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 Standardized Root Mean Squared Error (SRMR) with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). We use Unweighted Least Squares (ULS) estimation with a mean and variance corrected test statistic. 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 (e.g., p = 10) 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.
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The Effect of Estimation Methods on SEM Fit Indices
We examined the effect of estimation methods, maximum likelihood (ML), unweighted least squares (ULS), and diagonally weighted least squares (DWLS), on three population SEM (structural equation modeling) fit indices: the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual (SRMR). We considered different types and levels of misspecification in factor analysis models: misspecified dimensionality, omitting cross-loadings, and ignoring residual correlations. Estimation methods had substantial impacts on the RMSEA and CFI so that different cutoff values need to be employed for different estimators. In contrast, SRMR is robust to the method used to estimate the model parameters. The same criterion can be applied at the population level when using the SRMR to evaluate model fit, regardless of the choice of estimation method.
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- Award ID(s):
- 1659936
- NSF-PAR ID:
- 10299614
- Date Published:
- Journal Name:
- Educational and Psychological Measurement
- Volume:
- 80
- Issue:
- 3
- ISSN:
- 0013-1644
- Page Range / eLocation ID:
- 421 to 445
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/0013164419885164
