HOMOGENEITY ANALYSIS OF TRANSITION MATRICES FOR SPATIALLY REPRESENTING A TRANSITION TREND

Abstract

An optimal scaling method is proposed for spatially representing the trend of individuals' transition described by a square contingency table. The method gives the low dimensional configuration of category points and the trend vector representing an overall tendency of the individuals' transition under the framework of homogeneity analysis. The configuration is obtained analytically with simple eigen-decomposition. Some examples are given to illustrate the method and its relationships to ordinary homogeneity analysis, correspondence analysis and the slide vector model of asymmetric multidimensional scaling are discussed.