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Theory & Methods: Estimating Main Effects with Pareto Optimal Subsets
Author(s) -
Raghavarao Damaraju,
Wiley James B.
Publication year - 1998
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00047
Subject(s) - mathematics , pareto principle , pareto optimal , mathematical optimization , set (abstract data type) , construct (python library) , multi objective optimization , combinatorics , mathematical economics , computer science , programming language
A subset T of S is said to be a Pareto Optimal subset of m ordered attributes (factors) if for profiles (combination of attribute levels) ( x 1 , …, x m ) and ( y 1 , …, y m ) ∈ T , no profile ‘dominates’ another; that is, there exists no pair such that x i ≤ y i , for i = 1, …, m . Pareto Optimal designs have specific applications in economics, cognitive psychology, and marketing research where investigators use main effects linear models to infer how respondents values level of costs and benefits from their preferences for sets of profiles offered them. In such studies, it is desirable that no profile dominates the others in a set. This paper shows how to construct a Pareto Optimal subset, proves that a single Pareto Optimal subset is not a connected main effects plan, provides subsets of two or more attributes that are connected in symmetric designs and gives corresponding results for asymmetric designs.