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Parameterizing structural equation models as Bayesian multilevel regression models: An example with the Global Multidimensional Poverty Index

The goal of this paper is to frame structural equation models (SEMs) as Bayesian multilevel regression models. Framing SEMs as Bayesian regression models provides an alternative approach to understanding SEMs that can improve model transparency and enhance innovation during modeling. For demonstration, we analyze six indicators of living standards data from 101 countries. The data are proportions and we develop confirmatory factor analysis as regression while accommodating the fact that the data are proportions. We also provide extensive guidance on prior specification, which is relevant for estimating complex regression models such as these. Finally, we run through regression equations for SEMs beyond the scope of the demonstration.