Summary
In general, most of the techniques now in common use for the determination of the dimensionality of MDS spaces tend to under-estimate the number of dimensions needed to represent the underlying configuration accurately. This tendency is exaggerated when time-sequenced MDS observations are under study. Fortunately, econometric time-series (autocorrelation) procedures may prove helpful in resolving this problem [6].
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References
Barnett, G.A. (1976). “The determinants of semantic organization of bilinguals,” Paper presented at the annual meeting of International Communication Association, Portland, Oregon, April.
Box, G.E.P. and Jenkins, G.M. (1970). Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.
Cattell, R.B. (ed.) (1966). Handbook of Multivariate Experimental Research. Chicago: Rand McNally.
Cohen, H.S. and Jones, L.E. (1974). “The Effects of random error and subsampling of dimensions on recovery of configurations by nonmetric multidimensional scaling,” Psychometrika, 39: 69–90.
Danes, J. and Woelfel, J. (1975). “An alternative to the ‘Traditional’ scaling paradigm in mass communication research: multidimensional reduction of ratio judgments of separation,” Paper presented before international Communication Association, Chicago, Illinois, April.
Gillham, J. and Woelfel, J. (1977). “The Galileo system of measurement: preliminary evidence for stability and equivalence to traditional measures,” Human Communication Research, 3: 222–234.
Glass, G.V., Wilson, V.L. and Gottman, J.M. (1975). Design and Analysis of Time-Series Experiments. Boulder: Colorado: Colorado Associated U. Press.
Green, P. (1975). “On the robustness of multidimensional scaling techniques,” Journal of Marketing Research 12: 73–81.
Isaac, P.D. and Poor, D.D.S. (1974). “On the determination of appropriate dimensionality in data with error,” Psychometrika 39: 91–109.
Johnson, S.C. (1967). “Hierarchical clustering schemes,” Psychometrika 32: 241–245.
Jones, L.E. and Young, F.W. (1972). “Structure of a social environment: longitudinal individual differences scaling for an intact group,” Journal of Personality and Social Psychology 24: 108–121.
Klahr, D.A. (1969). “A Monte Carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure,” Psychometrika 34: 319–330.
Kruskal, J. (1964a). “Multidimensional scaling by optimizing goodness to fit to a nonmetric hypothesis,” Psychometrika 29: 1–27.
Kruskal, J. (1964b). “Nonmetric multidimensional scaling: a numerical method,” Psychometrika 29: 28–42.
Linn, R.L. (1968). “A Monte Carlo approach to the number of factors problem,” Psychometrika 33: 37–72.
Nobel, B. (1969). Applied Linear Algebra. Englewood Cliffs, N.J.: Prentice-Hall.
Serota, K.B. (1974). “Metric multidimensional scaling and communication: theory and implementation,” unpublished M.A. thesis, Michigan State University, East Lansing.
Shepard, R.N. (1966). “Metric structures in ordinal data,” Journal of Mathematical Psychology 3: 287–315.
Shepard, R.N. (1972). “Introduction to MDS workshop,” University of Pennsylvania, Philadelphia, June.
Shepard, R.N. (1974). “Representation of structures in similarity data: problems and prospects,” Psychometrika 39: 373–422.
Stenson, H.H. and Knoll, R.L. (1969). “Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure,” Psychological Bulletin 71: 122–126.
Tatsuoka, M.M. (1971). Multivariate Analysis Techniques for Education and Psychological Research. New York: Wiley.
Torgerson, W.S. (1958). Theory and Methods of Scaling. New York: Wiley.
Wish, M. (1972). “Brief comments about dimensionality,” MDS workshop, University of Pennsylvania, June.
Woelfel, J., Saltiel, J., McPhee, R., Danes, J., Cody, M., Barnett, G. and Serota, K. (1975). “Orthogonal rotation to theoretical criteria: comparison of multidimensional spaces,” Paper presented at the Annual Convention of the Mathematical Psychology Group, Purdue, Indiana, August.
Young, F.W. (1970). “Nonmetric multidimensional scaling: recovery of metric information,” Psychometrika 35(4): 455–473.
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Barnett, G.A., Woelfel, J. On the dimensionality of psychological processes. Qual Quant 13, 215–232 (1979). https://doi.org/10.1007/BF00170038
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DOI: https://doi.org/10.1007/BF00170038