OPTIMAL PAIRED CHOICE BLOCK DESIGNS

Choice experiments help manufacturers, service providers, policymakers, and other researchers to make business decisions. Traditionally, in a discrete-choice experiment, each respondent is shown the same collection of choice pairs (i.e., the choice design). In addition, as the number of attributes and/or the number of levels under each attribute increases, the number of choice pairs in an optimal paired choice design increases rapidly. Moreover, in the literature on utility-neutral setups, random subsets of theoretically obtained optimal designs are often allocated to respondents. This raises the question of whether we can do better than simply using a random allocation of subsets. We answer this question using a linear paired-comparison model (or, equivalently, a multinomial logit model), where we first incorporate the fixed respondent effects (also referred to as the block effects), and then obtain optimal designs for the parameters of interest. Our approach is simple and theoretically tractable, unlike other approaches that are algorithmic in nature. We present several constructions of optimal block designs that can be used to estimate main effects or main plus two-factor interaction effects. Our results show when and how an optimal design for the model without blocks can be split into blocks such that the optimality properties are retained under the block model.