A1002
Title: Optimal designs for a linear paired comparison model with continuous predictors in a restricted design region
Authors: Heiko Grossmann - Otto-von-Guericke-University Magdeburg (Germany) [presenting]
Heinz Holling - Univeristy of Munster (Germany)
Nadja Malevich - University of Munster (Germany)
Rainer Schwabe - Otto-von-Guericke University Magdeburg (Germany)
Abstract: A linear model is considered with a continuous response for pairwise comparisons of alternatives characterized by several continuous factors. For each pair of alternatives, the response may then be interpreted as the difference between the expected utilities of the two alternatives, plus a random error. Other interpretations arise from the fact that the model is formally equivalent to a multiple linear regression model without an intercept, where the factor levels of one alternative in each pair enter the systematic component of the model additively, while the factor levels of the other are included in a subtractive manner. For example, this corresponds to experimental settings in which two simultaneously applied factors exert opposing effects on the outcome for each experimental unit. In standard design problems, the design region consists of all pairs of vectors in the Cartesian product of certain intervals. However, a restricted design region and an associated design locus are considered, both of which are the union of certain lower-dimensional sets. Optimal continuous designs and efficiency comparisons are presented for various criteria, including D-, A-, and MV-optimality. Illustrative examples of potential applications of the model and the proposed designs are outlined.
