On the design of paired comparison experiments with application

In practice, paired comparison experiments involving pairs of either full or partial profiles are frequently used. When all attributes have a general common number of levels, the problem of finding optimal designs is considered in the presence of a second-order interactions model. The D-optimal designs for the second-order interactions model in this setting have both types of pairs in which either all attributes have different levels or approximately half of the attributes are different. The proposed optimal designs can be used as a benchmark to compare any design for estimating main effects and two and three attribute interactions. A practical situation that incorporates the corresponding second-order interactions is covered.