ABSTRACT
Multidimensional scaling (MDS) is a multivariate statistical method for estimating the scale values along one or more continuous dimensions such that those dimensions account for proximity measures defined over pairs of objects. It has been used to study such things as dimensions underlying perceptions of human speech, patterns of vocational/academic interests, and growth over time in reading and math achievement. We will limit ourselves to discussion of analyses based on Euclidean distance models. While this list is not exhaustive, there are three major applications of MDS which differ in the nature of the objects, the proximity measure defined over those objects, and the purpose. In perception studies, perhaps the most typical form of MDS, the objects are stimuli (e.g., speech samples), the proximity measures are judgments about the similarity of stimulus pairs (e.g., a rating of similarity), and the purpose is to identify the attributes (dimensions) along which stimuli are perceived to vary and that account for the similarity judgments. In cross-sectional studies, the objects are (typically continuous) variables measured at a single time point (e.g., score on a vocational interest scale). The proximity measure is an index of association defined over pairs of variables, such as a squared Euclidean distance or correlation coefficient. The purpose of the analysis of these proximity measures is to identify dimensions that point toward one or more within-person patterns needed to account for the associations among the variables. In longitudinal studies, which are a relatively recent extension of cross-sectional studies, the objects are occasions, and thus the data consist of a single variable (e.g., math achievement) measured at several time points. The proximity measure is an index of association among the occasions. The goal is to find patterns of growth, decay, or change that account for the associations among the occasions.
