, Volume 50, Issue 4, pp 509–537

Statistical consistency and hypothesis testing for nonmetric multidimensional scaling

  • Henry E. Brady

DOI: 10.1007/BF02296267

Cite this article as:
Brady, H.E. Psychometrika (1985) 50: 509. doi:10.1007/BF02296267


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.

Key words

nonmetric multidimensional scaling maximum likelihood estimation hypothesis testing 

Copyright information

© The Psychometric Society 1985

Authors and Affiliations

  • Henry E. Brady
    • 1
  1. 1.Department of GovernmentHarvard UniversityCambridge

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