Modifying the Wide Format Approach To Multilevel Structural Equation Modeling To Mitigate Estimation Problems

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Zitierfähiger Link (URI): http://hdl.handle.net/10900/167435
http://nbn-resolving.org/urn:nbn:de:bsz:21-dspace-1674359
http://dx.doi.org/10.15496/publikation-108762
Dokumentart: Dissertation
Erscheinungsdatum: 2025-07-01
Originalveröffentlichung: Walther, J. K., Hecht, M., Nagengast, B., Zitzmann, S. (2024). To Be Long or To Be Wide: How Data Format Influences Convergence and Estimation Accuracy in Multilevel Struc- tural Equation Modeling. Structural Equation Modeling: A Multidisciplinary Journal, 31(5), 759–774. https://doi.org/10.1080/10705511.2024.2320050; Walther, J. K., Hecht, M., Zitzmann, S. (2024). Shrinking Small Sample Problems in Multilevel Structural Equation Modeling via Regularization of the Sample Covariance Matrix. Structural Equation Modeling: A Multidisciplinary Journal, 32(1), 45-65. https: //doi.org/10.1080/10705511.2024.2380919; Walther, J. K., Hecht, M., Nagengast, B., Zitzmann, S. (2025). Multilevel Multigroup Structural Equation Modeling In A Single-Level Framework. Structural Equation Model- ing: A Multidisciplinary Journal, 1–32. https://doi.org/10.1080/10705511.2024.2434596
Sprache: Englisch
Fakultät: 6 Wirtschafts- und Sozialwissenschaftliche Fakultät
Fachbereich: Psychologie
Gutachter: Zitzmann, Steffen (Prof. Dr.)
Tag der mündl. Prüfung: 2025-05-26
DDC-Klassifikation: 150 - Psychologie
300 - Sozialwissenschaften, Soziologie, Anthropologie
Freie Schlagwörter:
Multilevel
SEM
Small Samples
Large p, small N
Highdimensional
Wide Format
Heterogeneous Variances
Regularization
Data Format
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Abstract:

In psychology and the education sciences, multilevel data is omnipresent. In this data structure observational units are nested within higher level units, such as students within classes. A powerful tool for estimating parameters across these different levels is multilevel structural equation modeling (SEM). Multilevel data can be arranged in two data formats, long (LF) and wide (WF) format, and for both, multilevel SEM approaches are available. While both approaches are applicable within the established lavaan package in the free and open-source software R, the major advantage of the WF approach is its modifiability. Within my thesis, I first (1) redefine „small samples“ for multilevel data and compare the performance of both approaches here. I then show that the WF approach can be modified to mitigate estimation problems such as non-convergence and inaccuracy under conditions of (2) small samples and (3) heterogeneous variances. Findings suggest that both approaches exhibit comparable performance in small samples and that the proposed extensions of the WF approach offer an accessible avenue for researchers dealing with multilevel analysis, particularly when data acquisition is limited or heterogeneous populations are under investigation.

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