Abstract
This paper presents a new methodology for estimating the weights or saliences of subcriteria (attributes) in a composite criterion measure. The inputs to the estimation procedure consist of (i) a set of stimuli or objects with each stimulus defined by its subcriteria profile (set of attribute values) and (ii) the set of paired comparison dominance (e.g., preference) judgments on the stimuli made by a single judge (expert) in terms of the global criterion. A criterion of fit is developed and its optimization via linear programming is illustrated with an example. The procedure is generalized to estimate a common set of weights when the pairwise judgments on the stimuli are made by more than one judge. The procedure is computationally efficient and has been applied in developing a composite criterion of managerial success yielding high concurrent validity.
This methodology can also be used to perform ordinal multiple regression—i.e., multiple regression with an ordinally scaled dependent variable and a set of intervally scaled predictor variables. The approach is further extended to “internal analysis” (unfolding) using the vector model of preference and to the additive model of “conjoint measurement.”
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References
Bechtel, G. Individual differences in the linear multidimensional scaling of choice. Paper presented at meeting of the Psychometric Society in Princeton, N. J., April, 1969.
Blum, M. L. and Naylor, J. C.Industrial Psychology—its theoretical and social foundations. New York: Harper and Row, 1968.
Carroll, J. D. Individual differences and multidimensional scaling. In Shepard, R. N., Romney, A. K., and Nerlove, S. B. (Eds.)Multidimensional scaling: Theory and applications in the behavioral sciences. Vol. I (Theory). New York: Seminar Press, 1972, 105–155.
Carroll, J. D. and Chang, J. J. Nonparametric multidimensional analysis of paired-comparisons data. Paper presented at the joint meeting of the Psychometric and Psychonomic Societies at Niagara Falls, October, 1964.
Charnes, A. and Cooper, W. W.Management models and industrial applications of linear programming (Vol. 1). New York: Wiley, 1961.
Dantzig, G. B.Linear programming and extensions. Princeton, N. J.: Princeton University Press, 1963.
Gass, S. I.Linear programming: methods and applications. New York: McGraw-Hill Book Company, 1958.
Green, P. E. and Rao, V. R. Conjoint measurement for quantifying judgmental data.Journal of Marketing Research, 1971,8, 355–363.
Hoffman, P. J. The paramorphic representation of clinical judgment.Psychological Bulletin, 1960,57, 116–131.
Kristy, N. F. Criteria of occupational success among post office counter clerks. Unpublished Ph.D. thesis. London: University of London Library, 1952.
Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–27. (a).
Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, 1964,29, 115–129. (b).
Kruskal, J. B. Analysis of factorial experiments by estimating monotone transformations of the data.Journal of the Royal Statistical Society, 1965,27 (Series B), 251–263.
Luce, R. D., and Tukey, J. W. Simultaneous conjoint measurement: a new type of fundamental measurement.Journal of Mathematical Psychology, 1964,1, 1–27.
MacCrimmon, K. R. Decision making among multiple-attribute alternatives: A survey and consolidated approach. Memorandum RM-4823-ARPA, Santa Monica, California: The RAND Corporation, 1968.
Shepard, R. N. On subjectively optimum selections among multi-attribute alternatives. In M. W. Shelly and G. L. Bryan (Eds.),Human judgment and optimality. New York: Wiley, 1964.
Shocker, A. D. A methodological approach to the identification of a feasible mass transit configuration for maximal satisfaction to users. In Hopfe, M. (Ed.)Proceedings of the 1971 AIDS Conference. St. Louis: American Institute of Decision Sciences, 1971.
Slater, P. The analysis of personal preferences.British Journal of Statistical Psychology, 1960,13, 119–135.
Sluckin, W. Combining criteria of occupational success: Part I.Occupational Psychology, 1956,30, 20–26 (a).
Sluckin, W. Combining criteria of occupational success: Part II.Occupational Psychology, 1956,30, 57–67 (b).
Srinivasan, V., Linear programming computational procedures for ordinal regression. Working paper, Rochester, New York: The University of Rochester, The Graduate School of Management, 1973.
Srinivasan, V., and Shocker, A. D. Linear programming techniques for multidimensional analysis of preferences.Psychometrika, 1973,38, 337–369.
Srinivasan, V., Shocker, A. D., and Weinstein, A. G. Measurement of a composite criterion of managerial success.Organizational Behavior and Human Performance, 1973,9, 147–167.
Tucker, L. R Intra-individual and inter-individual multidimensionality. In H. Gullicksen and S. Messick (Eds.)Psychological Scaling: Theory and Applications. New York: Wiley, 1960, 155–167.
Wagner, H. M. Linear programming techniques for regression analysis.Journal of the American Statistical Association, 1959,54, 206–212.
Wallace, S. R. Criteria for what?American Psychologist, 1965,20, 411–417.
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Srinivasan, V., Shocker, A.D. Estimating the weights for multiple attributes in a composite criterion using pairwise judgments. Psychometrika 38, 473–493 (1973). https://doi.org/10.1007/BF02291490
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DOI: https://doi.org/10.1007/BF02291490