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Statistical Consistency and Hypothesis Testing for Nonmetric Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Henry E. Brady
Henry E. Brady*
Affiliation:
Department of Government, Harvard University
*
Requests for reprints should be sent to Henry E. Brady, Department of Government, Harvard University, Cambridge, MA 02138.
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Abstract

The properties of nonmetric multidimensional scaling (NMDS) are explored by specifying statistical models, proving statistical consistency, and developing hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. For these models, statistical consistency often depends crucially upon how error enters the model and how data are collected and summarized (e.g., by means, medians, or rank statistics). A maximum likelihood estimator for NMDS is developed, and its relationship to the standard Shepard-Kruskal estimation method is described. This maximum likelihood framework is used to develop a method for testing the overall fit of the model.

Keywords

nonmetric multidimensional scalingmaximum likelihood estimationhypothesis testing
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 4 , December 1985 , pp. 509 - 537
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

In the preparation of this manuscript Chris Achen helped in innumerable ways by providing a judicious combination of criticism and encouragement. Professors J. O. Ramsay and Roger Shepard generously took the time to respond to an earlier version. I take responsibility for all remaining errors.

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