Abstract
There are a number of points in the development of dual scaling which have escaped our attention. In my Beijing paper, problems with joint graphical display were discussed to fill the gap of understanding, and the current paper deals with some other points. These two papers can be regarded as a sequel to my paper, entitled “Gleaning in the field of dual scaling,” written 20 years ago. Noting that the basic premise of dual scaling lies in duality of exhaustive analysis, we will look at a few more points in this paper. Outcry one is on linear and nonlinear analysis. As is well known, dual scaling is a method for simultaneous regressions of row variates and column variates on data, capturing all linear and nonlinear relations contained in the data. From this point of view, Likert scores, used as scores for data analysis, are far from satisfactory, for it is a strictly linear and data-independent procedure. Outcry two is on our definition of multidimensional quantification space, because the traditional framework needs to be modified so as to satisfy our objective, that is, describing both row and column structure of data in a symmetric comprehensive way. Outcry three is on a logical alternative to problem-plagued joint graphical display, and a recommended alternative is cluster analysis. Finally, outcry four is on the distinction between dual space and total space, leading to the suggestion that simple correspondence analysis fails to provide exhaustive analysis of information in data.
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Acknowledgment
Due to an unexpected circumstance, the author could not present the paper at the conference, but Dr. Pieter M. Kroonenberg kindly offered his help and presented it for the author. His kind help is noted here and much appreciated. Computational assistance of Dr. J.G. Clavel is also appreciated.
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Nishisato, S. (2017). Outcries of Dual Scaling: The Key Is Duality. In: van der Ark, L.A., Wiberg, M., Culpepper, S.A., Douglas, J.A., Wang, WC. (eds) Quantitative Psychology. IMPS 2016. Springer Proceedings in Mathematics & Statistics, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-319-56294-0_10
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