Optimal Paired Choice Block Designs

Abstract

Choice experiments mirror real world situations closely and helps manufacturers, policy-makers and other researchers in taking business decisions on their product characteristics based on its perceived utility. In a paired choice experiment, several pairs of options are shown to respondents. The respondents are asked to give their preference among the two options for each of the choice pairs shown to them. In order to conduct an experiment, a choice design is customarily used to efficiently estimate the parameters of interest which essentially consists of either the main effects only or the main plus two-factor interaction effects of the attributes. Traditionally, every respondent is shown the same collection of choice pairs under an untenable assumption that the respondents are alike in every respect. Also, as the attributes or the number of levels under each attribute increases, the number of choice pairs in an optimal paired choice design increases rapidly. To address these concerns, under the multinomial logit model or the linear paired comparison model, we first incorporate the respondent effects and then present optimal designs for the parameters of interest. We provide optimal paired choice designs for estimating the main effects for symmetric and asymmetric multi-level attributes with smaller number of choice pairs shown to each respondent. We also provide optimal paired choice designs for estimating the main effects only and the main plus two-factor interaction effects under the main plus two-factor interaction effects model.