Dual Scaling: Gleaning in the Field Revisited with Reminiscences

Abstract

In the presidential address at the annual meeting of the Psychometric Society, held in Banff, Canada, Nishisato (1996) delivered his view on quantification theory under the title of “Gleaning in the field of dual scaling.” He identified a number of unsolved problems at that time. It is almost twenty years since then. Are those problems satisfactorily solved? Yes and no. From the current stage of progress, this paper was written about his view on the future perspectives of quantification theory. Given that the main purpose of quantification of categorical data lies in its strong desire to analyze both row variables and column variables on the equal footing, an immediate concern is around the current practice of multidimensional joint graphical display. This paper directs our attention to the difficulty underlying our joint graphical display of both row variables and column variables, where principal coordinates of both variables need to be plotted. The solution rests in the use of doubled multidimensional space, and the current paper recommends a step forward to total information analysis and the use of cluster analysis, instead of highly problematic multidimensional joint graph, an approach that most researchers, under the strong doctrine of `correspondence analysis,' have unsuccessfully pursued. In discussion, it was stated that the current practice of symmetric, non-symmetric scaling and biplot all fail to satisfy the basic premise of joint graphical display, that is, multidimensional plot of principal coordinates of both row and column variables. The paper emphasizes the importance of the understanding of the basic objective of joint analysis of row and column variables on the equal footing.