The authors examine the cross-cultural equivalence of the internal structure of the values domain, as measured by the Schwartz Value Survey. Data come from 38 countries, each represented by a student and a teacher sample. In seeking to distinguish lack of fit of the theorized value model from a lack of equivalence in the data and the impact of random sampling fluctuations from valid structural differences, the authors find the following: (a) The Schwartz value theory provides an excellent representation of the average value structure across samples; (b) sampling fluctuation causes deviations from this average structure; (c) sampling fluctuation cannot account for all these deviations; (d) samples of students fit the overall value structure better than samples of teachers, and samples from Western countries better than those from non-Western countries; and (e) the deviations from the average structure exhibit a systematic pattern: the higher the level of societal development of a country, the greater the contrast between protection and growth values.

A multidimensional unfolding technique that is not prone to degenerate solutions and is based on multidimensional scaling of a complete data matrix is proposed: distance information about the unfolding data and about the distances both among judges and among objects is included in the complete matrix. The latter information is derived from the permutation polytope supplemented with the objects, called the preference sphere. In this sphere, distances are measured that are closely related to Spearman's rank correlation and that are comparable among each other so that an unconditional approach is reasonable. In two simulation studies, it is shown that the proposed technique leads to acceptable recovery of given preference structures. A major practical advantage of this unfolding technique is its relatively easy implementation in existing software for multidimensional scaling.

unfolding, degeneracy, mixed plots, squared correlation, iterative majorization,