Optimal scaling of paired comparison and rank order data: An alternative to guttman's formulation |
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Authors: | Shizuhiko Nishisato |
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Affiliation: | (1) Department of Measurement, Evaluation and Computer Applications, The Ontario Institute for Studies in Education, 252 Bloor Street West, M5S 1V6 Toronto, Ontario, Canada |
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Abstract: | A formulation, which is different from Guttman's is presented. The two formulations are both called the optimal scaling approach, and are proven to provide identical scale values. The proposed formulation has at least two advantages over Guttman's. Namely, (i) the former serves to clarify close relations of the optimal scaling approach to those of Slater and the vector model of preferential choice, and (ii) in addition to the stimulus scale values, it provides scores for the subjects, which indicate the degrees of response consistency (transitivity), relative to the optimum solution. The method is assumption-free and capable of multidimensional analysis.This study was partly supported by the National Research Council Grant (No. A4581) to S. Nishisato. The author is indebted to Dr. Bert F. Green, Jr., Mr. Tomoichi Ishizuka, and anonymous reviewers for their valuable comments on an earlier draft. |
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Keywords: | Guttman's model Slater's model the vector model of preferential choice ranking and individual differences |
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