Abstract
A new regression algorithm for multidimensional scaling is given to find an optimal monotone function which approximates the given data with partial order restrictions under a least squares criterion. In multidimensional scaling, Kruskal's “Up-and-Down Blocks Algorithm” has been used extensively, which is only applicable to the simple order restrictions, and ordinal data which produces the partial order restrictions has been preprocessed in order to get simple order restrictions. Our algorithm makes it possible to analyze such data rather directly.
