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Research Article

Parameter Estimation and Evaluation for the Thurstone Case Ⅲ and Case Ⅴ Model

Seoil Chaiy

Published: January 1984 · Vol. 14, No. 1 · pp. 49-76
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Abstract

Social scientists have long been interested in and conducted extensive research on human choice processes. Thurstone's Comparative Judgment Model has been widely utilized across the social sciences as a model for explaining human choice processes. Thurstone's model has been widely used as a method for obtaining interval scales for each object by deriving ordinal scales through paired comparisons from experimental subjects. This Comparative Judgment Model has been developed into various subcases, and among the models developed to date, Case V has been the most widely used because it offers the simplest method for obtaining scale values. Case V can be an efficient model when the experimental stimuli involve homogeneous and simple comparisons, such as measuring psychological elements like brightness or color of light. However, when making comparisons of heterogeneous and complex objects used in business administration, particularly in marketing, the assumptions employed in Case V do not hold because the differing characteristics of objects—especially the fact that they are perceived differently by individual experimental subjects—necessitate the use of a Case III model, where these differences are represented through the concept of standard deviation. The purpose of this paper is to derive scale values for the Case III model, which has remained unresolved despite considerable effort, and to evaluate the solutions. The estimation methods employed include least squares, maximum likelihood, and minimum chi-square methods, and the optimal solution computation processes utilized two computer-based optimization procedures: the gradient search method and the direct search method. By evaluating the six different solution methods resulting from combinations of the above estimation methods and optimization procedures through Monte Carlo simulation, guidelines were provided for users of the Comparative Judgment Model. The simulation results indicate that, first, when the sample size is small, the Case V model should be used; the least squares method, while less accurate than maximum likelihood or minimum chi-square, does not differ enough to significantly affect practical use; and using the gradient search method substantially reduces computation time, making it convenient for practical application. Finally, a maximum likelihood test employing a statistical method was used to help users determine whether the Case III or Case V model should be applied, and the discriminating power of this test was found to be satisfactory.