Optimal Designs for Stated Choice Experiments that Incorporate Position Effects |
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Authors: | Stephen Bush Deborah J Street Leonie Burgess |
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Institution: | 1. School of Mathematical Sciences , University of Technology Sydney , Sydney , NSW , Australia stephen.bush@uts.edu.au;3. School of Mathematical Sciences , University of Technology Sydney , Sydney , NSW , Australia |
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Abstract: | 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. |
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Keywords: | Bradley–Terry model Davidson–Beaver position effects model Multinomial logit model Multiple comparisons Paired comparisons |
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