Abstract
Within the linear model framework the problem of determining optimal designs for paired comparisons of alternatives which are described by a set of discrete attributes is considered under the constraint that the alternatives in a pair are only allowed to differ with regard to a certain number of attributes. Whereas in previous treatments of this problem it was assumed that all attributes possess the same number of levels, here the general asymmetric case is discussed. We provide a characterization of optimal designs and demonstrate how this can be used to derive a solution of the design problem for many situations of interest.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bradley RA (1976) Science, statistics, and paired comparisons. Biometrics 32:213–232
David HA (1988) The method of paired comparisons, 2nd edn. Charles Griffin, London
Fraenkel L, Bodardus S, Wittink DR (2001) Understanding patient preferences for the treatment of lupus nephritis with adaptive conjoint analysis. Med Care 39:1203–1216
Graßhoff U, Schwabe R (2003) On the analysis of paired observations. Stat Probab Lett 65:7–12
Graßhoff U, Großmann H, Holling H, Schwabe R (2003) Optimal paired comparison designs for first-order interactions. Statistics 37:373–386
Graßhoff U, Großmann H, Holling H, Schwabe R (2004) Optimal designs for main effects in linear paired comparison models. J Stat Plan Inference 126:361–376
Green PE, Srinivasan V (1978) Conjoint analysis in consumer research: Issues and outlook. J Consum Res 5:103–123
Großmann H, Holling H, Graßhoff U, Schwabe R (2004) Optimal designs for asymmetric linear paired comparisons with a profile strength constraint. Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Preprint Nr. 26/2004
Kiefer J (1959) Optimum experimental designs. J R Stat Soc Ser B 21:272–304
Kiefer J, Wolfowitz J (1960) The equivalence of two extremum problems. Can J Math 12:363–366
Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York
Scheffé H (1952) An analysis of variance for paired comparisons. J Am Stat Assoc 47:381–400
Schwabe R (1996) Optimum designs for multi-factor models. Lecture notes in statistics 113 Springer, Berlin Heidelberg New York
Street DJ, Burgess L (2004) Optimal and near-optimal pairs for the estimation of effects in 2-level choice experiments. J Stat Plan Inference 118:185–199
Street DJ, Bunch DS, Moore BJ (2001) Optimal designs for 2k paired comparison experiments. Commun Stat Theory Methods 30:2149–2171
van Berkum EEM (1987) Optimal paired comparison designs for factorial and quadratic models. J Stat Plan Inference 15:265–278
van Berkum EEM (1989) Reduction of the number of pairs in paired comparison designs and exact designs for quadratic models. Comput Stat Data Anal 8:93–107
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Großmann, H., Holling, H., Graßhoff, U. et al. Optimal Designs for Asymmetric Linear Paired Comparisons with a Profile Strength Constraint. Metrika 64, 109–119 (2006). https://doi.org/10.1007/s00184-006-0038-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-006-0038-y