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Least Squares Metric, Unidimensional Unfolding

Published online by Cambridge University Press:  01 January 2025

Keith T. Poole
Keith T. Poole*
Affiliation:
Graduate School of Industrial Administration, Carnegie-Mellon University
*
Requests for reprints should be addressed to Keith T. Poole, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213.
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Abstract

The partial derivatives of the squared error loss function for the metric unfolding problem have a unique geometry which can be exploited to produce unfolding methods with very desirable properties. This paper details a simple unidimensional unfolding method which uses the geometry of the partial derivatives to find conditional global minima; i.e., one set of points is held fixed and the global minimum is found for the other set. The two sets are then interchanged. The procedure is very robust. It converges to a minimum very quickly from a random or non-random starting configuration and is particularly useful for the analysis of large data sets with missing entries.

Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 3 , September 1984 , pp. 311 - 323
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

This paper benefits from many conversations with and suggestions from Howard Rosenthal.

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