A-efficient discrete choice designs for attributes with unequal numbers of levels

Sun and Dean proposed an approach for finding A-optimal and A-efficient discrete choice designs without a large computational effort, for estimating orthonormal contrasts, and for both balanced and unbalanced profile utilities. Their method was based on the “contribution” made by each choice set to the contrasts being estimated, and was illustrated for the setting of two-level attributes and orthonormal main effect and interaction contrasts. In this article, the use of the Sun and Dean methodology is extended to encompass pairwise comparisons. The methodology is illustrated for the construction of A-efficient designs for attributes having different numbers of levels and where contrasts of interest are either orthonormal factorial contrasts or pairwise comparisons in the attribute levels. When the designs are large, issues involved with finding smaller subdesigns are discussed briefly.