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Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment

Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit s...

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Autor principal: Lubbe, Dirk
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10188575/
https://www.ncbi.nlm.nih.gov/pubmed/37071271
http://dx.doi.org/10.1007/s11336-023-09909-6
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author Lubbe, Dirk
author_facet Lubbe, Dirk
author_sort Lubbe, Dirk
collection PubMed
description Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit statistic. While a noncentrality parameter estimate is well suited for quantifying the amount of systematic error, the complex weighting function involved in its calculation makes indices derived from it challenging to interpret. Moreover, noncentrality-parameter-based fit indices yield systematically different values, depending on the indicators’ level of measurement. For instance, RMSEA and CFI yield more favorable fit indices for models with categorical as compared to metric variables under otherwise identical conditions. In the present article, approaches for obtaining an approximation discrepancy estimate that is independent from any specific weighting function are considered. From these unweighted approximation error estimates, fit indices analogous to RMSEA and CFI are calculated and their finite sample properties are investigated using simulation studies. The results illustrate that the new fit indices consistently estimate their true value which, in contrast to other fit indices, is the same value for metric and categorical variables. Advantages with respect to interpretability are discussed and cutoff criteria for the new indices are considered. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11336-023-09909-6.
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spelling pubmed-101885752023-05-18 Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment Lubbe, Dirk Psychometrika Theory & Methods Fit indices are highly frequently used for assessing the goodness of fit of latent variable models. Most prominent fit indices, such as the root-mean-square error of approximation (RMSEA) or the comparative fit index (CFI), are based on a noncentrality parameter estimate derived from the model fit statistic. While a noncentrality parameter estimate is well suited for quantifying the amount of systematic error, the complex weighting function involved in its calculation makes indices derived from it challenging to interpret. Moreover, noncentrality-parameter-based fit indices yield systematically different values, depending on the indicators’ level of measurement. For instance, RMSEA and CFI yield more favorable fit indices for models with categorical as compared to metric variables under otherwise identical conditions. In the present article, approaches for obtaining an approximation discrepancy estimate that is independent from any specific weighting function are considered. From these unweighted approximation error estimates, fit indices analogous to RMSEA and CFI are calculated and their finite sample properties are investigated using simulation studies. The results illustrate that the new fit indices consistently estimate their true value which, in contrast to other fit indices, is the same value for metric and categorical variables. Advantages with respect to interpretability are discussed and cutoff criteria for the new indices are considered. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11336-023-09909-6. Springer US 2023-04-18 2023 /pmc/articles/PMC10188575/ /pubmed/37071271 http://dx.doi.org/10.1007/s11336-023-09909-6 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Theory & Methods
Lubbe, Dirk
Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment
title Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment
title_full Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment
title_fullStr Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment
title_full_unstemmed Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment
title_short Advantages of Using Unweighted Approximation Error Measures for Model Fit Assessment
title_sort advantages of using unweighted approximation error measures for model fit assessment
topic Theory & Methods
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10188575/
https://www.ncbi.nlm.nih.gov/pubmed/37071271
http://dx.doi.org/10.1007/s11336-023-09909-6
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