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    Some Results on Pareto Optimal Choice Sets for Estimating Main Effects and Interactions in 2n and 3n Factorial Plans

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    Genre
    Thesis/Dissertation
    Date
    2015
    Author
    Xiao, Jing
    Advisor
    Chitturi, Pallavi
    Committee member
    Zhao, Zhigen
    Krafty, Robert T.
    Viswanathan, Krupa S.
    Department
    Statistics
    Subject
    Statistics
    Mathematics
    Design
    Choice-based Sets
    Conjoint Analysis
    A- and E-optimality
    Information Per Profile
    Pareto Optimal Design
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/4061
    
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    DOI
    http://dx.doi.org/10.34944/dspace/4043
    Abstract
    Choice-based conjoint experiments are used when choice alternatives can be described in terms of attributes. The objective is to infer the value that respondents attach to attribute levels. This method involves the design of profiles on the basis of attributes specified at certain levels. Respondents are presented sets of profiles called choice sets, and asked to select the one they consider best. Sets with no dominating or dominated profiles are called Pareto Optimal sets. Information Per Profile (IPP) is used as an optimality criteria to compare designs with different numbers of profiles. For a 2^n experiment, the optimality of connected main effects plans based on two consecutive choice sets, Sl and Sl+1, has been examined in the literature. In this thesis we examine the IPP of both consecutive and non-consecutive choice sets and show that IPP can be maximized under certain conditions. We show that non-consecutive choice sets have higher IPP than consecutive choice sets for n ≥ 4. We also examine the optimality of connected first-order-interaction designs based on three choice sets and show that non-consecutive choice sets have higher IPP than consecutive choice sets under certain conditions. Further, we examine the D-, A- and E-optimality of consecutive and non-consecutive PO choice sets with maximum IPP. Finally, we consider 3^n choice experiments. We look for the optimal PO choice sets and examine their IPP, D-, A- and E-optimality, as well as comparing consecutive and non-consecutive choice sets.
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