The DOI matches its DataCite record; 71 of the 73 references it cites were found in a registry or an index.
Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures
Open accessAbstract
For structural equation models, a huge variety of fit indices has been developed. These indices, however, can point to conflicting conclusions about the extent to which a model actually matches the observed data. The present article provides some guidelines that should help applied researchers to evaluate the adequacy of a given structural equation model. First, as goodness-of-fit measures depend on the method used for parameter estimation, maximum likelihood (ML) and weighted least squares (WLS) methods are introduced in the context of structural equation modeling. Then, the most common goodness-of-fit indices are discussed and some recommendations for practitioners given. Finally, we generated an artificial data set according to a "true" model and analyzed two misspecified and two correctly specified models as examples of poor model fit, adequate fit, and good fit.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Furthermore, additional fit indices such as GFI = 0.92, AGFI = 0.89 and RMS = 0.06 also indicated an acceptable fit of the data to the model (Schermelleh-Engel et al., 2003).”
From Psychometric Evaluation of the Polish Version of the Mindfulness Inventory for Sport (MIS-PL) (2024) · cites this paper as Schermelleh-Engel et al., 2003
Citations
Cites
Hu, L., & Bentler, P. M. (1999) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519909540118 · Cited by 108,788
An Introduction to the Bootstrap
Efron, B., & Tibshirani, R. J. (1994) · doi:10.1201/9780429246593 · Cited by 40,500
Alternative Ways of Assessing Model Fit
Browne, M. W., & Cudeck, R. (1992) · Sociological Methods & Research · doi:10.1177/0049124192021002005 · Cited by 27,200
Comparative fit indexes in structural models.
Bentler, P. M. (1990) · Psychological Bulletin · doi:10.1037/0033-2909.107.2.238 · Cited by 25,266
Significance tests and goodness of fit in the analysis of covariance structures.
Bentler, P. M., & Bonett, D. G. (1980) · Psychological Bulletin · doi:10.1037/0033-2909.88.3.588 · Cited by 20,015
Structural Equations with Latent Variables.
Clogg, C. C., & Bollen, K. A. (1991) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2072165 · Cited by 17,475
Power analysis and determination of sample size for covariance structure modeling.
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996) · Psychological Methods · doi:10.1037/1082-989x.1.2.130 · Cited by 10,418
EQS : structural equations program manual
Bentler, P. M. (1989) · Medical Entomology and Zoology · Cited by 9,669
Testing Structural Equation Models.
Clogg, C. C., Bollen, K. A., & Long, J. S. (1995) · Social Forces · doi:10.2307/2580595 · Cited by 8,246
(1993) · Medical Entomology and Zoology · Cited by 7,690
Structural model evaluation and modification: An interval estimation approach
Steiger, J. H. (1990) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2502_4 · Cited by 7,408
A Reliability Coefficient for Maximum Likelihood Factor Analysis
Tucker, L. R., & Lewis, C. (1973) · Psychometrika · doi:10.1007/bf02291170 · Cited by 7,330
LISREL 7 : user's reference guide
Jöreskog, K. G., & Sörbom, D. (1989) · Medical Entomology and Zoology · Cited by 6,783
A Beginner's Guide to Structural Equation Modeling: Fourth Edition
Schumacker, R. E., & Lomax, R. G. (2015) · doi:10.4324/9781315749105 · Cited by 6,604
Practical issues in structural modeling
BENTLER, P. M., & CHOU, C.-P. (1987) · Sociological Methods & Research · doi:10.1177/0049124187016001004 · Cited by 5,804
Curran, P. J., West, S. G., & Finch, J. F. (1996) · Psychological Methods · doi:10.1037/1082-989x.1.1.16 · Cited by 5,512
A scaled difference chi-square test statistic for moment structure analysis
Satorra, A., & Bentler, P. M. (2001) · Psychometrika · doi:10.1007/bf02296192 · Cited by 5,282
Bozdogan, H. (1987) · Psychometrika · doi:10.1007/bf02294361 · Cited by 4,468
Model Selection and Inference: A Practical Information-Theoretic Approach
Strawderman, R. L., Burnham, K. P., & Anderson, D. R. (2000) · Journal of the American Statistical Association · doi:10.2307/2669574 · Cited by 4,194
Book Review: Structural Equation Modeling: Concepts, Issues, and Applications
Rigdon, E. E., & Hoyle, R. H. (1997) · Journal of Marketing Research · doi:10.2307/3151904 · Cited by 4,088
Akaike, H. (1987) · Springer Series in Statistics · doi:10.1007/978-1-4612-1694-0_29 · Cited by 4,027
(1995) · Cited by 4,008
Evaluation of goodness-of-fit indices for structural equation models.
Mulaik, S. A., James, L. R., Alstine, J. V., Bennett, N., Lind, S., & Stilwell, C. D. (1989) · Psychological Bulletin · doi:10.1037/0033-2909.105.3.430 · Cited by 2,927
Corrections to test statistics and standard errors in covariance structure analysis.
Satorra, A., & Bentler, P. M. (1994) · Cited by 2,388
How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power
Muthén, L. K., & Muthén, B. O. (2002) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0904_8 · Cited by 2,362
(1993) · Cited by 2,269
Statistical Strategies for Small Sample Research
Hoyle, R. H. (1999) · Cited by 1,896
Structural Equation Modeling with LISREL
Hayduk, L. A. (1988) · Johns Hopkins University Press eBooks · doi:10.56021/9780801834783 · Cited by 1,874
Structural Equation Modeling: Foundations and Extensions
Kaplan, D. E. (2000) · University of Maribor digital library (University of Maribor) · Cited by 1,814
(1995) · Cited by 1,801
A comparison of some methodologies for the factor analysis of non‐normal Likert variables
Muthén, B., & Kaplan, D. (1985) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1985.tb00832.x · Cited by 1,778
Anderson, J. C., & Gerbing, D. (1984) · Psychometrika · doi:10.1007/bf02294170 · Cited by 1,775
Model modifications in covariance structure analysis: The problem of capitalization on chance.
MacCallum, R. C., Roznowski, M., & Necowitz, L. B. (1992) · Psychological Bulletin · doi:10.1037/0033-2909.111.3.490 · Cited by 1,758
Single Sample Cross-Validation Indices for Covariance Structures
Browne, M. W., & Cudeck, R. A. (1989) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2404_4 · Cited by 1,688
Fan, X., Thompson, B., & Wang, L. (1999) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519909540119 · Cited by 1,664
Can test statistics in covariance structure analysis be trusted?
Hu, L.-T., Bentler, P., & Kano, Y. (1992) · Psychological bulletin · doi:10.1037/0033-2909.112.2.351 · Cited by 1,568
Choosing a multivariate model: Noncentrality and goodness of fit.
McDonald, R. P., & Marsh, H. W. (1990) · Psychological Bulletin · doi:10.1037/0033-2909.107.2.247 · Cited by 1,485
Is More Ever Too Much? The Number of Indicators per Factor in Confirmatory Factor Analysis
Marsh, H. W., Hau, K.-T., Balla, J. R., & Grayson, D. (1998) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr3302_1 · Cited by 1,307
Causal Analysis: Assumptions, Models, and Data
Schriesheim, C. A., James, L. R., Muliak, S. A., & Brett, J. M. (1984) · Academy of Management Review · doi:10.2307/258244 · Cited by 1,240
Overall Fit in Covariance Structure Models: Two Types of Sample Size Effects
Bollen, K. (1990) · Psychological Bulletin · doi:10.1037/0033-2909.107.2.256 · Cited by 998
Multifaceted conceptions of fit in structural equation models
Tanaka, J. S. (1993) · Medical Entomology and Zoology · Cited by 941
The problem of equivalent models in applications of covariance structure analysis.
MacCallum, R. C., Wegener, D. T., Uchino, B. N., & Fabrigar, L. R. (1993) · Psychological Bulletin · doi:10.1037/0033-2909.114.1.185 · Cited by 937
Scaled and Adjusted Restricted Tests in Multi-Sample Analysis of Moment Structures
Satorra, A. (2000) · Advanced studies in theoretical and applied econometrics · doi:10.1007/978-1-4615-4603-0_17 · Cited by 886
Cause and Correlation in Biology
Shipley, B. (2016) · Cambridge University Press eBooks · doi:10.1017/cbo9781139979573 · Cited by 771
Discovering Statistics Using SPSS for Windows: Advanced Techniques for Beginners
Field, A. P. (2000) · Sage eBooks · Cited by 737
Robustness Studies in Covariance Structure Modeling: An Overview and a Meta-Analysis
HOOGLAND, J. J., & BOOMSMA, A. (1998) · Sociological Methods & Research · doi:10.1177/0049124198026003003 · Cited by 734
Muthén, B., & Kaplan, D. (1992) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1992.tb00975.x · Cited by 690
CFI versus RMSEA: a comparison of two fit indexes for structural equation modeling
Rigdon, E. E. (1996) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705519609540052 · Cited by 668
Chou, C., Bentler, P. M., & Satorra, A. (1991) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1991.tb00966.x · Cited by 666
Reporting Analyses of Covariance Structures
Boomsma, A. (2000) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0703_6 · Cited by 655
Olsson, U. H., Foss, T., Troye, S. V., & Howell, R. D. (2000) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1207/s15328007sem0704_3 · Cited by 648
Nonconvergence, Improper Solutions, and Starting Values in Lisrel Maximum Likelihood Estimation
Boomsma, A. (1985) · Psychometrika · doi:10.1007/bf02294248 · Cited by 621
Sample Size Effects on Chi Square and Other Statistics Used in Evaluating Causal Models
Bearden, W. O., Sharma, S., & Teel, J. E. (1982) · Journal of Marketing Research · doi:10.2307/3151716 · Cited by 610
Basic Principles of Structural Equation Modeling
Mueller, R. O. (1996) · Springer texts in statistics · doi:10.1007/978-1-4612-3974-1 · Cited by 587
COVARIANCE STRUCTURE ANALYSIS: Statistical Practice, Theory, and Directions
Bentler, P. M., & Dudgeon, P. (1996) · Annual Review of Psychology · doi:10.1146/annurev.psych.47.1.563 · Cited by 566
Improper Solutions in Structural Equation Models: Causes, Consequences, and Strategies
CHEN, F., BOLLEN, K. A., PAXTON, P., CURRAN, P. J., & KIRBY, J. B. (2001) · Sociological Methods & Research · doi:10.1177/0049124101029004003 · Cited by 512
Basic Principles of Structural Equation Modeling: An Introduction to LISREL and EQS
Franke, G. R., & Mueller, R. O. (1996) · Journal of Marketing Research · doi:10.2307/3152154 · Cited by 511
On the Multivariate Asymptotic Distribution of Sequential Chi-Square Statistics
Steiger, J. H., Shapiro, A., & Browne, M. W. (1985) · Psychometrika · doi:10.1007/bf02294104 · Cited by 482
Analysis of linear structural relationships by maximum likelihood and least squares methods
Jöreskog, K. G., & Sörbom, D. (1983) · Medical Entomology and Zoology · Cited by 447
Akaike, H. (1985) · Springer eBooks · doi:10.1007/978-1-4613-8560-8_1 · Cited by 373
Latent variable models of multitrait-multimethod data.
Marsh, H. W., & Grayson, D. A. (1995) · Cited by 362
LISREL Issues, Debates and Strategies
Williams, R. A., & Hayduk, L. A. (1997) · Contemporary Sociology A Journal of Reviews · doi:10.2307/2654075 · Cited by 322
Confirmatory hierarchical factor analyses of psychological distress measures.
Tanaka, J. S., & Huba, G. J. (1984) · Journal of Personality and Social Psychology · doi:10.1037/0022-3514.46.3.621 · Cited by 307
A Simple Rule for Generating Equivalent Models in Covariance Structure Modeling
Lee, S., & Hershberger, S. L. (1990) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2503_4 · Cited by 220
Atkinson, A. C., & Fienberg, S. E. (1985) · Springer eBooks · doi:10.1007/978-1-4613-8560-8 · Cited by 217
Using the friedman method of ranks for model comparison in structural equation modeling
Rigdon, E. E. (1999) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519909540131 · Cited by 51
A metric measure for direct comparison of competing models in covariance structure analysis
Kumar, A. S., & Sharma, S. (1999) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519909540127 · Cited by 32
Robust Standard Errors and Chi-Squares for Interaction Models
Yang‐Wallentin, F., & Jöreskog, K. G. (2001) · Psychology Press eBooks · doi:10.4324/9781410601858-11 · Cited by 25
The robustness of estimation methods for covariance structure analysis.
Hoogland, J. J. (1999) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 22
Nested structural equation models: Noncentrality and power of restriction test
Raykov, T., & Penev, S. I. (1998) · Structural Equation Modeling A Multidisciplinary Journal · doi:10.1080/10705519809540103 · Cited by 21
Introduction to Special Section
Takane, Y., & Bozdogan, H. (1987) · Psychometrika · doi:10.1007/bf02294358 · Cited by 6
Cited by
Sorted by citations
Construction and factorial validation of a short form of the Self-Compassion Scale
Raes, F., Pommier, E., Neff, K. D., & Van Gucht, D. (2011) · Clinical Psychology & Psychotherapy · doi:10.1002/cpp.702 · Cited by 2,997
Microbial diversity drives multifunctionality in terrestrial ecosystems
Delgado-Baquerizo, M., Maestre, F. T., Reich, P. B., Jeffries, T. C., Gaitan, J. J., Encinar, D., Berdugo, M., Campbell, C. D., & Singh, B. K. (2016) · Nature Communications · doi:10.1038/ncomms10541 · Cited by 2,624
Structural Equation Modeling and Natural Systems
Grace, J. B. (2006) · doi:10.1017/cbo9780511617799 · Cited by 2,432
Reporting practices in confirmatory factor analysis: an overview and some recommendations
Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009) · Psychological Methods · doi:10.1037/a0014694 · Cited by 2,242
Increasing aridity reduces soil microbial diversity and abundance in global drylands
Maestre, F. T., Delgado‐Baquerizo, M., Jeffries, T. C., Eldridge, D. J., Ochoa, V., Gozalo, B., Quero, J. L., García‐Gómez, M., Gallardo, A., Ulrich, W., et al. (2015) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1516684112 · Cited by 1,182
Metadata
- Authors
- Schermelleh-Engel, K., Moosbrugger, H., & Müller, H.
- Affiliations
- Goethe University Frankfurt (DE)
- University of Erfurt (DE)
- Venue
- Department of Psychology - University of Koblenz-Landau
- Publisher
- Department of Psychology - University of Koblenz-Landau
- Published
- 2003
- Volume
- 8
- Pages
- 23-74
- OpenAlex
- W1627191216
- Cited by
- 8,975
- References
- 73
- Citations by year
- 2026: 128 · 2025: 749 · 2024: 891 · 2023: 928 · 2022: 910 · 2021: 879 · 2020: 837 · 2019: 538 · 2018: 489 · 2017: 420 · 2016: 392 · 2015: 395 · 2014: 348 · 2013: 284 · 2012: 212
- FWCI
- 19.63
- Type
- journal article
- Language
- en
- Open access
- green
- hdl.handle.net
- Licence
- Locations
- Psychology Archives
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Keywords
- structural equation modeling, model fit assessment, goodness-of-fit indices, significance tests, maximum likelihood estimation, weighted least squares estimation, model misspecification
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
