# Level-specific fit index performance with diagonally weighted least squares estimation of multilevel structural equation models

- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- John Cameron Lee Sessoms (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- John Willse

**Abstract:** Level-specific fit indices generally are advised (but rarely used in practice) for evaluating fit of multilevel structural equation models (MSEM). Level-specific fit indices assess model fit for each level separately. Aggregate fit indices combine (mis)fit across levels and are used predominantly in practice. Diagonally Weighted Least Squares (DWLS) estimation generally is recommended for MSEM with categorical variables. Previous evaluations of level-specific fit indices only used continuous, normally distributed variables, small models, and Maximum Likelihood estimation. However, MSEM applications often use large models and categorical, non-normal variables. Single-level DWLS fit indices usually become less sensitive to misfit as model size and distributional skew/asymmetry increases. This simulation study evaluated how categorical variables, distributional skew, Level-2 sample size, intraclass correlation, model size, and model misspecification affected level-specific and aggregate fit indices. Level-1 and aggregate fit indices usually performed similarly. Level-1 and aggregate fit indices usually detected large Level-1 misfit but not small Level-1 misfit. Aggregate fit indices never identified Level-2 misfit. Level-1 and aggregate fit indices never rejected correct Level-1 models. Level-2 fit indices usually had low power to reject Level-2 misfit except with very optimal data. Level-2 fit indices often rejected correct Level-2 models. Researchers likely should consider alternatives to Level-2 fit indices and MSEMs.

Level-specific fit index performance with diagonally weighted least squares estimation of multilevel structural equation models

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Created on 5/1/2019

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## Additional Information

- Publication
- Dissertation
- Language: English
- Date: 2019
- Keywords
- Level-specific fit, Multilevel structural equation models, Weighted least squares
- Subjects
- Structural equation modeling $x Data processing
- Least squares $x Data processing
- Estimation theory $x Data processing
- Path analysis (Statistics) $x Data processing

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