Discrete choice 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. Respondents are presented sets of profiles based on attributes specified at certain levels and asked to select the profile they consider best. When the number of attributes or attribute levels becomes large, the profiles in a single choice set may be too numerous for respondents to make precise decisions. One strategy for reducing the size of choice sets is the sub-setting of attributes. However, the optimality of these reduced size choice sets has not been examined in the literature. We examine the optimality of reduced size choice sets for 2^n experiments using information per profile (IPP) as the optimality criteria. We propose a new approach for calculating the IPP of designs obtained by dividing attributes into two or more subsets with one, two, and in general, r overlapping attributes, and compare the IPP of the reduced size designs with the original full designs. Next we examine the IPP of choice designs based on 3^n factorial experiments. We calculate the IPP of reduced size designs obtained by sub-setting attributes in 3^n plans and compare them to the original full designs. / Statistics

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. / Statistics