Model-Robust Estimation of Multiple-Group Structural Equation Models
Structural equation models (SEM) are widely used in the social sciences. They model the relationships between latent variables in structural models, while defining the latent variables by observed variables in measurement models. Frequently, it is of interest to compare particular parameters in an S...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Algorithms |
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| Online Access: | https://www.mdpi.com/1999-4893/16/4/210 |
| _version_ | 1797606687769624576 |
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| author | Alexander Robitzsch |
| author_facet | Alexander Robitzsch |
| author_sort | Alexander Robitzsch |
| collection | DOAJ |
| description | Structural equation models (SEM) are widely used in the social sciences. They model the relationships between latent variables in structural models, while defining the latent variables by observed variables in measurement models. Frequently, it is of interest to compare particular parameters in an SEM as a function of a discrete grouping variable. Multiple-group SEM is employed to compare structural relationships between groups. In this article, estimation approaches for the multiple-group are reviewed. We focus on comparing different estimation strategies in the presence of local model misspecifications (i.e., model errors). In detail, maximum likelihood and weighted least-squares estimation approaches are compared with a newly proposed robust <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> loss function and regularized maximum likelihood estimation. The latter methods are referred to as model-robust estimators because they show some resistance to model errors. In particular, we focus on the performance of the different estimators in the presence of unmodelled residual error correlations and measurement noninvariance (i.e., group-specific item intercepts). The performance of the different estimators is compared in two simulation studies and an empirical example. It turned out that the robust loss function approach is computationally much less demanding than regularized maximum likelihood estimation but resulted in similar statistical performance. |
| first_indexed | 2024-03-11T05:18:36Z |
| format | Article |
| id | doaj.art-1fb35dcbac2b443a96f9905e3b84a5f5 |
| institution | Directory Open Access Journal |
| issn | 1999-4893 |
| language | English |
| last_indexed | 2024-03-11T05:18:36Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Algorithms |
| spelling | doaj.art-1fb35dcbac2b443a96f9905e3b84a5f52023-11-17T17:59:19ZengMDPI AGAlgorithms1999-48932023-04-0116421010.3390/a16040210Model-Robust Estimation of Multiple-Group Structural Equation ModelsAlexander Robitzsch0IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, GermanyStructural equation models (SEM) are widely used in the social sciences. They model the relationships between latent variables in structural models, while defining the latent variables by observed variables in measurement models. Frequently, it is of interest to compare particular parameters in an SEM as a function of a discrete grouping variable. Multiple-group SEM is employed to compare structural relationships between groups. In this article, estimation approaches for the multiple-group are reviewed. We focus on comparing different estimation strategies in the presence of local model misspecifications (i.e., model errors). In detail, maximum likelihood and weighted least-squares estimation approaches are compared with a newly proposed robust <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mi>p</mi></msub></semantics></math></inline-formula> loss function and regularized maximum likelihood estimation. The latter methods are referred to as model-robust estimators because they show some resistance to model errors. In particular, we focus on the performance of the different estimators in the presence of unmodelled residual error correlations and measurement noninvariance (i.e., group-specific item intercepts). The performance of the different estimators is compared in two simulation studies and an empirical example. It turned out that the robust loss function approach is computationally much less demanding than regularized maximum likelihood estimation but resulted in similar statistical performance.https://www.mdpi.com/1999-4893/16/4/210structural equation modelingmodel robustnessrobust loss functionregularized estimationmodel errormeasurement noninvariance |
| spellingShingle | Alexander Robitzsch Model-Robust Estimation of Multiple-Group Structural Equation Models Algorithms structural equation modeling model robustness robust loss function regularized estimation model error measurement noninvariance |
| title | Model-Robust Estimation of Multiple-Group Structural Equation Models |
| title_full | Model-Robust Estimation of Multiple-Group Structural Equation Models |
| title_fullStr | Model-Robust Estimation of Multiple-Group Structural Equation Models |
| title_full_unstemmed | Model-Robust Estimation of Multiple-Group Structural Equation Models |
| title_short | Model-Robust Estimation of Multiple-Group Structural Equation Models |
| title_sort | model robust estimation of multiple group structural equation models |
| topic | structural equation modeling model robustness robust loss function regularized estimation model error measurement noninvariance |
| url | https://www.mdpi.com/1999-4893/16/4/210 |
| work_keys_str_mv | AT alexanderrobitzsch modelrobustestimationofmultiplegroupstructuralequationmodels |