Comparing a Fuzzy Hybrid Approach with Invariant MGCFA to Study National Identity

Abstract

National identity studies diverge on several issues, such as the number of factors and their respective items' adscription. Multi-Group Confirmatory Factor Analysis (MGCFA) is the standard method applied to cross-national datasets. Differences between groups can be the result of measurement artefacts. We argue that these problems can be better addressed by an alternative approach that builds a synthetic indicator named Relative National Identity Synthetic Indicator (RNISI), based on a Fuzzy Hybrid Analysis (FHA). The study aims to shed some light on the study of the latent variable national identity by comparing two methodologies: the classic method most often used (MGCFA) and the Fuzzy-Hybrid Approach, which, to our knowledge, has not been previously applied. This empirical study was based on a dataset from across ten countries using two waves (2003 and 2013) of the International Social Survey Programme (ISSP). The FHA results were compared with those obtained by two MGCFA models in which national identity was built as a second-order construct that depends on the ethnic, ancestry and civic first-order latent variables. The comparison lets us conclude that FHA can be considered a valid tool to measure the national identity by groups, and to provide additional information in form of elasticity figures. These figures can be employed to analyse the indicator's sensitivity by group and for each of the items included in the national identity construct.