Design of paired comparison experiments when treatments are levels of a single quantitative variable
A paired comparison experiment is an extension of a binomial experiment; the treatments are compared pairwise and the response is binary. These experiments are often conducted in areas such as taste testing, where it may be difficult to quantify the taste of a sample, but it may be relatively easy to state which of two samples is preferred. The Bradley-Terry model without ties [\textit{R. A. Bradley} and \textit{M. E. Terry}, Biometrika 39, 324-345 (1952; Zbl 0047.129)] is used in this paper. Treatments are levels of continuous, independent variables. The logarithm of the Bradley-Terry parameters are expressed as a regression- type model. Optimal designs are obtained for linear and quadratic models. Optimality criteria considered are minimization of the variance of the maximum likelihood estimate of a single parameter and D-optimality.
minimization of the variance of the maximum likelihood estimate
scientific article; zbMATH DE number 3974115