Functional relations in multidimensional scaling

Abstract

Theory testing with multidimensional scaling models requires the ability to specify models with functional relations among parameters, to estimate the parameters of such models, and to compare the resulting models to models without functional constraints. The non‐linear optimization theory relevant to general multidimensional scaling models with functional relations is developed via first‐order necessary conditions. A Gauss‐Newton based algorithm is developed to implement the theory. The specific case of constraints to yield a circular configuration in the linear Euclidian distance model is studied in detail, and it is applied to some classical colour data.