cole, S. T., & Chancellor, C. H. (2014) · Journal of Travel Research · doi:10.1177/0047287514535848 · Cited by 27 · see citing works
“Even with acceptable fit indices, a saturated and complex model is questionable because of its high dependence on estimation of data samples rather than theory, and thus has less theoretical rigor (Crowley and Fan 1997; Mulaik et al. 1989).”
BackgroundFoster, M., Whitehead, L., & Arabiat, D. H. (2019) · Journal of Advanced Nursing · doi:10.1111/jan.14099 · Cited by 26 · see citing works
“…on a model fit, yet it is recommended to test and report on a variety of indices to reflect the various aspects of the model that are most insensitive to sample size, model misspecification and parameter estimates (Crowley & Fan, 1997; Statistics Solutions, 2018; Tabachnick & Fidell, 2007).”
BackgroundDhladhla, T. J. (2011) · SUNScholar (Stellenbosch University) · Cited by 25 · see citing works
Enhancing nurses' empowerment: the role of supervisors' empowering management practices
Montani, F., Courcy, F., Giorgi, G., & Boilard, A. (2015) · Journal of Advanced Nursing · doi:10.1111/jan.12665 · Cited by 25 · see citing works
Relationships among e-learning systems and e-learning outcomes: A path analysis model
Eom, S. B. (2012) · Human Systems Management · doi:10.3233/hsm-2011-0752 · Cited by 28 · see citing works
“Although there are no golden rules that can be agreed upon, Table 1 includes a set of indices that have been frequently reported and suggested to be reported in the literature [44–50].”
A Confirmatory Factor Analysis of a Newly Integrated Multidimensional School Engagement Scale
Hashim, R. A., & Sani, A. M. (2008) · Malaysian Journal of Learning and Instruction · doi:10.32890/mjli.5.2008.7595 · Cited by 26 · see citing works
Effective material logistics in urban construction sites: a structural equation model
Spillane, J. P., & Oyedele, L. O. (2017) · Construction Innovation · doi:10.1108/ci-11-2015-0063 · Cited by 25 · see citing works
“Numerous authors such as Kline (2005), Hooper, et al. (2008), Crowley and Fan (1997), in addition to Kenny and McCoach (2003) all advocate the importance of, and necessity, to undertake and assess the structural model.”
BackgroundCeresa, F., Kranebitter, P., Monrós, J. S., et al. (2021) · PeerJ · doi:10.7717/peerj.12560 · Cited by 24 · see citing works
“Using and reporting such a variety of fi t metrics is recommended in structural equation modelling, because each one re fl ects a different aspect of model fi t ( Crowley & Fan, 1997 ; Hooper, Coughlan & Mullen, 2008 ).”
Mortenson, S., Liu, M., Burleson, B. R., & Liu, Y. (2006) · Journal of Cross-Cultural Psychology · doi:10.1177/0022022106288475 · Cited by 25 · see citing works
“Chi-square values predict whether the covariance matrix the model predicts is different than the observed covariance matrix (Crowley & Fan, 1997).”
Background
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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