Exploratory graph analysis for configural invariance assessment of a test

In cross-country comparative analyses, self-report survey tools are widely used to examine variations among respondents from different groups, such as citizens of various nations. An important methodological issue, in this situation, relates to the configural invariance of the measurement tool, which holds if the latent structure exhibits the same pattern across various groups. To address this issue, we take an exploratory approach grounded in the paradigm of graph theory. We discuss the use of exploratory graph analysis to assess the configural invariance in the context of a multi-group comparative analysis with measurement instruments comprised of ordered categorical indicators. In this framework, networks are utilised to represent latent constructs, and the covariance between observable indicators is explained through a pattern of causal interactions between the items. Therefore, we postulate that group-specific correlation-based networks would have a comparable structure if the measuring instrument operates consistently across groups. Network embedding will be utilised to look into the similarity of the network structures estimated using a Bayesian approach with sparse-inducing priors and mixture models to identify subgroups of homogeneous graphs. We show through a simulation analysis and real-world applications that the suggested technique can distinguish differences in the latent structure.