Constrained multidimensional scaling, including confirmation

Abstract

Constrained and confirmatory multidimensional scaling (MDS) are not equivalent. Constraints refer to the translation of either theoretical or data analytical objectives into computational specifications. Confirmation refers to a study of the balance between systematic and random variation in the data for modeling of the systematic part. Among the topics discussed from this perspective are the role of substantive theory in MDS studies, the type of constraints currently envisaged, and the relationships with other data analysis methods. This paper points out the possibility of using either sampling models or resampling schemes to study the stability of MDS solutions. Parallel to Akaike’s (1974) information criterion for choosing one out of many models for the same data, a general stability criterion is proposed and illustrated, based on the ratio of within to total spread of configurations issued from resampling.