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Utility Balance and Design Optimality in Logistic Models with One Unrestricted Quantitative Factor

by Schwabe, R., Graßhoff, U., Großmann, H., Holling, H..

Series: 2005-06, Preprints

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

In this paper we show that product type designs
are optimal in partially heteroscedastic
multi-factor linear models.
This result is applied to obtain locally $D$-optimal
designs in multi-factor generalized linear models
by means of a canonical transformation.
As a consequence we can construct optimal designs
for logistic response in paired comparison experiments
which are close to the concept of utility balance.

optimal design, paired comparison, Bradley-Terry model, logistic model,