Optimal Designs for Stated Choice Experiments that Incorporate Position Effects

Davidson and Beaver (1977 Davidson , R. R. , Beaver , R. J. ( 1977 ). On extending the Bradley–Terry model to incorporate within-pair order effects . Biometrics 33 : 693 – 702 .Crossref], Web of Science ®] , Google Scholar]) extended the Bradley–Terry model to incorporate the possible effect of position within a choice set on the choices made in paired comparisons experiments. We further extend the Davidson–Beaver result to choice sets of any size and show, under a mild restriction, that designs optimal for the multinomial logit model are still optimal. Designs balanced for carry-over effects of all orders can be used to construct designs with a diagonal information matrix for attribute effects. The theoretical results are derived assuming equal merits and we discuss the possible consequences of assuming unequal merits in an example.