Optimal Designs for Asymmetric Linear Paired Comparisons with a Profile Strength Constraint

by Grossmann, H.; Holling, H.; Grasshoff, U.; Schwabe, R.


Preprint series: 04-26, Preprints

62K05 Optimal designs
62J15 Paired and multiple comparisons


Abstract: Within the linear model framework the problem of determining optimal designs for paired comparisons of alternatives which are described by a set of discrete attributes is considered under the constraint that the alternatives in a pair are only allowed to differ with regard to a certain number of attributes. Whereas in previous treatments of this problem it was assumed that all attributes possess the same number of levels, here the general asymmetric case is discussed. We provide a characterization of optimal designs and demonstrate how this can be used to derive a solution of the design problem for many situations of interest. Moreover, optimal designs are presented for all settings in which there are two or three groups of attributes with equal numbers of levels within each group.

Keywords: Optimal design, paired comparisons, profile strength

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