D-optimal conjoint choice designs with no-choice options for a nested logit model

Despite the fact that many conjoint choice experiments offer respondents a no-choice option in every choice set, the optimal design of conjoint choice experiments involving no-choice options has received only a limited amount of attention in the literature. In this article, we present an approach to construct D-optimal designs for this type of experiment. For that purpose, we derive the information matrix of a nested multinomial logit model that is appropriate for analyzing data from choice experiments with no-choice options. The newly derived information matrix is compared to the information matrix for the multinomial logit model that is used in the literature to construct designs for choice experiments. It is also used to quantify the loss of information in a choice experiment due to the presence of a no-choice option.