Exploratory Graph Analysis for Configural Invariance Assessment of a Test

Self-report survey instruments are frequently used to investigate differences between groups of respondents, such as citizens of different nations in cross-country comparative analyses. In this context, a main methodological problem pertain to the configural invariance of the measurement instrument, which holds if the latent structure has the same pattern across different groups across the groups. In this work, to address this issue, we adopt an exploratory approach rooted in the framework of graph theory. Specifically, considering a multi-group comparative analysis and measurement instruments consisting of ordered categorical indicators, we discuss the use of exploratory graph analysis to assess the instrument configural invariance. In this framework, networks are used to represent latent constructs, and the covariance between observable indicators is explained in terms of a pattern of causal interactions between the items. Hence, we assume that if the measurement instrument functions invariantly across the groups, the group specific correlation-based networks will be characterised by a similar structure. The network structures are estimated through a Bayesian approach with sparse inducing priors and network embedding will be used to investigate the structure similarity. Through a simulation study we demonstrate that the proposed method is able to identify the differences. Finally, the proposed approach is applied to test the configural invariance of the Democracy Scale adopted in the European Social Survey.