Capturing bias in structural equation modeling

Equivalence studies are coming of age. Thirty years ago there were few conceptual models and statistical techniques to address sources of systematic measurement error in cross-cultural studies (for early examples, see Cleary & Hilton, 1968; Lord, 1977, 1980; Poortinga, 1971). This picture has changed; in the last decades conceptual models and statistical techniques have been developed and refined. Many empirical examples have been published. There is a growing awareness of the importance of the field for the advancement of cross-cultural theorizing. An increasing number of journals require authors who submit manuscripts of cross-cultural studies to present evidence supporting the equivalence of the study measures. Yet the burgeoning of the field has not led to a convergence in conceptualizations, methods, and analyses. For example, educational testing focuses on the analysis of items as sources of problems of cross-cultural comparisons, often using item response theory (e.g., Emenogu & Childs, 2005). In personality psychology, exploratory factor analysis is commonly applied as a tool to examine similarity of factors underlying a questionnaire (e.g., McCrae, 2002). In survey research and marketing, structural equation modeling (SEM) is most frequently employed (e.g., Steenkamp & Baumgartner, 1998). From a theoretical perspective, these models are related; for example, the relationship of item response theory and confirmatory factor analysis (as derived from a general latent variable model) has been described by Brown (2015; see also Glockner-Rist & 4Hoijtink, 2003). However, from a practical perspective, the models can be seen as relatively independent paradigms; for a critical outsider the link between substantive field and analysis method is rather arbitrary and difficult to comprehend