Quantitative Analysis of Paired Comparison Data Using the Bradley-Terry Model with a Normal Distribution

概要

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The analysis of paired comparison experiments with frequency data such as win-loss records is usually dealt with using the Bradley-Terry model, wherein the number of wins is supposed to have a binomial distribution. This assumption of probability distribution is inappropriate and inconvenient in quantitative analysis with continuous variables such as preference tests of consumers in biology. In this paper, a practical method is proposed to apply the Bradley-Terry model to the repeated pair-comparison experiments with quantitative data. It is obtained by the nonlinear least squares method under the assumption of the additive normal error structure. Some simple methods for the estimation of precision and for the hypothesis testing are also given. An application to the food preference test of a captive northern fur seal suggests the validity and advantage of the method.