771 research outputs found
Automatic generation of generalised regular factorial designs
Open Access for this article was paid for by the French Research Agency (ANR), project Escapade (ANR-12-AGRO-0003).The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.Publisher PDFPeer reviewe
Probabilistic models of set-dependent and attribute-level best-worst choice
We characterize a class of probabilistic choice models where the choice probabilities depend on two scales, one with a value for each available option and the other with a value for the set of available options. Then, we develop similar results for a task in which a person is presented with a profile of attributes, each at a pre-specified level, and chooses the best or the best and the worst of those attribute-levels. The latter design is an important variant on previous designs using best-worst choice to elicit preference information, and there is various evidence that it yields reliable interpretable data. Nonetheless, the data from a single such task cannot yield separate measures of the "importance" of an attribute and the "utility" of an attribute-level. We discuss various empirical designs, involving more than one task of the above general type, that may allow such separation of importance and utility. © 2008 Elsevier Inc. All rights reserved
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