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Assessing fit in ordinal factor analysis models : SRMR vs. RMSEA

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Abstract
This study introduces the statistical theory of using the Standardized Root Mean Squared Error (SRMR) to test close fit in ordinal factor analysis. We also compare the accuracy of confidence intervals (CIs) and tests of close fit based on the SRMR with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). The current (biased) implementation for the RMSEA never rejects that a model fits closely when data are binary and almost invariably rejects the model in large samples if data consist of five categories. The unbiased RMSEA produces better rejection rates, but it is only accurate enough when the number of variables is small and the degree of misfit is small. In contrast, across all simulated conditions, the tests of close fit based on the SRMR yield acceptable type I error rates. SRMR tests of close fit are also more powerful than those using the unbiased RMSEA.
Keywords
STRUCTURAL EQUATION MODELS, WEIGHTED LEAST-SQUARES, ITEM RESPONSE, THEORY, MONTE-CARLO, DISTINGUISHING OPTIMISM, CONFIDENCE-INTERVALS, TEST, STATISTICS, SIZE, PERFORMANCE, VARIABLES, Ordinal factor analysis, SRMR, RMSEA, close fit

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MLA
Shi, Dexin, et al. “Assessing Fit in Ordinal Factor Analysis Models : SRMR vs. RMSEA.” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL, vol. 27, no. 1, 2020, pp. 1–15.
APA
Shi, D., Maydeu-Olivares, A., & Rosseel, Y. (2020). Assessing fit in ordinal factor analysis models : SRMR vs. RMSEA. STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL, 27(1), 1–15.
Chicago author-date
Shi, Dexin, Alberto Maydeu-Olivares, and Yves Rosseel. 2020. “Assessing Fit in Ordinal Factor Analysis Models : SRMR vs. RMSEA.” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL 27 (1): 1–15.
Chicago author-date (all authors)
Shi, Dexin, Alberto Maydeu-Olivares, and Yves Rosseel. 2020. “Assessing Fit in Ordinal Factor Analysis Models : SRMR vs. RMSEA.” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL 27 (1): 1–15.
Vancouver
1.
Shi D, Maydeu-Olivares A, Rosseel Y. Assessing fit in ordinal factor analysis models : SRMR vs. RMSEA. STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL. 2020;27(1):1–15.
IEEE
[1]
D. Shi, A. Maydeu-Olivares, and Y. Rosseel, “Assessing fit in ordinal factor analysis models : SRMR vs. RMSEA,” STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL, vol. 27, no. 1, pp. 1–15, 2020.
@article{8642363,
  abstract     = {{This study introduces the statistical theory of using the Standardized Root Mean Squared Error (SRMR) to test close fit in ordinal factor analysis. We also compare the accuracy of confidence intervals (CIs) and tests of close fit based on the SRMR with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). The current (biased) implementation for the RMSEA never rejects that a model fits closely when data are binary and almost invariably rejects the model in large samples if data consist of five categories. The unbiased RMSEA produces better rejection rates, but it is only accurate enough when the number of variables is small and the degree of misfit is small. In contrast, across all simulated conditions, the tests of close fit based on the SRMR yield acceptable type I error rates. SRMR tests of close fit are also more powerful than those using the unbiased RMSEA.}},
  author       = {{Shi, Dexin and Maydeu-Olivares, Alberto and Rosseel, Yves}},
  issn         = {{1070-5511}},
  journal      = {{STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL}},
  keywords     = {{STRUCTURAL EQUATION MODELS,WEIGHTED LEAST-SQUARES,ITEM RESPONSE,THEORY,MONTE-CARLO,DISTINGUISHING OPTIMISM,CONFIDENCE-INTERVALS,TEST,STATISTICS,SIZE,PERFORMANCE,VARIABLES,Ordinal factor analysis,SRMR,RMSEA,close fit}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{1--15}},
  title        = {{Assessing fit in ordinal factor analysis models : SRMR vs. RMSEA}},
  url          = {{http://dx.doi.org/10.1080/10705511.2019.1611434}},
  volume       = {{27}},
  year         = {{2020}},
}

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