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Multilevel Structural Equation Modeling for Cross-National Comparative Research

Mehrebenen-Strukturgleichungsmodelle für ländervergleichende Forschung

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Abstract

This contribution focuses on a model that is gaining currency in cross-national research, namely multilevel structural equation modelling (MSEM). Similarly to standard multilevel modelling (MLM), this model distinguishes between various levels of analysis (e. g., individuals nested within countries) and, in doing so, takes the hierarchical structure of cross-national data into account. However, MSEM incorporates a latent-variable approach into the multilevel framework, making it possible to assess the measurement quality of latent constructs. As such, MSEM is a synthesis of structural equation modeling (SEM) and MLM that combines the best of both worlds. The MSEM approach makes it possible to model multilevel mediations and group-level outcomes, and therefore provides a more complete representation of Coleman’s bathtub model. This contribution presents the statistical and conceptual background of MSEM in a formal but accessible manner. The paper discusses applications of MSEM that are particularly useful for cross-national comparative research (CNCR), namely two-level confirmatory factor analysis (CFA), multilevel mediation models, and models for group-level outcomes. A practical step-by-step strategy on how MSEM can be used for applied research is provided and illustrated by means of a didactical example.

Zusammenfassung

Dieser Beitrag konzentriert sich auf ein Modell, das in der ländervergleichenden Forschung immer mehr an Bedeutung gewinnt, nämlich die Mehrebenen-Strukturgleichungsmodellierung (MSEM, „multilevel structural equation modelling“). Ähnlich wie Standard-Mehrebenenmodelle (MLM, „multi-level models“) unterscheidet dieses Modell zwischen verschiedenen Analyseebenen (z. B. Personen in Ländern) und berücksichtigt die hierarchische Struktur der ländervergleichenden Daten. Bei MSEM werden jedoch latente Variablen in das Mehrebenenmodell integriert, um die Messqualität nicht direkt beobachteter Konstrukte beurteilen zu können. So ist MSEM eine Synthese aus Strukturgleichungsmodellen (SEM „structural equation models“) und MLM, die das Beste aus beiden Welten vereint. Der MSEM-Ansatz ermöglicht Mediationsanalysen in Mehrebenendaten und die Modellierung von Outcomes auf der Makroebene und kann daher sehr viel besser das Badewannenmodell von Coleman abbilden. In diesem Beitrag wird der statistische und konzeptionelle Hintergrund von MSEM auf formale, aber leicht zugängliche Weise dargestellt. Es werden Anwendungen von MSEM erörtert, die für ländervergleichende Forschung besonders nützlich sind, nämlich die konfirmatorische Mehrebenen-Faktorenanalyse, Mehrebenen-Mediationsmodelle und Modelle für Outcomes auf der Makroebene. Schritt für Schritt wird anhand eines didaktischen Beispiels erläutert und veranschaulicht, wie MSEM für angewandte Forschung eingesetzt werden kann.

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Notes

  1. Orthogonally means here that the variance components at both levels are independent, i. e., they are not correlated. As a result, a clear-cut separation between the two levels is possible.

  2. In Mplus, this is done by specifying the indicators at “within” variables in the “variable” statement.

  3. It is of course possible to start with a Bayesian estimator from the outset; however, the Bayesian estimation procedure implemented in Mplus has the disadvantage that it offers few useful tools to assess model fit.

  4. The basic idea of a Monte Carlo simulation study is that a large number of random samples are generated according to a population model. Subsequently, each of the generated random samples (replications) is analyzed, and the results obtained are compared to the true population parameters. This procedure makes it possible to assess how accurate estimation and statistical inference are. See Muthén and Muthén (2002) for more details.

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Acknowledgements

I would like to thank the editors of the special issue for their useful comments on an earlier version of this paper. Furthermore, I am grateful to Sharon Baute, who assisted in setting up the empirical illustration and the replication materials.

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    Bart Meuleman

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Meuleman, B. Multilevel Structural Equation Modeling for Cross-National Comparative Research. Köln Z Soziol 71 (Suppl 1), 129–155 (2019). https://doi.org/10.1007/s11577-019-00605-x

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