A Structural Equation Multidimensional Scaling Model for One-Mode Asymmetric Dissimilarity Data

Abstract

A multidimensional scaling (MDS) model is proposed for 2-way 1-mode asymmetric dissimilarity data, to estimate the unknown symmetric subjacent dissimilarity matrix while the objects are represented in a low-dimensional space. In the context of least squares MDS allowing transformations, and considering both triangular parts of the asymmetric dissimilarity matrix as effects of the unobserved symmetric dissimilarities, an alternating estimation procedure is proposed in which the unknown symmetric dissimilarity matrix is estimated in a covariance structure framework. Real and artificial data are analyzed to illustrate the proposed procedure.

Keywords:

• asymmetry
• dissimilarity
• effect indicator
• multidimensional scaling
• STRESS structural equation model

Acknowledgments

The authors would like to thank Albert Satorra and three anonymous reviewers for valuable comments on an earlier draft of this article.

Notes

¹The program and data sets are available on request.