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2006-16

Optimal Designs for the Bradley-Terry Paired Comparison Model

by Graßhoff, U., Schwabe, R..


Series: 2006-16, Preprints

MSC:
62K05 Optimal designs
62J15 Paired and multiple comparisons
62J12 Generalized linear models

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.

Keywords:
Optimal design, paired comparison, Bradley-Terry model, logistic model, $D$-optimal design, maximin efficient design, product-type design