Optimal design for the Bradley–Terry paired comparison model |
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Authors: | Ulrike Graßhoff Rainer Schwabe |
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Institution: | (1) Institute for Mathematical Stochastics, Otto-von-Guericke-University, PF 4120, 39016 Magdeburg, Germany |
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Abstract: | Paired comparisons are a popular tool for questionnaires in psychological marketing research. The quality of the statistical
analysis of the responses heavily depends on the design, i.e. the choice of the alternatives in the comparisons. In this paper
we show that the structure of locally optimal designs changes substantially with the parameters in the underlying utility.
This fact is illustrated by elementary examples, where the optimal designs can be completely characterized. As an alternative
maximin efficient designs are proposed which perform well for all parameter settings.
Research supported by grant Ho 1286 of the German Research Council (Deutsche Forschungsgemeinschaft). |
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Keywords: | Optimal design Paired comparison Bradley– Terry model Logistic model D-optimal design Maximin efficient design |
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