Restricted multidimensional scaling models

A class of multidimensional scaling models are developed wherein certain parameters may be fixed as known constants, or proportional to one another. Traditional multidimensional scaling can be obtained as a special case by fixing only the orientation and origin of a configuration. Methods of obtaining least-square estimates of the parameters via nonlinear programming are discussed, and an effective computer program is developed to implement application of the models to data. Several well-known data sets are reanalyzed under various restricted models, and the results demonstrate the possibility of achieving insight not attainable under the traditional approach. The potential distortion arising from inadequate model specification is discussed, and the importance of substantive theory to multidimensional scaling research is emphasized.