Sequential Choice Designs to Estimate the Distribution of Willingness-to-Pay

Abstract

The concept of willingness-to-pay (WTP) has attracted the attention of marketeers because of its use-fulness in many applications. Nowadays one aims at describing the market heterogeneity by estimating the distribution of WTP. However, this poses several problems that have been discussed repeatedly in the literature. Many authors report unrealistic, extreme or inaccurate individual-level WTP estimates. We propose to use an adaptive sequential approach to construct conjoint choice designs for estimating the distribution of WTP. It uses Bayesian methods to generate individually optimized choice sets. These choice sets are computed sequentially based on the prior information of each individual which is updated after each choice. The choices made by all respondents are then used to estimate the mixed logit model which yields individual-level utility coefficients and corresponding individual-level WTP estimates from which the distribution of WTP can be derived. This sequential approach is compared in a simulation study with two non-sequential designs: a semi-Bayesian D-optimal design for the conditional logit model and a nearly orthogonal design. The results shows that the sequential design performs much better than the benchmark designs. It yields more accurate individual-level WTP estimates and produces a more accurate picture of the heterogeneity.