Structural equation modelling (SEM) has become one of the most prominent approaches to testing substantive theories about the relations among observed and/or unobserved variables. Applying this multivariate procedure, researchers are faced with several methodological decisions, including the treatment of indicator variables (e.g. categorical vs. continuous treatment), the handling of missing data, and the selection of an appropriate level of analysis. The PIAAC data pose additional issues, such as the clustering of individual-level data, the large number of participating countries, the representation of performance scores by a set of plausible values, and the differences in the selection probabilities. Therefore, a flexible software package is required to handle them. This chapter introduces readers to analysing PIAAC data with SEM in the software Mplus by (a) presenting the key concepts behind SEM, (b) discussing the complexities of the PIAAC data and their possible handling, (c) illustrating the specification and evaluation of measurement and structural models, and (d) pointing to current developments in the areas of measurement invariance testing and multilevel SEM. Sample input and output files are provided.
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