Optimal designs for main effects in linear paired comparison models

Graßhoff, Ulrike; Großmann, Heiko; Holling, Heinz; Schwabe, Rainer

doi:10.1016/j.jspi.2003.07.005

Cited by 67 publications

(93 citation statements)

References 16 publications

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“…Simultaneously, Graßhoff et al (2003) and Graßhoff et al (2004) tions again depends on the difference matrix P p = P p1 −P p2 . More precisely, the response is described by the model, Z = u 1 − u 2 + = (P p1 − P p2 )θ + = P p θ + , where is the random error vector.…”

Section: Preliminaries and The Model Incorporating Respondent Effectsmentioning

confidence: 99%

“…D-optimal designs have been obtained in the literature either under the utility-neutral setup or using the locally D-optimal/Bayesian approach. D-optimal designs have been obtained theoretically under the utility-neutral setup, for example, see Graßhoff et al (2003), Graßhoff et al (2004), Street and Burgess (2007), Street and Burgess (2012), Demirkale, Donovan, and Street (2013), Bush (2014), Großmann and Schwabe (2015) and Singh, Chai, and Das (2015). In contrast, in the locally-optimal and the Bayesian approach, D-optimal designs have been obtained using computer algorithms (see, Huber and Zwerina (1996), Sándor and Wedel (2001), Sándor and Wedel (2002), Sándor and Wedel (2005), Kessels, Goos, and Vandebroek (2006), , , Kessels et al (2009), Yu, Goos, and Vandebroek (2009)).…”

Section: Introductionmentioning

confidence: 99%

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Optimal Paired Choice Block Designs

Singh¹,

Das²,

Chai³

2019

STAT SINICA

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Choice experiments help manufacturers, service-providers, policy-makers and other researchers in taking business decisions. Traditionally, while using designs for discrete choice experiments, every respondent is shown the same collection of choice pairs (that is, the choice design). Also, as the attributes and/or the number of levels under each attribute increases, the number of choice pairs in an optimal paired choice design increases rapidly. Moreover, in the literature under the utility-neutral setup, random subsets of the theoretically obtained optimal designs are often allocated to respondents. The question therefore is whether one can do better than a random allocation of subsets. To address these concerns, in the linear paired comparison model (or, equivalently the multinomial logit model), we first incorporate the fixed respondent effects (also referred to as the block effects) and then obtain optimal designs for the parameters of interest. Our approach is simple and theoretically tractable, unlike other approaches which are algorithmic in nature. We present several constructions of optimal block designs for estimating main effects or main plus two-factor interaction effects. Our results show when and how an optimal design for the model without blocks can be Statistica Sinica: Newly accepted Paper (accepted version subject to English editing) Optimal Paired Choice Block Designs 2 split into blocks so as to retain the optimality properties under the block model.

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Section: Preliminaries and The Model Incorporating Respondent Effectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Paired Choice Block Designs

Singh¹,

Das²,

Chai³

2019

STAT SINICA

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“…We refer to Burgess and Street (2005); Grasshoff et al (2003Grasshoff et al ( , 2004; Grossmann et al (2006Grossmann et al ( , 2009and Street and Burgess (2007) for D-optimal designs derived under that assumption. Under the assumption that the model parameters are zero, the information matrix for the multinomial logit model is proportional to the information matrix for a linear regression model, in case the experiment is run in blocks (Kessels et al, 2011b).…”

Section: Literature Reviewmentioning

confidence: 99%

Bayesian D-Optimal Choice Designs for Mixtures

2014

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Consumer products and services can often be described as mixtures of ingredients. Examples are the mixture of ingredients in a cocktail and the mixture of different components of waiting time (e.g., in-vehicle and out-of-vehicle travel time) in a transportation setting. Choice experiments may help to determine how the respondents' choice of a product or service is affected by the combination of ingredients. In such studies, individuals are confronted with sets of hypothetical products or services and they are asked to choose the most preferred product or service from each set. However, there are no studies on the optimal design of choice experiments involving mixtures. We propose a method for generating an optimal design for such choice experiments. To this end, we first introduce mixture models in the choice context and next present an algorithm to construct optimal experimental designs, assuming the multinomial logit model is used to analyze the choice data. To overcome the problem that the optimal designs depend on the unknown parameter values, we adopt a Bayesian D-optimal design approach. We also consider locally D-optimal designs and compare the performance of the resulting designs to those produced by a utility-neutral (UN) approach in which designs are based on the assumption that individuals are indifferent between all choice alternatives. We demonstrate that our designs are quite different and in general perform better than the UN designs. Terms of use: Documents in

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“…To cope with partial profiles the regression functions F have to be modified to keep track of the selection and, more importantly, restrictions have to be imposed onto the set X of possible pairs to be presented. The necessary ramifications are detailed in Graßhoff et al (2004).…”

Section: Paired Comparison Models In Conjoint Analysismentioning

confidence: 99%

“…From an applied point of view, this criterion appears to be particularly appropriate, since it matches the conception of a good design as intuitively conceived by many practitioners of conjoint analysis: a good design should yield estimates which are close to the parameters. Recently developed D-optimal paired comparison designs (Graßhoff et al, 2004) with a manageable number of evaluations also happen to be optimal with regard to the distance criterion. Empirical tests of these designs are performed in two experiments.…”

Section: Introductionmentioning

confidence: 99%

On the Empirical Relevance of Optimal Designs for the Measurement of Preferences

Großmann

Holling

Brocke

et al. 2005

Applied Optimal Designs

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The paper presents an application of optimal designs to the measurement of preferences. Optimal designs are compared to more common design strategies in two experiments. Taking a new perspective for investigating the differences between designs, efficiency gains can be grasped more easily. Both experiments demonstrate that the improvement of designs is not only a matter of academic interest but also of empirical relevance.

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Optimal designs for main effects in linear paired comparison models

Cited by 67 publications

References 16 publications

Optimal Paired Choice Block Designs

Optimal Paired Choice Block Designs

Bayesian D-Optimal Choice Designs for Mixtures

On the Empirical Relevance of Optimal Designs for the Measurement of Preferences

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