Partial-profile Choice Designs for Estimating Main Effects and Interactions of Two-Level Attributes from Paired Comparison Data

A new method to generate designs for estimating main effects and two-factor interactions of two-level attributes from choice experiments is presented for the situation where the choice sets are pairs and the alternatives are specified by a subset of the attributes. Partial-profile designs are constructed by using Hadamard matrices and factorial and incomplete block designs as building blocks. Their information matrix under the multinomial logit model is derived under the indifference assumption of equal choice probabilities by exploiting the relationship between the multinomial logit model for pairs and the linear paired comparison model. The information matrix depends only on the incomplete block designs but not on the other building blocks. Efficient partial-profile designs with relatively small numbers of choice sets are found by performing computer searches inspired by these results.