A new solution to the additive constant problem in metric multidimensional scaling

A new solution to the additive constant problem in metric multidimensional scaling is developed. This solution determines, for a given dimensionality, the additive constant and the resulting stimulus projections on the dimensions of a Euclidean space which minimize the sum of squares of discrepancies between the formal model for metric multidimensional scaling and the original data. A modification of Fletcher-Powell style functional iteration is used to compute solutions. A scale free index of the goodness of fit is developed to aid in selecting solutions of adequate dimensionality from multiple candidates.This research is based in part on the author's Ph.D. dissertation at the University of Illinois at Urbana-Champaign. Computer time was provided by the Campus Computing Network of the University of California, Los Angeles.