This chapter focuses on data analytic methods to investigate whether the internal structures of measurement instruments are equivalent between cultural groups. For example, is the structure of values that guide individuals’ lives similar between Western and Far Eastern countries? Do employees use the same dimensions to evaluate their organization and their supervisors in different cultural groups? Is the structure of personality between the United States and China the same, or are there culture-specific personality dimensions? This chapter introduces the four most commonly used data analytic methods to investigate the equivalence of the internal structure between cultural groups – namely, multidimensional scaling (MDS), principal component analysis (PCA), exploratory factor analysis (EFA), and confirmatory factor analysis. Before presenting these four data analytic methods, the concept of structural equivalence is explained and situated within the equivalence framework. Moreover, at the end of this chapter two general issues about sample size and data transformation before the analyses are discussed.

The concept of structural equivalence

The investigation of the internal structure forms a key element in the validation process of a measurement instrument within a cultural group (e.g., Messick, 1989). The question is whether the item responses adequately capture the underlying dimensions or factors of the domain one wants to assess. For instance, the responses to the items of a Big Five personality instrument should be captured by five underlying factors, and each of the items has to contribute to the assessment of the specific personality factor it has been constructed for. Thus, the investigation of the internal structure answers two questions: (a) what are the underlying dimensions or factors that capture the interrelationships between the observed item responses and (b) how does each item relate to these underlying dimensions or factors? The more the expected underlying dimensions emerge from the observed item–response relationships and the more each item relates to the expected underlying dimension, the more evidence there is for the construct validity of the instrument.