MINIMUM DIMENSION ANALYSIS MDA

ONE OF THE METHODS OF MULTIDIMENSIONAL QUANTIFICATION (MDQ)

Abstract

In the present paper, the method of minimum dimension analysis (MDA) is given with examples. This method belongs to the same genre as smallest space analysis (SSA) by L. Guttman. Let R_ij be the relation between i-element and j-element, i, j = 1, 2, ..., N. If R_ij is given in the form of rank order, SSA gives the configuration of the elements with less inconsistancy in Euclidean space having smallest dimension. MDA reveals the configuration of those in the case where R_ij is given in the form of rank ordered group.
The author gives the algorithm to solve this problem using correlation ratio the main process of which is based on repeated linear programming method and e_ij-type quantification method.