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

摘要

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. Information Per Profile (IPP) is used as an optimality criteria to compare designs with different numbers of profiles. The optimality of connected main effects plans based on two consecutive choice sets, S-l and Sl+1 has been examined in the literature. However, the optimality of nonconsecutive choice sets has not been examined. In this paper we examine the IPP of non-consecutive choice sets and show that IPP can be maximized under certain conditions. Further, we show that non-consecutive choice sets have higher IPP than consecutive choice sets for n >= 4. In addition, we 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 check the D-, A- and E-optimality of best 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.