Monotone Regression

I. Borg and J. Lingoes
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I. Borg: Justus-Liebig-Universität, Department of Psychology
J. Lingoes: University of Michigan, Computing Center

Chapter 3 in Multidimensional Similarity Structure Analysis, 1987, pp 28-40 from Springer

Abstract: Abstract In the scatter diagram of the data against their corresponding SSA distances (Shepard diagram), a monotone curve is sought which approximates the points as closely as possible. More precisely, the best monotone regression of the SSA-distances onto the data is sought. The values of the monotone regression curve can then be used as target distances in the SSA construction process. Equal data values (tied data) need not be represented by equal distances in the primary approach, whereas in the secondary approach tied data have to be mapped into tied distances.

Keywords: Shepard diagram; monotonically increasing function; strictly and weakly monotone; order-preserving transformation; quadratic deviation; disparity; monotone regression; block formation and averaging; missing data; ties; complete order; primary and secondary approach to ties; breaking of ties; tie block; descending and ascending regression (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4768-5_3

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