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Researchers in comparative research are increasingly relying on individual level data to test theories involving unobservable constructs like attitudes and preferences. Estimation is carried out using large-scale cross-national survey data providing responses from individuals living in widely varying contexts. This strategy rests on the assumption of equivalence, that is, no systematic distortion in response behavior of individuals from different countries exists. However, this assumption is frequently violated with rather grave consequences for comparability and interpretation. I present a multilevel mixture ordinal item response model with item bias effects that is able to establish equivalence. It corrects for systematic measurement error induced by unobserved country heterogeneity, and it allows for the simultaneous estimation of structural parameters of interest

Apples and Oranges? The Problem of Equivalence in Comparative Research