Abstract
The concept of sequential estimation is introduced in multidimensional scaling (MDS). The sequential estimation method developed in this paper refers to continually updating estimates of a configuration as new observations are added. This method has a number of advantages, such as a locally optimal design of the experiment can be easily constructed, and dynamic experimentation is made possible. Using artificial data, the performance of our sequential method is illustrated.
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References
Beck, J. V. & Arnold, K. J.Parameter estimation in engineering and science. New York: Wiley, 1977.
deLeeuw, J. & Heiser, W. Convergence of correlation-matrix algorithms for multidimensional scaling. In J. C. Lingoes (Ed.),Geometric representations of relational data. Ann Arbor, Michigan: Mathesis Press, 1977.
Fedorov, V. V.Theory of optimal experiments. New York: Academic Press, 1972.
Girard, R. A. & Cliff, N. A monte carlo evaluation of interactive multidimensional scaling.Psychometrika, 1976,41, 43–64.
Lingoes, J. C. & Roskam, E. E. A mathematical and empirical analysis of two multidimensional scaling algorithms.Psychometrika Monograph Supplement, 1973, 38.
Ramsey, J. O. Confidence regions for multidimensional scaling.Psychometrika, 1978,43, 145–160.
Takane, Y., Young, F. & deLeeuw, J. Nonmetric individual differences multidimensional scaling: An alternative least squares method with optimal scaling features.Psychometrika, 1977,42, 7–67.
Young, F. & Cliff, N. Interactive scaling with individual subjects.Psychometrika, 1972,37, 385–415.
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We are indebted to anonymous reviewers for their suggestions. In addition, we thank Dr. Frank Critchley for his helpful comments on our Q/S algorithm.
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Miyano, H., Inukai, Y. Sequential estimation in multidimensional scaling. Psychometrika 47, 321–336 (1982). https://doi.org/10.1007/BF02294163
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DOI: https://doi.org/10.1007/BF02294163