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

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

Series: 2004-26, Preprints

62K05 Optimal designs
62J15 Paired and multiple comparisons

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.

Optimal design, paired comparisons, profile strength